ORDER ON PLAINTIFF’S AND DEFENDANT’S MOTIONS FOR JUDGMENT AS MATTER OF LAW OR FOR A NEW TRIAL, AND ON PLAINTIFF’S MOTION TO ALTER OR AMEND THE JUDGMENT

Re: Dkt. Nos. 361, 362, 363

INTRODUCTION

In this lawsuit involving technology used in digital cameras and cellular telephones, *1019 a jury found defendant Motorola Mobility LLC (“Motorola”) liable for infringement of plaintiff Fujifilm Corporation (“Fuji-film”)’s U.S. Patent No. 6,144,763 (the ’763 patent), which concerns monochrome conversion in digital photography, and awarded $10.24 million in damages after a two-week trial. The jury also considered Fuji-film’s claims of infringement of U.S. Patents Nos. 8,306,285 (the ’285 patent) and 7,327,886 (the ’886 patent), which concern human face detection in digital photography, and U.S. Patent No. 6,915,119 (the ’119 patent), which concerns wireless data transmission. The jury found that the ’285 and ’886 patents were invalid and not infringed, and that the ’119 patent was infringed but invalid. Each party now moves for judgment as a matter of law or for a new trial on virtually every issue on which the jury did not find in its favor. In addition, Fujifilm moves under Federal Rule of Civil Procedure 59(e) to alter or amend the judgment to provide for an award of prejudgment interest.

This Order upholds the jury verdict, except that Fujifilm is entitled to judgment as a matter of law on the validity of the asserted claims of the ’285 and ’886 patents (the “face detection patents”) and on Motorola’s licensing defense concerning claims 1 and 35 of the ’119 patent. I also award prejudgment interest at the prime rate, compounded quarterly. Fujifilm’s motion for JMOL or for a new trial is GRANTED IN PART and DENIED IN PART, Motorola’s motion is DENIED, and Fujifilm’s motion to alter or amend the judgment is GRANTED.

BACKGROUND

Fujifilm filed its original complaint in this matter on July 10, 2012 and its first amended complaint on November 19, 2012. Dkt. Nos. 1, 16. The first amended complaint, the operative complaint in this case, asserts infringement by Motorola of Fuji-film’s ’763 patent, ’285 patent, ’886 patent, ’119 patent, and U.S. Patent No. 5,734,427 (the ’427 patent) (which concerns low-resolution displays in digital cameras). Dkt. No. 16.

On December 9, 2014, Motorola moved for summary judgment of noninfringement on each of the asserted claims, and also on the issue of willful infringement. Dkt. No. 153. I granted the motion with respect to the ’427 patent and denied the motion in all other respects. Dkt. No. 196 (“Summary Judgment Order”).

A jury trial was held from April 20 through May 1, 2015. At trial, Fujifilm asserted infringement of claims 1,2, 7, and 11 of the ’763 patent; claim 1 of the ’285 patent; claim 11 of the ’886 patent; and claims 1, 13, and 35 of the T19 patent.

At the close of Fujifilm’s case, Motorola moved for judgment as a matter of law on all claims of infringement, including willful infringement, and on damages. Dkt. No. 307. At the close of all evidence, Motorola renewed its request for judgment as a matter of law on infringement of the ’886 patent and on willful infringement, and also moved for judgment as a matter of law on the validity on each of the asserted claims. Dkt. No. 328. Fujifilm moved for judgment as a matter of law on all claims of infringement, including willful infringement, on the validity of each of the asserted claims, on the licensing of the asserted claims of the ’119 patent, and on damages. Trial Tr. at 1757:20-1759:04. I allowed all issues to pass to the jury. Id. at 1761:21-23 .

The jury returned its verdict on May 4, 2015. Dkt. No. 337 (“Verdict”). It found that Motorola had infringed claims 1, 7, and 11 of the ’763 patent and claims 1, 13, and 35 of the ’119 patent, but that it had not infringed claim 2 of the ’763 patent, claim 1 of the ’285 patent, or claim 11 of the ’886 patent. Verdict at 3-4. It also found that claims 1, 2, 7, and 11 of the ’763 *1020 patent were not invalid, but that claim 1 of the ’285 patent, claim 11 of the ’886 patent, and claim 13 of the ’119 patent were invalid as anticipated and obvious, and that claims 1 and 35 of the ’119 patent were invalid as obvious. Id. at 5 . In addition, the jury found that the ’119 patent was not invalid for improper inventorship, and that Motorola was licensed under the Bluetooth Patent/Copyright License Agreement (“BPLA”) (Trial Ex. 901) as to claims 1 and 35 of the 119 patent, but not as to claim 13 of the 119 patent. Id. at 6 . The jury awarded $10,24 million to Fujifilm for past and future damages for infringement of the ’763 patent. Id. at 8 . I entered Final Judgment on August 6, 2015. Dkt. No. 357.

The parties filed their respective post-trial motions on September 3, 2015. I heard argument on December 9, 2015. Dkt. No. 379.

LEGAL STANDARD

The Federal Circuit “reviews decisions on motions for JMOL, motions for a new trial, and evidentiary rulings under the law of the regional circuit.” InTouch Techs., Inc. v. VGO Commc’ns, Inc., 751 F.3d 1327, 1338 (Fed.Cir.2014). In the Ninth Circuit, judgment as a matter of law is appropriate where “the evidence, construed in the light most favorable to the nonmoving party, permits only one reasonable conclusion, and that conclusion is contrary to that of the jury.” White v. Ford Motor Co., 312 F.3d 998, 1010 (9th Cir. 2002). This standard requires a court to uphold “any jury verdict supported by substantial evidence,” substantial evidence being “evidence that a reasonable mind would accept as adequate to support a conclusion.” Callicrate v. Wadsworth Mfg., Inc., 427 F.3d 1361, 1366 (Fed.Cir.2005). Neither a “mere scintilla” of evidence, nor pure speculation, is enough to sustain a verdict against a motion for JMOL. Lakeside-Scott v. Multnomah Cty., 556 F.3d 797, 802-03 (9th Cir.2009).

Under Federal Rule of Civil Procedure 59(a), a trial court “may grant a new trial, even though the verdict is supported by substantial evidence, if the verdict is contrary to the clear weight of the evidence, or is based upon evidence which is false, or to prevent, in the sound discretion of the trial court, a miscarriage of justice.” United States v. 4.0 Acres of Land, 175 F.3d 1133, 1139 (9th Cir.1999) (internal quotation marks omitted); accord Wordtech Sys., Inc v. Integrated Networks Sols., Inc., 609 F.3d 1308, 1313 (Fed.Cir.2010). In considering a motion for a new trial, a court, “has the duty to weigh the evidence as the court saw it, and to set aside the verdict of the jury, even though supported by substantial evidence, where, in the court’s conscientious opinion, the verdict is contrary to the clear weight of the evidence.” Molski v. M.J. Cable, Inc., 481 F.3d 724, 729 (9th Cir.2007) (internal quotation marks and alterations omitted). The Ninth Circuit “review[s] [a] district court’s ruling on a motion for a new trial under Rule 59(a) for an abuse of discretion.” E.E.O.C. v. Go Daddy Software, Inc., 581 F.3d 951, 962 (9th Cir.2009). The denial of a motion for a new trial is reversible “only if the record contains no evidence in support of the verdict or if the district court made a mistake of law.” Id. (internal quotation marks omitted).

DISCUSSION

Fujifilm moves for judgment as a matter of law that: (1) Motorola has infringed the face detection patents; (2) the asserted claims of the face detection patents are not invalid; (3) claims 1,-13, and 35 of the ’119 patent are not invalid; and (4) Motorola is not licensed under the BPLA to practice claims 1 and 35 of the ’119 patent. Fujifilm Mot. at 1 (Dkt. No. 362). In the alternative, Fujifilm requests a new trial on each of these issues. Id. Fujifilm also requests a new trial as to willfulness and damages *1021 with respect to Motorola’s infringement of the face detection patents and of the ’119 patent. Id.

Motorola moves for judgment as a matter of law that: (1) it has not infringed claims 1, 13, and 35 of the 119 patent; (2) it has not infringed claims 1, 7, and 11 of the ’763 patent; (3) the asserted claims of the ’763 patent are invalid; and (4) the lump sum award of $10.24 million for infringement of the ’763 patent is not supported by the evidence and is excessive. Motorola Mot. at i (Dkt. No. 361). In the alternative, it asks for a new trial (and, with respect to damages, remittitur) on each of these issues. Id. Motorola identifies no basis for ordering a new trial on any of the infringement or validity issues except to state that “for each of the reasons outlined in [its motion for JMOL], the jury’s verdict is clearly not supported by the evidence and is unreasonable.” Id. at 41.

I address the parties’ arguments by patent, starting with the face detection patents, then the 119 patent, and finally the ’763 patent. I then address Fujifilm’s request under Federal Rule of Civil Procedure 59(e) for an award of prejudgment interest. I uphold the jury’s verdict except for the finding of invalidity of the face detection patents, because the prior art reference on which Motorola relied did not anticipate or make obvious the asserted claims of those patents, and the finding on the licensing of claims 1 and 35 of the 119 patent, because the plain language of the BPLA compels the conclusion that Motorola was not granted a license to those claims. With respect to the other issues raised by the parties, I cannot find that the jury’s verdict was either unreasonable or contrary to the clear weight of the evidence.

I. THE FACE DETECTION PATENTS

The face detection patents share a specification and are titled “Photographing Apparatus, Method and Program.” ’285 patent (Trial Ex. 8); ’886 patent (Trial Ex. 6). Claim 1 of the ’285 patent discloses:

’285 patent at 18:34-67. Claim 11 of the ’885 patent discloses a substantially similar invention:

’886 patent at 21:06-22:20. Fujifilm challenges the jury’s findings of invalidity and noninfringement of these claims. See Fuji-film Mot. at 4-27; Fujifilm Reply at 2-13 (Dkt. No. 375).

A. Invalidity

The jury found claim 1 of the ’285 patent and claim 11 of the ’886 invalid as both anticipated and obvious. Verdict at 5. Fuji-film contends that these findings were unreasonable and moves for judgment as a matter of law or a new trial.

1. Anticipation

“Anticipation requires clear and convincing proof that a single prior art reference not only discloses all of the elements of the claim within the four corners *1023 of the document, but also discloses those elements arranged as in the claim.” Cheese Sys., Inc. v. Tetra Pak Cheese & Powder Sys., Inc., 725 F.3d 1341, 1351 (Fed.Cir.2013) (internal quotation marks and alterations omitted). The reference may disclose the elements of the claim either “expressly or inherently.” Trintec Indus., Inc. v. Top-U.S.A. Corp., 295 F.3d 1292, 1295 (Fed.Cir.2002). “Inherent anticipation requires that the missing descriptive material is ’necessarily present,’ not merely probably or possibly present, in the [reference].” Id.; see also Bettcher Indus., Inc. v. Bunzl USA Inc., 661 F.3d 629, 639 (Fed.Cir.2011) (inherent anticipation “may not be established by probabilities or possibilities”). “The dispositive question regarding anticipation is whether one skilled in the art would reasonably understand or infer from the prior art reference’s teaching that every claim limitation was disclosed in that single reference.” Akamai Techs., Inc. v. Cable & Wireless Internet Servs., Inc., 344 F.3d 1186, 1192 (Fed.Cir.2003) (internal quotation marks and alterations omitted).

Motorola’s anticipation ease at trial centered on- U.S. Patent No. 7,269,292 to Steinberg (“Steinberg” or “Steinberg patent”) (Trial Ex. 960). Fujifllm contends that the jury could not have reasonably concluded that Steinberg anticipates the asserted claims of the face detection patents because Steinberg does not disclose the “multiple face judgments” required by those claims. See Fujifllm Mot. at 14-16. Fujifilm points to the language in claim 1 of the ’285 patent requiring “a judgment ... as to whether the face is included in a first frame of the moving image,” and then “[a] judgment.. .as to whether the face is included in a second frame of the moving image.” ’285 patent at 18:54-59. Claim 11 of the ’886 patent similarly requires “judging whether a human face is included in a frame included in the moving image,” then “judging whether the face is included in the next frame after the predetermined time,” and then “judging whether the face is included in the next frame further after the predetermined time.” ’886 patent at 21:20-22:13. The relevant portion of Steinberg is a flow diagram that includes a box stating, “Track face movement,” without further explanation. See Steinberg at Fig. 7b. Fujifllm asserts that, rather than “multiple face judgments,” Steinberg discloses “a single face judgment, followed by face tracking.” Fujifilm Mot. at 14.

In response, Motorola essentially argues that there was substantial evidence at trial indicating that there is no difference between performing “multiple face judgments,” as required by the face detection patents, and performing “face tracking,” as disclosed by Steinberg. See Motorola Oppo. at 11-14 (Dkt. No. 373).

I agree with Fujifllm that there was insufficient evidence at trial to support this conclusion. The parties do not dispute that to perform “multiple face judgments” within the meaning of the face detection patents, there must be successive determinations of whether an object in the image is a human face—that is, there must be multiple instances of “face detection,” or “deter-min[ing] whether there is a face in the image and, if there is, determining] [its] coordinates.” Motorola Oppo. at 12 (emphasis added). 1 By contrast, the jury was told that “face tracking” does not necessarily involve repeatedly determining whether the tracked object is indeed a *1024 human face. Fujifilm’s expert, Dr. Kenneth Castleman, testified that “[i]n this field, tracking generally means keeping track of the location of something as it moves in a series of frames,” and that “there are a lot of [tracking] techniques that don’t determine what the object is you’re tracking; just, did the'thing.. .in the last frame move? and where did it move to?” Trial Tr. at. 1576:06-20; see also id. at 1577:10-12 (“So the point is, with tracking you’re keeping track of where the object is and where it has been, but you are not, generally, making a determination of what the object is.”). Dr. Castleman then addressed Steinberg in particular and opined that it does not disclose all of the elements of the face detection patents because “[i]t finds the face one time and does not do the step of repeatedly finding the face or making a judgment that there’s a face in the image. It’s just not in there.” Id. at 1599:23-1600:01 . -The jury also heard testimony that Motorola had previously employed “face tracking”' but had abandoned that process in favor of one that “serially continues to detect faces and identify the location of those faces, frame by frame by frame.” Id. at 1434:03-07 ; see also Trial Ex. 505. In line with this evidence, Motorola explicitly conceded in its motion for JMOL at the close of all evidence that the prior art did not disclose “multiple face judgments.” See Dkt. No. 328 at 20. It stated: “The only thing that was not specifically disclosed in the prior art was performing these [face detection] techniques more than once.” Id.

Motorola now points to. excerpts from the testimony of its expert, Dr. Alan Bovik, as substantial evidence of an equivalence between the “multiple face judgments” required by the face detection patents and the “face tracking” disclosed by Steinberg. See Motorola Oppo. at 11-12. For the most part, however, the excerpts merely reinforce the conclusion that to perform the “multiple face judgments” required by the face detection patents, there must be successive instances of determining whether there is a human face in the image. See Trial Tr. at 1312:04-1313:02; id. at 1323:13-20 ; id. at 1328:11-14 . The excerpts do not indicate that the “face tracking” disclosed by Steinberg involves such a process. The one possible exception is Dr. Bovik’s testimony that “face tracking” is the “process of predicting where the face is in the next frame and then making a face detector operate around that region,” and his subsequent testimony that the “Track face movement” box in Steinberg shows that “[o]ver frames, face tracking is being conducted.” Id. at 1312:24-1313:02, 1342:17 . But even assuming that this testimony provided a substantial basis for the conclusion that “face tracking” can involve “multiple face judgments,” there was not sufficient evidence to conclude that this is the type of “face tracking” disclosed by Steinberg. As stated above, “[i]nherent anticipation requires that the missing descriptive material is ’necessarily present,’ not merely probably or possibly present, in the [reference].” Trintee, 295 F.3d at 1295 . Motorola identifies nothing in Stein-berg regarding the “face tracking” reflected in the “Track face movement” box other than the box itself. I agree with Fujifilm that this passing reference, even when considered in combination with Dr. Bovik’s testimony, does not provide a substantial basis for the conclusion that the “face tracking” disclosed in Steinberg necessarily involves “multiple face judgments.”

Motorola also relies on the following testimony from Dr. Castleman’s cross-examination regárding the meaning of “face tracking” and the sort of “face tracking” disclosed by Steinberg:

Trial Tr. at 1624:18-1625:19. Motorola contends that this testimony amounts to an admission that “a person of skill in the art reading Steinberg would know that once a face is detected in a frame, the system should determine whether that face is present in successive frames and, if so, determine the position of the face in each of the successive frames.” Motorola Oppo. at 14. If that is an accurate characterization of Dr. Castleman’s testimony, it is not a characterization that helps Motorola. Under this characterization, Dr. Castleman did not testify that Steinberg discloses the use of “multiple face judgments.” Rather, he testified that Steinberg discloses a system that detects a human face in a frame and then “determine[s] whether that face is present in successive frames.” Id. Motorola does not dispute that this type of “face tracking” is different from performing “multiple face judgments,” i.e., repeatedly “determining] whether there is a face in the image.” Id. at 12.

The evidence at trial did not provide a substantial basis for finding, by clear and convincing evidence, that Steinberg anticipates the asserted claims of the face detection patents. Accordingly, Fujifilm’s motion for JMOL on this issue is GRANTED. 2 Its request for a new trial is DENIED AS MOOT.

2. Obviousness

Without the finding of anticipation, the finding of obviousness cannot stand either. Motorola concedes that the only obviousness theory it presented at trial with respect to the face detection patents was predicated on Steinberg combined with the skill and knowledge of a person of ordinary skill in the art. See Motorola Oppo. at 15-16. The problem is that Motorola did not actually present this theory to the jury. Dr. Bovik’s testimony regarding Steinberg was focused exclusively on anticipation and did not address obviousness. For example, he introduced his analysis of claim 11 of the ’886 patent and Steinberg as follows:

Trial Tr. at 1338:24 to 1339:18-23,

Motorola identifies no testimony by Dr. Bovik or any other witness that addresses the alleged obviousness of the face detection patents. See Motorola Oppo. at 15-16. 3 Without a defensible finding of anticipation or any testimony directed at Motorola’s purported obviousness theory, the obviousness verdict is not supported by substantial evidence. See InTouch, 751 F.3d at 1348-49 (holding that patentee was entitled to judgment as a matter of law of nonobviousness where defendant’s expert did not “identify sufficient reasons or motivations to combine the asserted prior references,” “focus on the relevant time frame,” or “consider any objective evidence of nonobviousness.”), Fujifilm’s motion for JMOL on this issue is GRANTED. Its motion for a new trial is DENIED AS MOOT.

B. Noninfringement

While Fujifilm is entitled to judgment as a matter of law on the validity of the face detection patents, it has not shown that the jury’s finding of nonin-fringement should be upset. Fujifilm’s argument for judgment as a matter of law or a new trial on this issue relies heavily on its contention that Motorola and Dr. Bovik presented improper claim construction evidence to the jury. See, e.g., Fujifilm Mot. at 8-11, 23-24. There is no question that a party cannot “argue claim construction to the jury.” Cordis Corp. v. Boston Sci Corp., 561 F.3d 1319, 1337 (Fed.Cir.2009); see also Dkt, No. 256 at 6-7 (“Order on Motions in Limine”). But I am not persuaded that Motorola and Dr. Bovik crossed over this line. I agree with Motorola that Dr. Bovik permissibly rebutted the testimony of Barbara Fredericksen-Cross, Fujifilm’s expert, and. that Fujifilm failed to carry its burden regarding infringement.

I also disagree with Fujifim that its proposed final jury instruction on “not.. .importing] limitations from the specification.. .into the claims” was erroneously denied, given the various model jury instructions that were delivered to the jury. See Final Jury Instruction No. 19 (Dkt. No. 329) (“The claims of a patent are important because it is the words of the claims that define what a patent covers. The figures and text in the rest of the patent provide a description and/or examples of the invention and provide a context for the claims, but it is the claims that define the breadth of the patent’s coverage.”); Final Jury Instruction No. 20 (“By understanding the meaning of the words in *1027 a claim and by understanding that the words in a claim set forth the requirements that a product or process must meet in order to be covered by that claim, you will be able to understand the scope of coverage for each claim.”); Final Jury Instruction No. 22 (“A patent’s claims define what is covered by the patent,”). And, in light of the standard applied in the Summary Judgment Order, I do not find that it was error to not instruct the jury on my “partial construction,” Fujifilm Mot. at 25-27, of the face detection patents,

Fujifilm’s motion for JMOL of infringement of the face detection patents, or for a new trial on the issue, is DENIED.

II. CLAIMS 1 AND 35 OF THE ’119 PATENT

The ’119 patent is titled “Telephone and Data Transmitting Method for Tele-: phone.” ’119 Patent (Trial Ex. 4). The parties do not dispute that its priority date is in October 1999. Claims 1 and 35 state as follows:

’119.Patent at 4:33-56, 9:41-63. Fujifilm challenges the jury’s findings on invalidity and licensing of claims 1 and 35, while Motorola challenges the jury’s findings on infringement. See Fujifilm Mot. at 28-36, *1028 44-46; Fujifilm Reply at 13-22, 24-28; Motorola Mot. at 31-40 (Dkt. No. 361); Motorola Reply at 20-30 (Dkt. No. 376).

A. Invalidity

The jury found claims 1 and 36 of the 119 patent invalid for obviousness. Verdict at 6. Fujifilm states that the only obviousness theory advanced by Motorola at trial was based on a combination of (1) manuals for certain models of the Nokia 9000i Communicator telephone (Trial Exs. 958,1060C) (the “Nokia Manuals”); and (2) Haartsen, et al. Bluetooth: Vision, Goals, and Architecture, Mobile Computing and Comms. R., Oct. 1998 (the “Bluetooth Vision Paper”). Fujifilm contends that this obviousness theory is defective because there was no evidentiary basis presented at trial for concluding that the Nokia Manuals were “printed publications” within the meaning of the applicable pre-AIA version of 35 U.S.C. § 102 . 4 In the alternative, Fujifilm contends that,, even assuming that it was adequately established that Nokia Manuals were printed publications, Motorola failed to present sufficient evidence that the combination of the Nokia Manuals and the Bluetooth Vision Paper rendered claims 1 and 35 obvious.

Motorola responds that Fujifilm’s argument “is nothing more than a red herring that attempts to distract the Court from the fact that Motorola relied on the Nokia 9000i Communicator device as the invalidating prior art reference, not the Nokia 9000i Communicator Manuals.” Motorola Oppo. at 37 (emphasis in original). Motorola states that it relied on the Nokia Manuals merely “as corroborating evidence to show the functionalities and existence of the Nokia 9000i Communicator before October 1999.” Id. “As such,” Motorola contends, “[it] did not need to show that the [Nokia Manuals] were printed publications.” Id. (internal quotation marks omitted). In the alternative, Motorola argues that it provided the jury with sufficient evidence to reasonably conclude that the Nokia Manuals qualified as printed publications before October 1999. Id. at 42-44 .

In support of its contention that it relied on the Nokia Communicator 9000i device and not the Nokia Manuals as the prior art reference, Motorola points to its Amended Reduction of Prior Art References, filed on February 27, 2015, which lists “Nokia Communicator 9000i” as a prior art reference for the 119 patent. Dkt. No. 230. Motorola also highlights its Motion to Strike Portions of Martin Haeberli’s Expert Reports, filed on February 4, 2015, where it attacked certain portions of Hae-berli’s rebuttal report regarding the Nokia 9000i Communicator and described the Nokia Manuals as “corroborative evidence.” Dkt. No. 190 at 13-14.

I agree with Motorola that the prior art reference here is the Nokia 9000i Communicator telephone, not the Nokia Manuals. Fujifilm contends that Motorola’s obviousness theory fails nonetheless because no actual Nokia 9000i Communicator phone was admitted at trial. The Federal Circuit has held, however, that materials other than the invalidating device itself may provide substantial evidence of the device’s functionality for the purposes of proving invalidity. In finding a patent in *1029 valid under 35 U.S.C. § 102 (b) in Sonoscan, Inc. v. Sonotek, Inc., 936 F.2d 1261 (Fed.Cir.1991), the Federal Circuit stated, “That the offered product'is in fact the claimed invention may be established by any relevant evidence, such as memoran-da, drawings, correspondence, and testimony of witnesses.” Id. at 1263 (internal quotation marks omitted). Similarly, in Unitherm Food Sys., Inc. v. Swift-Eckrich, Inc., 375 F.3d 1341 (Fed.Cir.2004), the Federal Circuit relied on a combination of “contemporaneous correspondence, color photographs, witness testimony, and promotional videos” to establish the characteristics' of an anticipating process. Id. at 1352-1354 .

Motorola could have made a stronger showing regarding the Nokia 9000i Communicator. Still, its expert, Dr. Harry Bims, gave detailed testimony regarding the specific functionality of the Nokia Communicator 9000i based on his review of the Nokia Manuals. See, e.g., Trial Tr. at 1099:10-1102:06; 1141:04-1142:15. Two other witnesses, including Fujifilm’s expert Martin Haeberli, also provided testimony, albeit less detailed than Dr. Bims’s, regarding the availability and functionality of the device. See Trial Tr. at 549:12-25; Trial Ex. 1236. The jury had a substantial basis from which to infer the relevant characteristics of the Nokia Communicator 9000i.

Fujifilm contends that Dr. Bim’s description of the Nokia Manuals cannot be reasonably attributed to an actual Nokia Communicator 9000i phone from the relevant time period, given that there were multiple models of the Nokia Communicator 9000i, not all of which were sold in the United States during that time. See Fuji-film Reply at 16-17. This argument might be persuasive if there were evidence of material variation among the different Nokia Communicator 9000i models—such as evidence that certain of the models did not possess the relevant functionality—but Fu-jifilm cites no evidence indicating that this was the case. Moreover, before the start of trial, I specifically authorized Mr. Haeberli to “offer his opinion on why a product manual.. .may fail to accurately describe the underlying product, and why in this case he believes there is insufficient evidence that the [Nokia Manuals] accurately describe the [Nokia Communicator 9000i].” Fujifilm Corp. v. Motorola Mobility LLC, No. 12-cv-03587-WHO, 2015 WL 1265009 , at *13 (N.D.Cal. Mar. 19, 2015). Despite this ruling, Mr. Haeberli did not offer any testimony at trial regarding the purported unreliability of the Nokia Manuals.

Fujifilm argues in the alternative that the Nokia 9000i Communicator and the Bluetooth Vision Paper fail to render claims 1 and 35 obvious because they do not disclose two elements of the claims: (1) the “designating device...for selectively designating an apparatus to which the received data is to be transmitted” element; and (2) the “displaying a designating address” element. Fujifilm Mot. at 32-34. It also contends that Motorola faded to present sufficient evidence that a person of ordinary skill in the art would have been motivated to combine the two references to arrive at the claimed invention. Id. at 34-36 . Neither of these arguments warrants upsetting the jury’s verdict. Dr. Bims specifically explained how both the Nokia Communicator 9000i and the Blue-tooth Vision Paper disclosed the “designating device” element, Trial Tr. at 1147:16-1149:14, and how the Bluetooth Vision Paper disclosed the “designating address” element,” id. at 1150:07-1151-02. The evidence presented by Fujifilm did not require the jury to reject this testimony. I also agree with Motorola that the jury was presented with sufficient evidence of a motivation to combine the two references to find that their combination *1030 rendered claims 1 and 35 obvious. Fuji-film’s motion for JMOL or for a new trial on this issue is DENIED.

B. Licensing

The jury found that Motorola is licensed under the BPLA as to claims 1 and 35 of the 119 patent. Verdict at 6. Fujifilm contends that this conclusion was unreasonable, and that it is entitled to judgment as a matter of law on licensing. Fujifilm Mot. at 44-46.1 agree.

Fujifilm is an Adopter Member of the Bluetooth SIG. Motorola is a Promoter Member of the Bluetooth SIG. Section 5(b) of the BPLA describes the license of “Necessary Claims” that each Associate and Adopter Member of the Bluetooth SIG grants to each Promoter Member:

BPLA § 5(b) (emphasis added). The BPLA defines “Necessary Claims” in the following two sentences:

Id. § 1(l) (paragraphing added). Finally, the term “Scope” is defined as

Id. (paragraphing added).

At trial, Motorola argued that claims 1 and 35 of the ’119 patent were “Necessary Claims” for the purposes of the Personal Area Network (“PAN”), Dial Up Network (“DUN”), and Object Push (“OP”) profiles. However, Motorola presented no evidence to the jury, and does not currently dispute, that claims 1 and 35 are not “necessarily infringed by implementing [the PAN, DUN, and OPP profiles] within the bounds of the Scope.” BPLA § l(i). Indeed, Motorola’s expert, Dr. James Lansford, admitted at trial that the PAN, DUN, and OP profiles can be implemented without infringing claims 1 and 35. See, e.g., Trial Tr. at 1250:23-25.

Motorola argues that there is nevertheless sufficient evidence to support the licensing verdict because, “[a]s Dr. Lansford explained during trial, claims 1 and 35 of the ’119 patent are Necessary Claims because they recite both (1) in-Scope technology, such as the implementation of the [OP profile], and (2) enabling technologies, such as wireless telephones, that are reasonably necessary to implement those technologies.” Motorola Oppo. at 49-50 (citing Trial Tr. at 1237:08-1241:01). This argument turns on the second provision of the second sentence of the “Necessary Claims” definition, which states that “Necessary Claims do not include any claims... that read solely on any implementations of any portion of the Bluetooth Specification or Foundation Specification that are not within the bounds of the Scope.” BPLA § l(i). Pointing to this sentence, Motorola contends that “[i]t follows that claims that combine enabling technologies with technologies that are within the Scope, i.e., those underlying the basic protocols and data formats required to communicate using the Bluetooth Standard, are Necessary Claims, unless another exception applies.” Motorola Oppo. at 49 (emphasis omitted).

This argument is not persuasive. Its dis-positive flaw is that it completely ignores the first sentence of the “Necessary Claims” definition, which plainly limits “Necessary Claims” to those that “are necessarily infringed by implementing those portions of a Bluetooth Specification and/or Foundation Specification within the bounds of the Scope.” BPLA § l(i) (emphasis added). Motorola’s position appears to be that it is okay to ignore the first sentence of the definition, because if the first sentence is given its plain meaning, then the second provision of the second sentence (i.e., the provision explaining that “Necessary Claims do not include any claims.. .that read solely on any implementations of any portion of the Bluetooth Specification or Foundation Specification that are not within the bounds of the Scope”) would merely serve to clarify the first sentence and would 'thus be “wholly unnecessary.” Motorola Oppo. at 49.

Motorola places far too much weight on the general rule that contract provisions should not be read as overlapping or re *1032 dundant. As Fujifilm points out, “[e]ven agreements tailored to particular transactions sometimes include overlapping or redundant or meaningless provisions.” Restatement ' (Second) of Contracts § 203 cmt. b; see also Fujifilm Reply at 25. This is clearly the case with the “Necessary Claims” definition. This is exemplified both in that Motorola’s reading of the second provision of the second sentence would effectively eviscerate the definition of “Necessary Claims” set out in the first sentence, and also by the first provision of the second sentence, which explains that “Necessary Claims do not include any claims... other than those set forth above even if contained in the same patent as Necessary Claims.” BPLA § 1(Z). This provision is obviously designed to clarify the first sentence; Motorola does not explain how it. could be reasonably read in any other way.

Motorola also contends that its position is supported by the BPLA’s purported purpose of “facilitating] sharing of intellectual property among [Bluetooth SIG] members and... avoiding] intellectual property disputes.” Motorola Oppo. at 48; see also id. at 49 (arguihg that Fujifilm’s position “would undermine the BPLA’s purpose of facilitating sharing of intellectual property necessary to practice the Blue-tooth standard”). Tellingly, however, Motorola does not provide a citation for this sentence and does not identify any evidence in the record to support it. The BPLA’s purported purpose does not provide a substantial basis for the conclusion that claims 1 and 35 of the ’119 patent are “Necessary Claims” under the BPLA.

Fujifilm’s motion for JMOL of no licensing of claims 1 and 35 of the ’119 patent is GRANTED. Its request for a new trial on this issue is DENIED AS MOOT.

C. Infringement

The jury found that the accused products infringe claims 1 and 35 of the ’119 patent. Motorola’s argument for judgment as a matter of law of nonin-fringement of these claims centers on their respective “menu” limitations. See Motorola Mot. at 37-40; Motorola Reply at 28-30. Claim 1 requires a “menu comprising] selections for a receive mode for indicating that data has been received, a transmit image mode for transmitting an image from the wireless telephone to an apparatus, a receive mail mode for receiving characters, and a transmit mail mode for transmitting characters.” ’119 patent at 4:51-46. Claim 35 likewise requires “a menu comprising selections for at least one of a transmit image mode for transmitting an image from the wireless telephone to an apparatus, a receive mail mode for receiving characters, and a transmit mail mode for transmitting characters.” ’119 patent at 9:59-63.

The parties do not dispute that to infringe claim l’s menu- limitation, the accused product must contain a menu with four modes: a receive data mode, a transmit image mode, a receive mail mode, and a transmit mail mode. See, e.g., Motorola Mot. at 38. Motorola argues that Mr. Haeberli’s testimony on infringement of this limitation was defective because it involved “navigating through a series of different applications and application menus.” Motorola Mot. at 38; see also Motorola Reply at 28 (“Motorola’s position is that the menu element as understood by one skilled in the art cannot be satisfied by combining individual selections that only exist across a variety of distinct applications that are not presented to the user at the same time or within the same menu.”). Motorola identifies nothing in the ’119 patent that required the jury to reject Mr. Haeberli’s testimony on claim l’s menu limitation, *1033 except to repeatedly refer to claim l’s recitation of “a menu.” Mr. Haeberli specifically addressed this same argument in his testimony, explaining that the claim says nothing about different applications or “having to jump between screens.” Trial Tr. at 1683:21-25. The jury was entitled to credit Mr. Haeberli’s testimony, and to rely on their own conclusions as to the menu limitation’s “plain and ordinary meaning to a person of ordinary skill in the art,” Final Jury Instruction No. 18, to find that the accused products infringe claim 1.

Motorola’s argument regarding claim 35’s menu limitation is substantially identical to its argument regarding claim l’s menu limitation. Motorola contends that Mr. Haeberli’s testimony failed to establish infringement of this limitation because the testimony relied on “a multistep process, involving multiple menu screens, multiple applications, and multiple .user inputs.” Motorola Mot. at 40. Motorola again identifies nothing in the ’119 patent to support this argument apart from the words “a menu” in claim 35. Mr. Haeberli testified that the accused products contain a menu comprising a selection for a transmit image mode because they contain a menu selection for transmitting an image to another device via Bluetooth and/or DLNA. Trial Tr. at 486:07-489:19. He also specifically addressed the same argument Motorola relies on now, explaining that claim 35 says nothing about applications or about “navigating through different screens,” and reiterating how the menu limitation is found in the accused products. Id. at 1681:01-1683:11. Again, the jury was entitled to credit Mr. Haeberli’s testimony, and to rely on their own conclusions as to the menu limitation’s “plain and ordinary meaning to a person of ordinary skill in the art,” Jury Instruction No. 18, to find that the accused products infringe claim 35.

Motorola’s motion for JMOL of nonin-fringement of claims 1 and 35 of the T19 patent, or for a new trial on the issue, is DENIED.

III. CLAIM 13 OF THE ’119 PATENT

Claim 13 of the ’119 patent recites:

’119 patent at 6:35-53. As with claims 1 and 35 of the ’119 patent, the jury found claim 13 invalid but infringed. Verdict at 4-5. It did not find the claim licensed under the BPLA. Id. at 6. Fujifilm challenges the invalidity verdict, while Motorola challenges the infringement verdict. See Fuji-film Mot. at 36-44; Fujifilm Reply at 22-24; Motorola Mot. at 32-37; Motorola Reply at 22-28.

A. Validity

The jury found claim -13 invalid as both anticipated and obvious. Verdict at 5. Fuji- *1034 film contends that neither invalidity finding is supported by sufficient evidence and requests both judgment as a matter of law and a new trial on the validity of claim 13.

1. Anticipation

Fujifilm asserts that Motorola’s only anticipation argument at trial rested on U.S. Patent No. 6,714,530 to Haartsen et al. (“Haartsen”), and that Haartsen does not disclose all of the elements of claim 13. Specifically, Fujifilm contends that Haart-sen does not disclose the claimed “data” of claim 13, because Haartsen discloses a “real-time voice transmission system,” and the “real-time voice data” transmitted by this system “would not be considered to be the claimed ‘data,’ as one of ordinary skill in the art would understand that term.” Fujifilm Mot. at 37. Fujifilm also contends that Haartsen fails to disclose the claimed “transmitting and receiving buffer” of claim 13, because, according to Mr. Hae-berli’s testimony, the only buffer identified in Haartsen must be located in the disclosed 'system’s transmitting circuit. Id. at 38 . Fujifilm asserts that “[t]he presence of the- buffer in the transmitting circuit. . .precludes it from being a transmitting and receiving buffer.” Id, (emphasis in original; internal quotation marks omitted).

I am not persuaded by either of these arguments. Dr. Bims testified that the system disclosed in Haartsen transmits data and identified multiple places in the patent that describe the transmission and receipt of data by the disclosed system. See, e,g., Trial Tr. at 1113:17-1115:07. He also gave his opinion that the plain and ordinary meaning of “data” as used in claim 13 is not limited to high-quality image data, but rather extends to low-quality image data, application data, text data, video data,, and, most relevant here, audio data. Id. at 1201:12-1202:04 ; see also id. at 1207:24-1208:02 (“Q: First of all, do you agree that audio data is not data within the meaning of claim 13? A: Audio data is, indeed, data within the meaning of claim 13.”). Mr. Haeberli disagreed that Haartsen discloses the sort of “data” recited in claim 13, but the jury was not required to credit Mr. Haeberli’s opinion over Dr. Bims’s.

With respect to the transmitting and receiving buffer limitation, Dr. Bims testified that the “first-in-first-out” (“FIFO”) buffer disclosed in Haartsen is a type of buffer in which the data enters the buffer in a particular order, and that this order is preserved when the data leaves the buffer. Trial Tr. at 1117:16-20. He specifically stated that the FIFO buffer disclosed in Haartsen both transmits and receives data. Id. at 1117:21-23 . He explained that this is because the disclosed system “relay[s] data in both directions.” Id. at 1117:24-1118:01 . The jury was also presented with an excerpt from Mr. Haeberli’s deposition, taken after Dr. Bims had already rendered his opinion that the FIFO buffer in Haart-sen satisfies the transmitting and receiving buffer limitation, in which Mr. Haeberli stated that he did not know whether a FIFO buffer would satisfy the transmitting and receiving buffer limitation, but that he “can’t imagine that there’s an argument that says [it] would not.” Trial Tr. at 1707:16-1708:08. Mr. Haeberli opined at trial that the FIFO buffer in Haartsen must be located in the system’s transmitting circuit, and that it does not make sense for the buffer to both transmit and receive data. See Trial Tr. 1665:21-1668:09. Again, however, the jury was not required to credit this testimony over that of Dr. Bims.

Fujifilm’s motion for JMOL of no anticipation of claim 13 of the ’119 patent, or for a, new trial on the issue, is DENIED.

2. Obviousness

“[A]nticipation is the ultimate of obviousness.” In re Baxter Travenol Labs., 952 F.2d 388, 391 (Fed.Cir.1991). Because the *1035 jury’s finding of anticipation is supported by substantial evidence, the same is necessarily true of its finding of obviousness. See id. Accordingly, Fujifilm’s motion for JMOL of no obviousness of claim 13 of the 119 patent, or for a new trial on the issue, is DENIED.

B. Infringement

To prove infringement of claim Í3, Fujifilm was required to show that the accused products include “a transmitting and receiving buffer” that is “coupled to” a “first transmitting and receiving circuit” and a “second transmitting and receiving circuit.” See 119 patent at 6:42-45. Motorola contends that Fujifilm failed to present sufficient evidence for the jury to reasonably conclude that the accused products contain a “transmitting and receiving buffer,” or that the transmitting and receiving buffer is “coupled to” the first and second transmitting and receiving circuits.

1. “Transmitting and Receiving Buffer”

Mr. Haeberli testified that this limitation is satisfied by the random access memory (“RAM”) in the accused phones. See Trial Tr. at 504:16-20 (“The phones each have random access memory, which is attached to the application processors in the phone. And a piece of that RAM memory is partitioned off for the purpose of holding buffers—that is, packets... of data that are flowing through the phone”). He explained that his opinion was based partly on his testing and analysis of data flow in the accused phones, partly on his review of some of the relevant source code, and also partly on the deposition testimony of Motorola’s own engineers, Vissa and Labana. See id. at 504:21-506:02 . Vissa agreed at his deposition that there is “separate RAM that’s somewhere in the phone in which the buffering occurs.”-Trial Ex. at 507 at 61:14-17. Labana similarly agreed at his deposition that “the data would then proceed from the transceiver and be temporarily stored in RAM.” Trial Ex. at 506 at 152:06-12. The relevant portions of these depositions were shared with the jury at trial.

Motorola argues that Mr. Haeberli’s testimony, and that of its engineers, cannot establish the “transmitting and receiving buffer” limitation because Fujifilm did not identify a particular structure in the accused phones that corresponds to the claimed “transmitting and receiving buffer.” Motorola cites Cross Med. Products, Inc. v. Medtronic Sofamor Danek, Inc., 424 F.3d 1293 (Fed.Cir.2005), for the propositions that a system claim such as claim 13 “cover[s] what a device is, not what a device does,” and that a device “must meet all of the structural limitations” of the asserted system claim to infringe. Id. at 1311-12 (emphasis in original; internal quotation marks omitted).

Even assuming that Motorola is right on the law, it is wrong that Fujifilm failed to identify a “transmitting and receiving buffer” structure in the accused phones. Mr, Haeberli clearly pointed to the RAM in the accused phones as the claimed “transmitting and receiving buffer.” See Trial Tr. at 504:16-20, In addition, Dr. Bims specifically identified the RAM in the accused phones for the jury using a block diagram. See Trial Tr. at 1094:02-18; Trial Ex. 265 at 7. Motorola does not dispute that RAM qualifies as a structure.

Motorola next contends that the RAM in the accused phones cannot satisfy the “transmitting and receiving buffer” limitation because the ’119 patent “expressly discloses the ’transmitting- and receiving buffer- and RAM as two distinct and separate structures.” Motorola Reply at 25. It is true that one figure in the ’119 patent displays the “transmitting and receiving buffer” and “RAM”, as two distinct structures. See ’119 patent at Fig. 2. But Motorola identifies nothing in the ’119 patent, *1036 much less in the language of claim 13, that requires the transmitting and receiving buffer and RAM to be separate structures, or that precludes RAM from serving as the transmitting and receiving buffer. The jury was permitted to reject Motorola’s reading of the “transmitting and receiving buffer” limitation and to rely instead on Mr. Haeberli’s testimony, which is apparently what it did. It did not act unreasonably, or without sufficient evidence to support its conclusion, in doing so.

2. “Coupled To”

Motorola’s contention that there was insufficient evidence that the transmitting and receiving buffer is coupled to the first and second transmitting and receiving circuits in the accused phones is also unconvincing. Mr. Haeberli specifically testified that the “coupled to” requirement is satisfied and explained that his testing and analysis of data flow between the relevant components confirmed that they are coupled together. See Trial Tr. at 503:01-504:03, 506:04-507:01; see also id. at 1658:10-15 (“[T]he data flows in through the cellular transceiver, through the.. .buffer portion or partition of RAM, and but through the WiFi and Bluetooth transceivers of the accused devices.”). Dr. Bims opined that the coupling requirement is not satisfied because the RAM in the accused phones is “connected to the CPU” and is not “in line” with the cellular transceiver and the Bluetooth and Wi-Fi transceivers. See id. at 1097 at 15-18. But there is no “in line” requirement in claim 13; Dr. Bims admitted on cross-examination that the claim does not contain those words. See id. at 1175:18-19. Again, the jury was permitted to reject Motorola’s reading of the “coupled to” limitation and to rely instead .on Mr. Haeberli’s testimony.

In sum, Motorola has not shown that the jury’s finding of infringement of claim 13 of the ’119 patent was not supported by substantial evidence, or that it was contrary to the clear weight of the evidence. Motorola’s motion for JMOL or for a new trial on this issue is DENIED.

IV. THE ’763 PATENT

The ’763 patent is titled, “Method and Apparatus for Compression Coding of Image Data Representative of a Color Image and Digital Camera Including the Same.” ’763 patent. At trial, Fujifilm asserted infringement of claim 1, an independent claim, and of claims 2, 7, and 11, each of which is dependent on claim 1. The jury found each of the asserted claims valid; claims 1, 7, and 11 infringed; and claim 2 not infringed. Verdict at 3, 5. The claims are as follows:

’768 patentat 13:49-14:59. Motorola challenges the jury’s findings on validity with respect to claims 1, 2, 7, and 11, and the jury’s findings on infringement and damages with respect to claims 1, 7 and 11. Motorola Mot. at 4-31; Motorola Reply at 2-20. Fujifilm does not raise any arguments with respect to the ’763 patent.

A. Validity

Motorola does not dispute the jury’s rejection of its anticipation argument for claims 1, 2, 7 and 11 but contends that the jury erred by failing to find the claims obvious. Specifically, Motorola asserts that the claims are obvious in view of U.S. Patent No. 6,486,981 to Shimura et al. (“Shimura”), “in combination with the skill and knowledge of one skilled in the art at the time of the invention.” Motorola Mot. at 15. 5

The problem with this argument is that Motorola failed to raise it at trial. Motorola did not develop for the jury a single obviousness theory involving Shimura. Dr. Bovik’s testimony regarding Shimura was focused exclusively on the theory that Shimura teaches all elements of claims 1, 2, 7 and 11 of the ’763 patent. See Trial Tr. at 1369:15-1379:08. Dr. Bovik’s demonstrative slides for Shimura contained two columns, one listing the elements of the asserted claims and another titled “Shimura” with an empty box next to each of the elements. See Fujifilm Mot. at 18-19. Counsel for Motorola added a check mark in each empty box as Dr. Bovik testified, indicating that the corresponding element is found in Shimura. See, e.g., Trial Tr. at 1377:02-04 (“Q: So in your opinion,., .does Shimura teach all the elements of claim 1 of the ’763 patent? A: Yeah. All the boxes have been checked. I didn’t ask you to, but you did it. Yeah, I think every element is met”). In line with Dr. Bovik’s testimony *1038 and slides, during closing argument counsel for Motorola stated:

Trial Tr. at 1864:03-08.

Motorola urges that Dr. Bovik and others provided testimony regarding the skill and knowledge of one skilled in the art at the time of the invention. See Motorola Reply at 6-7. Motorola also notes that Dr. B ovik’s slides were titled “Invalidity,” not “Anticipation.” Id. But Motorola fails to identify any testimony from the record that connects Shimura to the skill and knowledge of one skilled in the art at the time, of the invention, or that otherwise directly addresses this obviousness theory (or any obviousness theory) involving Shimura. I agree with Fujifilm that Motorola cannot raise the theory now. See Fractus, S.A. v. Samsung Elecs. Co., 876 F.Supp.2d 802, 838 (E.D.Tex.2012) (holding that defendant waived any indefiniteness argument where it “failed to present any explicit indefiniteness evidence at trial” and did not “make a single reference to indefiniteness during trial;” stating that “[allowing [defendant] to revive its [indefiniteness] defense post-trial deprives [plaintiff] of any opportunity to substantively respond with its own testimony or evidence”); Allergan, Inc. v. Barr Labs., Inc., 808 F.Supp.2d 716 , 736 (D.Del.2011) (finding that defendants “clearly present a different theory of obviousness post-trial than was presented at trial,” and that defendants could not “switc[h] horses by combining pieces of testimony.. .into new obviousness theories. As defendants did not allow [plaintiff] to mount a defense at trial to the [new obviousness] theories, the court does not entertain them here”).

Further, even assuming that Motorola’s obviousness argument is not technically waived, given Motorola’s total failure to coherently present an obviousness theory to the jury, Motorola’s position that the jury was required to find obviousness, despite its undisputedly correct conclusion that Shimura patent does not anticipate, is far from convincing. Motorola’s motion for JMOL of invalidity of the asserted claims of the ’763 patent, or for a new trial on the issue, is DENIED.

B. Infringement

Motorola makes two basic arguments regarding the jury’s verdict of infringement of claims 1, 7, and 11 of the ’763 patent. The first concerns Dr. Castleman’s testimony regarding claim l’s five hardware limitations, i.e., its “signal processing circuit,” “storage,” “compression coding circuit,” “compression coding circuit,” and “system controller” limitations. See Motorola Mot. at 7-9. The second concerns the “to fix” limitation in the final paragraph of claim 1. See id. at 10-15 . Motorola makes no arguments specific to claims 7 and 11 except to note that they are dependent on claim 1.

1. The Hardware Limitations

In its opening brief, Motorola argued that Dr. Castleman’s testimony regarding claim l’s five hardware limitations was deficient because Dr. Castleman merely stated that the limitations were found in the accused phones but did not identify any specific corresponding structures in the phones. Motorola Mot. at 8-9. Motorola asserted that “[s]uch an unsubstantiated statement, limited only to the functionality and not the structure required by the claim language, and without any support or linking to the accused Motorola products or any evidence beyond Dr. Castle-man’s conclusory opinion, cannot satisfy Fujifilm’s burden of proving” that the limi *1039 tations are found in .the accused phones. Id.

Fujifilm responded in its opposition brief by citing to Federal Rule of Evidence 705, which provides that “[ujnless the court orders otherwise, an expert may state an opinion—and give the reasons for it—without first testifying to the underlying facts or data. But the expert may be required to disclose those facts or data on cross-examination.” Fed. R. Evid. 705. Fujifilm noted that the Federal Circuit has recognized that Rule 705 is “fully applicable” to patent trials, which .are “particularly served” by Rule 705’s .purpose of “avoiding] complex and time consuming testimony.” Symbol Techs., Inc. v. Opticon, Inc., 935 F.2d 1569, 1576 (Fed.Cir.1991) (internal quotation marks omitted). Fujifilm also pointed out that Motorola declined to ask Dr. Castle-man any questions about the five hardware limitations on cross examination, and that Motorola’s own expert on the ’763 patent, Dr. Bovik, agreed that these limitations are present in the accused phones:

Trial Tr. at 1400:03-13. Motorola offers no counterargument in its reply brief and appears to have abandoned its initial position on the hardware limitations.

Whether or not Motorola has indeed abandoned the argument, I agree with Fu-jifilm that it is without merit. In light of the testimony of Dr. Castleman and Dr. Bovik, the total absence of cross-examination or any contrary. evidence regarding claim l’s hardware limitations, and Federal Rule of Evidence 705, there was more than enough evidence to support the jury’s conclusion that the limitations are found in the accused devices. Motorola’s first argument does not justify judgment as a matter of. law of noninfringement; nor does it justify a new trial on the issue.

2. The “To Fix” Limitation

Motorola’s second noninfringement argument is really a group of overlapping arguments concerning the “to fix” (or “fixing”) limitation of claim 1 of the ’763 patent. That limitation appears in the final paragraph of claim 1, .which reads, with emphasis added to the limitation:

'763 patent at 13:66-14:06 (emphasis added).

Motorola attacks Dr. Castleman’s opinion that the accused phones satisfy the “fixing” limitation because they employ a process that results in a monochrome image with fixed chrominance components. See Motorola Mot. at 10-11. According to Motorola, Dr. Castleman’s . opinion is flawed because it “reduces the fixing limitation to a tautology: if all monochrome images have zero-valued chrominance data, and any process that creates zero-valued chrominance data satisfies the fixing limitation, then there is no difference between *1040 the ’render a monochrome image’ limitation and the fixing limitation.” Id. at 11.

While it is unclear how best to characterize this argument, I agree with Fujifilm that it is' without merit however characterized. To the extent that it is a claim construction argument, it fails because it is not timely. The Federal Circuit has repeatedly held that “litigants waive their right to present new claim construction disputes if they are raised for thé first time after trial.” Lazare Kaplan Int’l, Inc. v. Photoscribe Techs., Inc., 628 F.3d 1359, 1376 (Fed.Cir.2010) (internal quotation marks omitted); see also, e.g., Eli Lilly & Co. v. Aradigm Corp., 376 F.3d 1352, 1360 (Fed.Cir.2004). At no point during the course of this litigation has Motorola requested- construction of the fixing limitation or offered a construction of it, except to argue at summary judgment that the preamble of claim 1 is limiting (an argument I rejected). To the extent that Motorola’s tautology argument is a claim construction argument, it is barred as waived.

To the extent that the argument is something óther than a claim construction argument, it fails because it assumes that there is a redundancy in claim 1 that does not exist—or at least that the jury was not required to avoid by rejecting Dr. Castle-man’s testimony. In its post-trial briefing, Motorola portrays the “fixing” limitation as part of one continuous phrase starting with “compressing and coding the image data such that the image data render a monochrome image.” See' Motorola Reply at 2-3. But this is not the way that Motorola portrayed the “fixing” limitation in its summary judgment briefing. There, Motorola portrayed the final paragraph of claim 1 as follows:

Dkt. No. 153 at 18 (emphasis in original). I did the same in the Summary Judgment Order. Summary Judgment Order at 23-24. Under this reading, the phrase “compressing and coding the image data such that the image data render a monochrome image” pertains to the claimed “monochrome mode,” while the “fixing” limitation pertains to the claimed “system controller.” In other words, claim 1 defines a “monochrome mode,” one that is “selected for compressing and coding the image data such that the image data render a monochrome image.” And claim 1 also defines how the “system controller” operates: “in response to a monochrome mode” and “to fix the chrominance components of the image data to a single, fixed value.” The phrase “compressing and coding the image data such that the image data render a monochrome image” explains when the “monochrome mode” is selected, while the “fixing” limitation explains what the “system controller” does. Under this reading, there is no redundancy in claim 1.

Motorola next contends that there was insufficient evidence that the “fixing” limitation is found in the accused phones because those devices do not process color image data in chrominance/luminance format. See Motorola Mot. at 11-12. Motorola states: “First, claim 1 recites a process (fixing) that is done to the chrominance components to create a monochrome image. This necessarily requires that there are color chrominance components to operate upon. However, color image data in chrominance/luminance format never exists in the accused Motorola products.” Id. Like the “tautology” argument, this argument is hard to characterize but fails how *1041 ever characterized. To the extent that it is a new claim construction argument, it is barred by the waiver doctrine discussed above. To the extent that it is not a new claim construction argument, it fails because it is substantially identical to an old one. Motorola raised essentially the same purported distinction between claim 1 and the accused products in its motion for summary judgment, albeit in the form of an argument that the preamble of claim 1 is limiting. See Summary Judgment Order at 24-25. I rejected the argument then, and Motorola does not identify, much less establish, grounds that justify reconsideration at this juncture.

Finally, Motorola argues that the “fixing” limitation “requires that the conversion to monochrome include fixing chromi-nance components to a single, fixed value,” and that “[t]he evidence was undisputed that Motorola generates monochrome output via calculation, not via the straightforward ’fixing’ of [claim 1].” Motorola Mot. at 12. Once again, to the extent that this is a new claim construction argument, it is barred by the waiver doctrine discussed above. To the extent that Motorola is arguing that the jury could not have reasonably concluded that the plain and ordinary meaning of “to fix” extends to the accused products, the parties presented competing expert testimony on this issue. Fujifilm’s expert, Ms. Frederickson Cross, testified that the algorithms employed by the accused products operate “to fix” the chromi-nance components in the image data, and that “there is really very little difference” between “fixed” and “calculated” from a software standpoint. See, e.g., Trial Tr. at 1564:19-1566:23. Motorola objects to this testimony as beyond the scope of Ms. Frederickson Cross’s expert report and deposition, but while Motorola objected to certain aspects of Ms. Frederickson Cross’s testimony on this ground, it identifies no point at which it objected to her testimony regarding whether the accused products perform the required “fixing.” See Motorola Reply at 5. In any event, while Dr. Bovik opined that there is a distinction between the “fixing” disclosed in claim 1 and the “calculating” performed by the accused phones, see Trial Tr. at 1368:10-12, I am not persuaded that the jury was required to apply his conception of “fixing,” even in the absence of competing testimony from Dr. Frederickson-Cross, in particular given that Dr. Castle-man’s infringement testimony also provided support for a broader reading of “to fix.”

Motorola’s motion for JMOL of nonin-fringement of claims 1, 7, and 11 of the ’763 patent, or for a new trial on the issue, is DENIED.

C. Damages

The jury found that Fujifilm was entitled to a lump-sum award of $10.24 million for past and future infringement of the ’763 patent. Verdict at 8. Motorola argues that there is no substantial basis' for this award, and that at most the record supports a lump-sum award of $2.45 million, the amount proposed by Motorola’s damages expert, Dr. Nisha Mody, for infringement of the ’763 patent. Motorola Mot. at 23.

Motorola’s basic argument for upsetting the jury’s damages award is that it far exceeds Dr. Mody’s proposed award for infringement of the ’763 patent, and that Fujifilm’s expert, Dr. Gareth Macartney, opined that the parties would have entered into a running royalty agreement, not a lump-sum agreement. ' Motorola emphasizes that “[r]unning-royalty agreements can be relevant to lump-sum damages,” but that “some basis for comparison must exist in the evidence presented to the jury.” Wordtech Sys., Inc v. Integrated Networks Sols., Inc., 609 F.3d 1308, 1320 (Fed.Cir.2010) (internal quotation -marks omitted). According to Motorola, there is *1042 no basis for comparison here because of various flaws in Dr, Macartney’s testimony.

This argument largely boils down to the position that because the jury did not specifically apply either of the parties’ experts’ damages figures, their damages award must be overturned. I am not convinced. The “factual determination of a reasonable royalty,. .need not be supported, and indeed, frequently is not supported, by the specific figures advanced by either party.” SmithKline Diagnostics, Inc. v. Helena Labs. Corp., 926 F.2d 1161, 1167 (Fed.Cir.1991). A jury is “entitled to choose a damages award within the amounts advocated by the opposing parties.” Spectralytics, Inc. v. Cordis Corp., 649 F.3d 1336, 1347 (Fed.Cir.2011); see also SmithKline, 926 F.2d at 1168 (“[T]he district court may reject the extreme figures proffered by the litigants as incredible and substitute an intermediate figure as a matter of its judgment from all of the evidence,”). The “jury’s choice simply must be within the range encompassed by the record as a whole.” Unisplay, S.A. v. Am. Elec. Sign Co., 69 F.3d 512, 519 (Fed.Cir.1995). The jury’s $10,24 million lump-sum award is well- within this range and is supported by substantial evidence.

Further, most if not all of Motorola’s critiques of Dr. Macartney’s damages opinions are reiterations of arguments I previously rejected in ruling on Motorola’s motion to exclude Dr. Macartney’s testimony from trial. See Dkt. No. 269 (“Order on Defendant’s Motion to Exclude Testimony of Keith Pardy and Dr. Gareth Macartney”). To the extent that the critiques are still relevant despite the jury’s decision to award a lump-sum figure instead of a running royalty, they go to weight, not admissibility, and do not provide a basis for upsetting the jury’s damages award.

The damages award is “within the range encompassed by the record as a whole,” Unisplay, 69 F.3d at 519 , and is supported by substantial evidence. Motorola’s motion for JMOL on damages is DENIED. Its requests for a new trial on damages and for remittitur are also DENIED.

V. PREJUDGMENT INTEREST

Fujifilm moves under Federal Rule of Civil Procedure 59(e) for a discretionary award of prejudgment interest. The Supreme Court has held that “prejudgment interest should ordinarily be awarded [under 35 U.S.C. § 284 ] absent some justification for withholding such an award.” Gen. Motors Corp. v. Devex Corp., 461 U.S. 648, 657 , 103 S.Ct. 2058 , 76 L.Ed.2d 211 (1983); see also Ecolab, Inc. v. FMC Corp., 569 F.3d 1335, 1353 (Fed.Cir.2009) (“When a patentee asserts a patent claim that is held to be valid and infringed, prejudgment interest is generally awarded.”). The purpose of a prejudgment interest award in this context is to “compensate[ ] the patent owner for the use of its money between the date of injury and the date of judgment.” Oiness v. Walgreen Co., 88 F.3d 1025, 1033 (Fed.Cir.1996). “In the typical ease, an award of prejudgment interest is necessary to ensure that the patent owner is placed in as good a position as he would have been in had the infringer entered into a reasonable royalty agreement.” Gen. Motors, 461 U.S. at 655 , 103 S.Ct. 2058 .

The rate of prejudgment interest is left to the discretion of the district court, which may award interest at or above the prime rate. Uniroyal, Inc. v. Rudlkin-Wiley Corp., 939 F.2d 1540, 1545 (Fed.Cir.1991). A court may use the prime rate, the prime rate plus a percentage, the United States Treasury Bill (“T-Bill”) rate, a state statutory rate, the corporate rate, or “whatever rate the court deems appropriate under the circumstances.” Junker v. HDC Corp., No. 07-ev-05094-JCS, 2008 *1043 WL 3385819 , at *6 (N.D.Cal. July 28, 2008); accord Apple, Inc. v. Samsung Elecs. Co., 67 F.Supp.3d 1100, 1121 (N.D.Cal.2014). In addition to determining the appropriate rate of prejudgment interest, the court must also determine whether to award simple or compound interest. Rite-Hite Corp. v. Kelley Co., 56 F.3d 1538, 1555 (Fed.Cir.1995). This matter is also “largely within the discretion of the district court.” Id.

Fujifilm seeks prejudgment interest at the California statutory interest rate of seven percent, compounded quarterly, from the start of infringement, which the parties agree is June 1, 2009, until the date that final judgment was entered, August 6, 2015. Rule 59 Mot. at 1-4 (Dkt. No. 363). In the alternative, Fujifilm asks that I apply the prime rate of 3.25 percent, also compounded quarterly. Id. at 4-5. Dr. Macartney calculates that the state statutory interest rate compounded quarterly would result in a prejudgment interest award of $5,486,277. Macartney Decl. ¶ 4, Ex. 1 (Dkt. Nos. 363-1, 363-2). He calculates that the prime rate compounded quarterly would result in an award of $2,268,562. Id. ¶ 5, Ex. 1.

Motorola opposes Fujifilm’s request. Dkt. No. 371 (“Rule 59 Oppo.”). It contends that “[g]iven the size of the jury’s award, the Court should deny prejudgment interest all together.” Rule 59 Oppo. at 1; see also id. at 2 (“[F]or the reasons set forth in Motorola’s Motion for Judgment as a Matter of Law and New Trial, the jury’s award of $10.24 million far exceeds the appropriate amount of damages for the ’763 patent supported by the record.”). In the alternative, Motorola asks that I apply the T-Bill rate, either without compounding or compounded annually, resulting in a prejudgment interest award of either $208,955 (without compounding) or $210,750 (compounded annually). Id. at 2-6; Mody Decl. ¶ 7 (Dkt. No. 371-1).

In support of their respective positions on the appropriate interest rate, the parties offer competing characterizations of the quantum of evidence (if any) necessary to justify a prejudgment interest award calculated at above the T-Bill rate, and of Fujifilm’s financial condition during the period of infringement. Motorola contends that “the [T-Bill] rate is appropriate absent evidence justifying a higher amount,” and that “Fujifilm has provided no evidence that it has borrowed money at any rate, much less that any debt Fujifilm has taken on could have been avoided if it had received the damages award in June 2009.” Rule 59 Oppo. at 2-3. Citing to Fujifilm’s annual reports, Motorola observes that Fu-jifilm maintained substantial reserves (over $2 billion) throughout the period of infringement. Id. at 3; Mody Decl. ¶ 4. Fujifilm responds that a review of its annual reports “reveals that [it] was only able to maintain its [cash] reserves through continuous and substantial cost reductions and structured reforms.” Rule 59 Reply at 4-5 (Dkt. No. 374). Fujifilm also points out that the Federal Circuit has squarely held that “it is not necessary that a patentee demonstrate that it borrowed at the prime rate in order to be entitled to prejudgment interest at that rate.” Uniroyal, Inc. v. Rudkin-Wiley Corp., 939 F.2d 1540, 1545 (Fed.Cir.1991); see also Studiengesellschaft Kohle, m.b.H. v. Dart Indus., Inc., 862 F.2d 1564, 1579-80 (Fed.Cir.1988) (holding that a patentee does not have to make “an affirmative demonstration, i.e., proof of borrowing at or above prime,...to be entitled to an award of prejudgment interest at the prime rate”) (internal quotation marks omitted).

I find that , the appropriate interest rate here is the prime rate, compounded quarterly. Motorola’s arguments for withholding prejudgment interest altogether are not convincing, and neither party offers more than a scintilla of evidence in support of its desired rate. Absent a more conclu *1044 sive record, I find that the “the prime rate more nearly approximates the position [Fujifilm] would have been in had [Motorola] entered into a reasonable royalty agreement.” A & L Tech. v. Resound Corp., No. 93-cv-00107-CW, 1995 WL 415146 , at *5 (N.D.Cal. June 29, 1995); see also Matter of Mahurkar Double Lumen Hemodialysis Catheter Patent Litig., 831 F.Supp. 1354, 1395 (N.D.Ill.1993) (“When the record is inconclusive, courts commonly supply the prime rate that banks charge for unsecured loans to creditworthy customers.”).

CONCLUSION

For- the foregoing reasons, Fujifilm’s motion for JMOL or for a new trial is GRANTED IN PART and DENIED IN PART, Motorola’s motion is DENIED, and Fujifilm’s motion to alter or amend the judgment is GRANTED. Fujifilm is awarded prejudgment interest at the prime rate, compounded quarterly. An amended Final Judgment in accordance with this Order will issue.

IT IS SO ORDERED.

. The parties vigorously dispute whether the face detection patents require successive determinations of whether the image includes the same human face (as opposed to just some human face). But they do not dispute that the face detection patents require successive determinations of whether an object in the image is a human face.

. I do not address Fujifilm’s other arguments for JMOL on anticipation of the face detection patents.

. Motorola does cite to one excerpt in which Dr, Bovik uses the word "obvious” in connection with the face detection patents. See Motorola Oppo. at 15 (citing Trial, Tr. at 1343:07-17), I agree with Fujifilm, however, that Dr. Bovik plainly used the word to mean "self-evident” or perhaps "necessarily present,” not to mean obvious within the meaning of 35 U.S.C. § 103 .

. The relevant pre-AIA version of 35 U.S.C, § 102 provides in relevant part:

35 U.S.C. § 102 (aMb).

. The day before the hearing on these motions, Motorola filed a notice informing the Court that Motorola had sought ex parte reexamination on claims 1, 2, 7 and 11 of the '763 patent, and that on November 17, 2015 the PTO had issued an office action rejecting the claims. Dkt. No. 378. The parties agreed at the hearing that this does not impact the resolution of these motions, and neither party has submitted any additional/updated information about the PTO proceedings.