This appeal is from the decision of the Patent and Trademark Office (PTO) Board of Appeals (board), affirming the examiner’s final rejection of claims 7-14 and 16-18 in application serial No. 303,693, filéd November 6, 1972, entitled “Seismic Prospecting System.” The sole ground of rejection of the claims is that they are directed to nonstatutory subject matter under 35 U.S.C. § 101. We affirm.
The Invention
Appellant’s invention is used in seismic prospecting and surveying. In this field, seismic source waves are generated and transmitted downwardly into the earth. There they are deflected by subsurface formations and anomalies. The deflected waves return to the earth’s surface and are detected by transducers, known as geophones, which are distributed on the surface over the area of exploration. The geophones convert the returning mechanical vibrations into electrical signals, which are then recorded on a record medium, such as magnetic tape or chart recorder, for analysis. By studying the records of the deflected waves, analysts are able to make determinations concerning the nature of the subsurface structure of the earth.
Several types of seismic source waves have been used in seismic prospecting and surveying. One type, known as impulse waves, are sharp pulses lasting 0.05 second or less and are generated by a powerful force of short duration, such as an explosion. Another type of seismic source wave, with which appellant’s invention is used, are “chirp” signals. A chirp signal is a frequency-modulated continuous wave in which the frequency of vibration is varied as a function of time, usually a linear function, over a substantial period of as much as several seconds. Chirp signals are often referred to as “sweep” signals, since the frequency is swept from one value to another. Chirp signals are generated by mechanical apparatus which vibrates against the surface of the earth.
*761As a chirp signal travels down into the earth, it is deflected by subsurface features which lie at varying depths and at different distances from the numerous geophones which are set out on the surface. At any given instant, therefore, a single geophone receives portions of the returning chirp signal which have been deflected from different depths and locations. This composite signal is a jumble of different frequency components. Before the results of the survey can be evaluated, the jumbled signal must be broken down into its components and its individual deflected portions identified.
Appellant has invented a method, and apparatus for performing the method, of cross-correlating the returning jumbled signal with the original chirp signal which was transmitted into the earth. As a result, the returning signal is effectively unscrambled; each of the trains of waves received at each geophone station is converted to a form equivalent to the type of signal which would have been produced had an impulse-type signal been used in place of the chirp signal. Appellant’s claims identify these end products as “partial product signals.”
Appellant’s method is performed on the record signal made from each geophone. The record signal is sampled and converted to a digital format. It is then divided into segments. Several mathematical operations are performed, including computing Fourier transforms and cross-correlation utilizing the Cooley-Tukey algorithm as modified by Bergland.1 Appellant’s claim 7 is illustrative of his invention:
7. In a method of seismic surveying in which a train of seismic source waves is transmitted downwardly into the earth and is there deflected by subsurface formations and in which corresponding trains of seismic waves deflected by such formation are received at geophone stations in a spread at the surface of the earth and wherein;
each train of received seismic waves is converted into a corresponding series of digital sample signals; and
a series of reference signals corresponding to sample of said transmitted seismic waves is developed;
the improved method of correlating said series of sample signals for each geophone station with respect to said series of reference signals that comprises
a) converting said, series of sample signals into an augmented series of sample signals divided into N + 1 segments of equal length thereby forming a series of sequential segments S¡ of said augmented series, including an empty end segment, where i = 1 . . . , N + 1;
b) forming a Fourier transform FTS; of each respective series of signals composed of pairs of successive segments S¡ and S¡ +1 of said augmented series, each said Fourier transform being represented by a first series of transform signals,
c) forming a combined segment of each segment Cj of said reference signals and an empty segment of equal length, where j = 1, . . . L, each said combined segment comprising a series of signals of double length, where L <C N.
d) forming a corresponding Fourier transform FTCj of each said combined segment, each said latter Fourier transform being represented by a second series of transform signals,
e) forming the non-zero conjugate complex vector products of pairs of the respective Fourier transforms and adding them together in accordance with the following expression:
*762where N represents the number of segments in the series of reference signals, and
0 < j + m-1 < M < N
where M is the number of segments to be produced in the cross-correlated result, to produce a series of partial product signals FTPm where m = 1, 2 . . M representative of the Fourier transform of said series of sample signals and said series of reference signals for each said geophone station.!2!
The Rejection
In his final rejection, the examiner stated that the claims were directed to the mathematical procedure outlined in the specification for cross-correlating the sets of signals. He found no reason to distinguish between the method and apparatus claims, holding that distinction to be legally immaterial “Where the only mode of practicing an invention is disclosed by way of an algorithm for use in a computer program.”
In affirming the rejection, the board agreed that the distinction between method and apparatus claims was of no significance because “It would be anomalous to grant apparatus claims encompassing any and every ‘means for’ practicing the method claimed in the method claims if the latter were nonstatutory * * It therefore addressed both categories of claims in a single discussion.
In analyzing the claims, the board viewed the activity recited in the preambles as being directed to the gathering of data. It found that steps like a) through e) of claim 7 serve to allocate the sample signals to various locations in the computer memory in accordance with the rules built into the programs for producing the end result — “a series of partial product signals . representative of the Fourier transform of said series of sample signals and said series of reference signals for each said geophone station,” quoting from the last clause of claim 7.
The board stated that practicing the method steps had to include processing the disclosed formulas and operating the computers according to the Cooley-Tukey algorithm as modified by Bergland. After reviewing the definition of the word “algorithm” as used by the Supreme Court in § 101 cases,3 the board characterized appellant’s claims as mathematical exercises giving the following three reasons (bracketed numerals ours):
Steps a)-e), at their most fundamental level as processed in the computer, must necessarily be carried out employing the radix or radices imposed by the architecture of the computer used, binary, binary coded decimal, or the like. It would be difficult, not to say misleading, to characterize such operations as non-mathematical.
At a secondary level, the steps referred to serve to accommodate the input data to a memory, finite in size, requiring the tailoring and configuring of the data to the particular architecture of the memory, note appellant’s Figures 13-16 and attendant description, pages 123-139. We think this is a mathematical operation.
Needless to say, the processing incident to the employment of the formulas to which we have referred must also be considered mathematical.
It is also apparent that the processing recited in these steps is directed to the solution of a problem, that of producing a series of partial product signals. Accordingly, we consider appellant’s claims to be directed to the processing of an algorithm.
*763Next, the board addressed the question of preemption of the algorithm, holding that it would be effectively preempted by the claims. Although it recognized that the calculations could be carried out by manual effort, the board found that
* * * the total amount of calculation required for the purposes of producing a practical or useful result would be, we think, so horrendous, and the effort so tedious and time consuming, as to render that alternative (if publicly available), or others like it, to be trivial in consequence.
The board distinguished In re Johnson, 589 F.2d 1070, 200 USPQ 199 (Cust. & Pat. App.1978), on its facts. According to the board, the method claims in Johnson
* * * called for computer programming which improved a signal, i. e., reduced noise, whereas the subject matter at bar purports, as the result of solving a mathematical problem, to produce partial product signals, that is, the method produces a solution.
Appellant’s Arguments
Appellant’s main contention is that his claims are not directed to a mathematical procedure but to a method that produces a physical result (the partial product signals) by physical processing of physical signals, all of which are described in mathematical terms, and to apparatus for carrying out special forms of the process.
In furtherance of this argument, appellant asserts that mathematics is an appropriate language to employ for describing inventions, and that programs, algorithms, radices, and calculations have long been commonly employed in inventions.
Appellant also asserts that the PTO has payed lip service to the proposition that claims are to be considered as entireties but has actually dissected the claims and then ignored the physical aspects or denied that they are physical by calling them mathematical or algorithmic in character.
With regard to the apparatus claims, appellant denies that they encompass any and all means for practicing the process covered by the method claims. Specifically, he argues that the apparatus claims call for the use of a unitary device in which all of the means interact to process the input signals to produce the output signals. He asserts that his method claims refer to steps which may be carried out at different locations, and that, by limiting the apparatus claims to a unitary device, he has avoided the situation where any and all means for practicing the method would be covered by the claims.
In response to the solicitor’s argument that the Supreme Court in Flook, supra, adopted a “point of novelty” approach to § 101 which supercedes the second step of the analysis this court applies to § 101 cases, In re Freeman, 573 F.2d 1237, 197 USPQ 464 (Cust. & Pat.App.1978), appellant relies on the opinion in Flook itself to refute that contention. According to appellant, by letting stand its earlier decision in Mackay Radio & Telegraph Co. v. Radio Corporation of America, 306 U.S. 86, 59 S.Ct. 427, 83 L.Ed. 506 (1939), the Court recognized that a claim could pass muster under § 101 where the point of novelty resided in a mathematical equation which defined a new relationship between other physical claim elements which were old in the art. On this issue, appellant suggests that any point of novelty approach which may appear in Flook be limited to claims where the point of novelty is in calculating without any apparatus at all — the factual setting in Flook.
Appellant attempts to distinguish this court’s recent cases, In re Maucorps, 609 F.2d 481, 203 USPQ 812 (Cust. & Pat.App. 1979), and In re Gelnovatch, 595 F.2d 32, 201 USPQ 136 (Cust. & Pat.App.1979), relied upon by the solicitor. Appellant’s position is that in both of those cases, the end product of the process was merely a number or numbers which had been calculated during the process. In contrast, he asserts that his claims produce a set of physical signals which represent physical phenomena — the characteristics of subterranean geostructure. Thus, rather than performing a non-statutory process involving the manipulation of mere numbers, appellant states that *764he performs a statutory process involving the manipulation and processing of actual physical phenomena; two sets of signals are interacted in a particular manner to produce a third set of signals.
In response to a comment by the solicitor that the provision for a magnetic tape recorder in dependent claim 18 comes the closest of any of the claims to assuring that there is a readable output recording or product, appellant makes the following argument. He states that a magnetic tape is a device, and that a magnetic tape on which data are recorded is a different device than a blank tape or a tape containing other data. Turning to language in Benson, supra, he urges error in the solicitor’s position that such a tape, not eye-readable, is not a proper end result of a patentable process. In Benson, the Court stated (409 U.S. at 70, 93 S.Ct. at 256):
Transformation and reduction of an article “to a different state or thing” is the clue to the patentability of a process claim that does not include particular machines.
Appellant urges that his signals, when recorded on the magnetic tape, cause changes of physical state in the tape and that the tape, after recording, is a new device due to these changes of state. Thus he asserts that his claims define statutory subject matter on the authority of Benson.
Finally, while admitting that his claim 12 is not limited to apparatus for seismic prospecting, appellant nonetheless asserts that the claim is limited to a particular art or technology — that of mechanical and electrical correlation of signals — and does not cover pencil-and-paper solutions of mathematical equations. It covers only apparatus for processing signals. Furthermore, with respect to the solicitor’s contention that the apparatus claims do not require a unitary device in a geographical sense, appellant points out that the best mode of the invention is disclosed as apparatus which is self-contained within a vehicle during the course of seismic exploration along a line of exploration.
OPINION
The determination of statutory subject matter under § 101 in the field here involved has proved to be one of the most difficult and controversial issues in patent law. The problem here, as we see it, is not one of computer-related inventions per se; it is one of mathematics-related inventions.
In,the computer arts, § 101 problems tend to center around the use of mathematics in the claims, which define the invention for which patent protection is sought. This is a natural consequence of the nature of computers. A computer is nothing more than an electronic machine. It is characterized by its ability to process data, usually by executing mathematical operations on the data at high speeds. By virtue of the speed with which computers operate, they are capable of executing complex or otherwise time-consuming calculations in fractions of a second. Their use in technology is analogous to the use of mechanical devices, such as levers, which provide mechanical advantage in inventions of a mechanical nature; they make possible, or practicable, the solution of mathematical problems which are impractical to solve manually due to the inordinate amount of time manual solution would consume.
A computer is not mysterious to one skilled in the ar.t; it is merely a distinct type of machine. It will facilitate understanding the applicability of patent law to computer-arts inventions if it is kept in mind that the issues under § 101 in this area have arisen because the function of the computer has been to perform mathematical operations. The problems revolve about the role of mathematics in the claimed inventions.4
*765It is “clear that a process is not unpatentable [in the sense of not being subject matter within the categories named in § 101] simply because it contains a law of nature or a mathematical algorithm.” Flook, 437 U.S. at 590, 98 S.Ct. at 2526. It is equally clear, from the footnote 18 holding in Flook, “that a claim for an improved method of calculation, even when tied to a specific end use, is unpatentable subject matter under § 101.” Id. at 595 n.18, 98 S.Ct. at 2528 n.18. Between these reference points a determination must be made with respect to whether a claim, which recites mathematical calculations, is directed to statutory subject matter when considered as a whole.
There exists a wealth of precedent, most of it predating the advent of computer technology, which aids in addressing the problem, which, as we have noted, is one of mathematics, not of computers. This precedent has been relied upon by the Supreme Court to answer the difficult questions concerning the statutory nature of computer-arts inventions, and thus remains a source from which to synthesize a reasoned analysis to resolve questions arising under § 101.5 No special mode of analysis is required simply because a controversy involves a computer-related invention.
The common thread running through prior decisions regarding statutory subject matter is that a principle of nature or a scientific truth (including any mathematical algorithm which expresses such a principle or truth) is not the kind of discovery or invention which the patent laws were designed to protect. Benson, 409 U.S. at 67, 93 S.Ct. at 255; Le Roy v. Tatham, 55 U.S. 156, 174, 14 How. 156, 14 L.Ed. 367 (1852); In re Bergy, 596 F.2d 952, 988-995, 201 USPQ 352, 384-389 (Cust. & Pat.App. 1979) (Baldwin, J., concurring). Since a statutory invention may employ a scientific truth, a decision as to whether the invention utilizing such truth is statutory must necessarily rest on the relationship which the truth or principle bears to the remainder of the substance of the invention as claimed.
The Supreme Court has given us its interpretation of what that relationship must be for an invention employing a scientific truth or principle of nature to be statutory. “Structure created with the aid of knowledge of scientific truth,” Mackay Radio, 306 U.S. at 94, 59 S.Ct. at 431, is statutory, as is “the application of the law of nature to a new and useful end,” Funk Bros. Seed Co. v. Kalo Inoculant Co., 333 U.S. 127, 130, 68 S.Ct. 440, 441, 92 L.Ed. 588. These princi*766pies were reaffirmed in Flook. 437 U.S. at 589-91, 98 S.Ct. at 2525-26.
The solicitor has suggested that the Supreme Court has, in Flook, adopted a “point of novelty” approach to § 101. Under such an approach, an invention would be nonstatutory if the mathematical algorithm in the claim, as an embodiment of scientific truth, is at the “point of novelty” of the claim.
If this approach were to be adopted it would immeasurably debilitate the patent system. We do not believe the Supreme Court has acted in a manner so potentially destructive. As an illustration of the utter failure of such an approach to resolve these questions, we offer the example of certain improvement inventions, wherein the improvement resides in the application of scientific truth, e. g., mathematical formulae, to previously-known structure or process steps.
Improvement inventions are expressly included within § 101, which provides that “Whoever invents any * * * new and useful improvement [of a process, machine, manufacture, or composition of matter] may obtain a patent therefor * * *.” (Emphasis ours.) There is no evidence that Congress intended a different criterion to apply to improvement inventions to determine whether they are statutory. Yet a strict “point of novelty” approach to improvement inventions involving the application of scientific truth as the improvement would effectively place them, as a class, outside the coverage of § 101 — and to no purpose.
It is well-settled that a statutory invention will result from the application of a scientific truth (law of nature) to an otherwise statutory structure or process. Mackay Radio, Funk Bros., Eibel Process Co., supra. In both Benson and Flook, the Court again relied on this well-settled precedent.6
This principle applies with equal force to basic inventions and improvement inventions. Thus, if an inventor succeeds in applying scientific truth in a specific manner, resulting in the improvement of a process, machine, manufacture, or composition of matter, his invention is statutory, subject to the caveat that the underlying subject matter which has been improved is itself within the bounds of § 101,7
The solicitor has invited us to reexamine our test in In re Freeman, 573 F.2d 1237, 197 USPQ 464, because the second step of the test is alleged to conflict with Flook. That step involves examination of the claim “to ascertain whether in its entirety it wholly preempts [the] algorithm.” Id. at 1245, 197 USPQ at 471.
We find the problem to be one of semantics. We do not read Flook as adopting a “point of novelty” test; as we have shown, such a test flies in the fact of Supreme *767Court precedent reaffirmed in Flook, and does violence to the statute.
We have observed that the Court in Flook reasoned that a patent claim must be considered as a whole when undergoing analysis under § 101.8 The “point of novelty” approach is incompatible with this directive since it necessarily ignores the claim as a whole in order to concentrate on a single claim component. Whatever implication the solicitor may find in Flook to support his belief that a “point of novelty” approach was adopted is dispelled by the Court’s explicit instructions that, under § 101, a claim must be considered as a whole.
The second step of the Freeman test is stated in terms of preemption. We note, however, that Flook does not require literal preemption of a mathematical algorithm found in a patent claim. The Court there stated that Flook’s claims did not “cover every conceivable application of the formula.” 437 U.S. at 586, 98 S.Ct. at 2524. Nevertheless, we believe that the Freeman test, as applied, is in no way in conflict with Flook.
In order to determine whether a mathematical algorithm is “preempted” by a claim under Freeman, the claim is analyzed to establish the relationship between the algorithm and the physical steps or elements of the claim. In Benson and Flook, no such relationship could be found; the entire claim was, in each case, drawn to the algorithm itself. The preamble in the claim involved in Flook, while limiting the application of the claimed method to “a process comprising the catalytic chemical conversion of hydrocarbons,” did not serve to ren-. der the method statutory because the claim, as a whole, was still directed to the solution of a mathematical problem.
When this court has heretofore applied its Freeman test, it has viewed it as requiring that.the claim be examined to determine the significance of the mathematical algorithm, i. e., does the claim implement the algorithm in a specific manner to define structural relationships between the elements of the claim in the case of apparatus claims, or limit or refine physical process steps in the case of process or method claims? The point of the analysis is the recognition that “A principle, in the abstract, is a fundamental truth; an original cause; a motive; these cannot be patented,” Le Roy v. Tatham, 55 U.S. (14 How.) at 175, 14 L.Ed. 367, and that, “a hitherto unknown phenomenon of nature” if claimed would not be statutory, but that “the application of the law of nature to a new and useful end,” Funk Bros., 333 U.S. at 130, 68 S.Ct. at 441, would be.
While we have stated the test in terms of preemption, we have consistently applied it in the spirit of the foregoing principles. Since we have noted that Flook does not require literal preemption of a mathematical algorithm by a claim for a finding that the claim is nonstatutory, we thus deem it appropriate to restate the second step of the Freeman test in terms other than preemption. Once a mathematical algorithm has been found, the claim as a whole9 must be further analyzed. If it appears that the mathematical algorithm is implemented in a specific manner to define structural relationships between the physical elements of the claim (in apparatus claims) or to refine or limit claim steps (in process claims), the claim being otherwise statutory, the claim passes muster under § 101. If, however, the mathematical algorithm is merely presented and solved by the claimed invention, as was the case in Benson and Flook, and is not applied in any manner to physical elements or process steps, no amount of post-solution activity will render the claim statutory; nor is it saved by a preamble merely reciting the field of use of the mathematical algorithm.
Various indicia are helpful in determining whether a claim as a whole calls merely for the solution of a mathematical algorithm. For instance, if the end-product *768of a claimed invention is a pure number, as in Benson and Flook, the invention is non-statutory regardless of any post-solution activity which makes it available for use by a person or machine for other purposes. If, however, the claimed invention produces a physical thing, such as the noiseless seismic trace in In re Johnson, supra, the fact that it is represented in numerical form does not render the claim nonstatutory.10
The “Means For” Apparatus Claims
Both the examiner and the board refused to separately consider appellant’s apparatus claims because the method and apparatus claims were deemed indistinguishable. This problem arises in computer-arts inventions when the structure in apparatus claims is defined only as “means for” performing specified functions as sanctioned by 35 U.S.C. § 112, sixth paragraph. If the functionally-defined disclosed means and their equivalents are so broad that they encompass any and every means for performing the recited functions, the apparatus claim is an attempt to exalt form over substance since the claim is really to the method or series of functions itself. In computer-related inventions, the recited means often perform the function of “number crunching” (solving mathematical algorithms and making calculations). In such cases the burden must be placed on the applicant to demonstrate that the claims are truly drawn to specific apparatus distinct from other apparatus capable of performing the identical functions.
If this burden has not been discharged, the apparatus claim will be treated as if it were drawn to the method or process which encompasses all of the claimed “means.” See In re Maucorps, 609 F.2d at 485, 203 USPQ at 815-16; In re Johnson, 589 F.2d at 1077, 200 USPQ at 206; In re Freeman, 573 F.2d at 1247, 197 USPQ at 472. The statutory nature of the claim under § 101 will then depend on whether the corresponding method is statutory.
We agree with the PTO that all of appellant’s claims should be treated as method claims. The apparatus claims differ from the method claims only in that the term “means for” has been inserted before each process step to convert the step into the “means” for performing it, wherefore they do not have separate meaning as apparatus claims.
Appellant argues that while the method claims refer to steps which may be carried out at different locations, the apparatus claims are limited to a unitary device in a physical location sense. For support of this proposition, he urges that his patent application be read as a whole, and that, so read, it shows that he is concerned with apparatus which is carried on a single vehicle during the course of seismic exploration. Indeed, his application does disclose this as the best mode for carrying out the invention.
Appellant’s claims, however, are not limited to a unitary device in any sense. There is no evidence that the best mode contemplated is the only operable mode. In effect, we are asked to read limitations into the claims which are not there. This court will not read limitations into claims merely because they are disclosed in the specification. In re Prater, 56 CCPA 1381, 1395-96, 415 F.2d 1393, 1404-05, 162 USPQ 541, 550 (1969); In re Kebrich, 40 CCPA 780, 785, 201 F.2d 951, 954, 96 USPQ 411, 414 (1953).
The Method Claims
Appellant’s claims clearly recite mathematical algorithms. The question is wheth*769er the claims implement the algorithms in such manner as to render them statutory, since, as we have pointed out, the mere presence of the algorithms in the claims is not fatal. Flook, 437 U.S. at 590, 98 S.Ct. at 2526.
We pause to explain a difference between our approach and that of the board, which characterized appellant’s claims as mathematical exercises. We have quoted above the three reasons given by the board to support its conclusion. In discussing steps (a) through (e) of the claims, the board stated that at a fundamental level the computer must employ radices imposed by its architecture to manage the data flow and that it “would be difficult, not to say misleading, to characterize such operations as nonmathematical.” This statement, if accepted, would suffice to remove all computer-arts inventions from the scope of § 101. It is itself misleading because it ignores what the computer is doing, concentrating instead on how it is being done. In re Phillips, 608 F.2d 879, 203 USPQ 971 (Cust. & Pat.App.1979). One could as easily say that the inclined paper-making wire in Eibel Process Co., supra, was on a fundamental level, mathematical in nature because it operated according to the law of gravity, which is expressible as a mathematical formula. However, as this court noted in In re Bradley, 600 F.2d 807, 812, 202 USPQ 480, 485 (Cust. & Pat.App.1979), cert. granted sub nom. Diamond v. Bradley, - U.S. -, 100 S.Ct. 1311, 63 L.Ed.2d 758 (1980), a computer may be retrieving a legal opinion from a computerized legal research service or setting a page from a telephone directory. An overall characterization of these operations as mathematical is too broad because in concentrating on the minutiae, it ignores the whole. Under such reasoning, a timed process step is mathematical in nature because “at a fundamental level” time is counted in minutes. We equally reject the board’s reasoning with respect to the steps used to accommodate the data to memory requiring the tailoring of the data to the particular computer architecture.
We view only the third reason given by the board as valid and substantial and as directly related to the heart of the § 101 issue as it manifests itself in the computer arts. It relates to the processing of the mathematical algorithms recited in appellant’s claims and is the only legitimate basis for the board’s rejection.
Appellant’s claims, except claims 10-12, are in Jepson 11 format. The claim preambles merely set forth the environment in which the improvement operates. They show only the context in which the mathematical exercises in the claims are to be used. In each claim, what is positively claimed, as distinguished from environment, is “the improved method of correlating” (claim 7), or “the improved method of cross-correlating” (claim 16). The same is true of claims 11-12, drafted in illusory apparatus format.
Correlation or cross-correlation is a mathematical exercise which relates two mathematical functions. It remains a mathematical exercise even when verbally tied to the specific end use of seismic prospecting. Although the claim preambles relate the claimed invention to the art of seismic prospecting, the claims themselves are not drawn to methods of or apparatus for seismic prospecting; they are drawn to improved mathematical methods for interpreting the results of seismic prospecting.
The specific end use recited in the preambles does not save the claims from the holding in Flook, since they are drawn to methods of calculation, albeit improved. Examination of each claim demonstrates that each has no substance apart from the calculations involved. The calculations are the beginning and end of the claims. Thus, this case falls squarely within the holding in Flook, and the claims must be held to be nonstatutory.
Furthermore, the nature of the resulting “partial product signals”, is not clear. While these products are termed “signals,” *770there is nothing necessarily physical about them beyond the fact that they are held in some physical storage medium.
Appellant’s specification states that these “signals” comprise “a record somewhat similar to that which would have been produced if the original seismic wave had been in the form of an impulse.” In In re Gelnovatch, supra, a .majority of this court affirmed the § 101 rejection of claims to a process invention for determining the component values in a mathematical model of a microwave circuit. Appellant there similarly argued unsuccessfully that his results were the same as if the circuit had been built and real components substituted.
We view the results here as being similar to those in Gelnovatch — a simulation of something physical is produced by a process akin to mathematical modeling. Each and every step in these claims involves or intimately relates to mathematical operations; we can view the end product in this case only as a mathematical result.
Claim 12, and claims 10 and 11 dependent therefrom, are not presented in Jepson format, but they suffer from a fundamental flaw which places them outside the bounds of § 101. These claims are directed to the process of cross-correlation in the abstract. They are not limited to any particular art or technology, unless pure mathematics is considered as an art or technology. The “signals” processed by the inventions of claims 10-12 may represent either physical quantities or abstract quantities; the claims do not require one or the other. The claims thus dominate the particular method of cross-correlation in any and all arts. They are classic examples of an attempt to embrace the algorithm or scientific truth itself rather than a particular application.
We address another of appellant’s arguments to correct a misconception. In arguing the patentability of claim 18 (apparatus format), appellant states that the solicitor was incorrect in his argument that the eye-readability of the tape upon which the “partial product signals” are recorded is in issue.
We find appellant’s argument to be without merit and his reliance upon the previously-quoted passage in Benson to be misplaced. If § 101 could be satisfied by the mere recordation of the results of a nonstatutory process on some record medium, even the most unskilled patent draftsman could provide for such a step, thus converting a nonstatutory process to a statutory one with relative ease. The fact that a tape containing recorded results is different from a blank tape or a tape containing other results is irrelevant to the inquiry under § 101 where the remaining claim steps provide only for the solution of a mathematical problem.
This case is distinguishable from In re Johnson, supra. There the claims were drawn to the enhancement of digital data in seismic records by removing the noise from the physical signals representing physical phenomena. Mathematics were employed to this end. The inventors in that case did not attempt to claim a mathematical exercise or method of calculation. Operation of the claimed process in Johnson converted the noise-containing physical seismic record present at the start to a new record minus the noise component. Here, appellant claims only an improved mathematical method for cross-correlation.
This case is also distinguishable from our recent In re Diehr, 602 F.2d 982, 203 USPQ 44 (CCPA 1979), cert. granted sub nom. Diamond v. Diehr, - U.S. -, 100 S.Ct. 1311, 63 L.Ed.2d 758 (1980). There appellants invented a process for molding synthetic rubber articles in which one physical step of the process, maintaining the blank in the mold for the proper period of time, was improved by refining and further defining the step with the aid of mathematics. The improvement yielded a higher quality product over prior processes which did not keep the blank in the mold for a sufficient time or kept it there too long. The equation used in the process remained available for others to use in the rubber-making art as well as other arts; in fact, the equation used had long been in use in rubber-molding processes. The inventors *771used it to refine a physical step in the process in a manner analogous to the manner in which mathematics and physical laws were employed in the inventions in Mackay Radio and Eibel Process Co., supra.
Here appellant claims the mathematical algorithm itself even though most of his claims limit its use to a particular art or technology. This may not be done under the patent law as it now exists.
The decision of the board is affirmed.
AFFIRMED.
. This algorithm is a mathematical procedure, the details of which are not relevant to the issues on this appeal. It is sufficient to note that both the computation of Fourier* transforms and the operation of the Cooley-Tukey algorithm are mathematical exercises or algorithms as defined by the Supreme Court in Parker v. Flook, 437 U.S. 584, 98 S.Ct. 2522, 57 L.Ed.2d 451 (1978), and Gottschalk v. Benson, 409 U.S. 63, 93 S.Ct. 253, 34 L.Ed.2d 273 (1972).
. Claims 7-9, 13-14, and 16 are method claims. Claims 10-12 and 17-18 are directed to a “system,” i. e., apparatus, and are identical in substance to the method claims with the exception that the term “means for” has been inserted in front of each method step to convert the claims from method to apparatus format.
. Parker v. Flook, 437 U.S. at 585 n.1, 98 S.Ct. at 2523; Gottschalk v. Benson, 409 U.S. at 65, 93 S.Ct. at 254.
. That the issue of mathematics in claims is at the heart of the controversy in § 101 cases involving computer-related inventions has been explicitly recognized by the Supreme Court in both of the instances in which it has addressed the problem. In Benson, supra, the Court stated:
A procedure for solving a given type of mathematical problem is known as an “algorithm.” The procedures set forth in the *765present claims are of that kind; that is to say, they are a generalized formulation for programs to solve mathematical problems of converting one form of numerical representation to another. [409 U.S. at 65, 93 S.Ct. at 254 (emphasis ours).]
Later, in Flook, supra, the Court said;
We use the word “algorithm” in this case, as we did in Gottschalk v. Benson * * * to mean “[a] procedure for solving a given type of mathematical problem.” [437 U.S. at 585 n.1, 98 S.Ct. at 2523 n.1.]
For the purposes of this opinion, we use the word algorithm in the above-defined sense to refer to methods of calculation, mathematical formulas, and mathematical procedures generally. We strongly disagree with the position taken by the PTO, see Petition of Commissioner of Patents and Trademarks for Certiorari, Diamond v. Bradley, -U.S. -, 100 S.Ct. 1311, 32 L.Ed.2d 758, that the word algorithm as applied by the Supreme Court in § 101 cases is not limited to mathematical algorithms, but extends to the general meaning of the word which connotes a step-by-step procedure to arrive at a given result. In re Chatfield, 545 F.2d 152, 156 n.5, 191 USPQ 730, 734 n.5 (Cust. & Pat. App.1976), cert. denied, 434 U.S. 875, 98 S.Ct. 226, 54 L.Ed.2d 155 (1977). Such a proposition, if accepted, would have the effect of totally reading the word “process” out of § 101, since any process is a step-by-step procedure to arrive at a given result.
. This precedent includes Funk Bros. Seed Co. v. Kalo Inoculant Co., 333 U.S. 127, 68 S.Ct. 440, 92 L.Ed. 588 (1948); Mackay Radio & Telegraph Co. v. Radio Corporation of America, 306 U.S. 86, 59 S.Ct. 427, 83 L.Ed. 506 (1939); Eibel Process Co. v. Minnesota and Ontario Paper Co., 261 U.S. 45, 43 S.Ct. 322, 67 L.Ed. 523 (1923); Tilghman v. Proctor, 102 U.S. 707, 26 L.Ed. 279 (1880); Rubber-Tip Pencil Co. v. Howard, 87 U.S. (20 Wall.) 498, 22 L.Ed. 410 (1874); O’Reilly v. Morse, 56 U.S. (15 How.) 61, 14 L.Ed. 601 (1853); Le Roy v. Tatham, 55 U.S. (14 How.) 156, 14 L.Ed. 367 (1852), as well as Benson and Flook, supra.
. In Flook, the Court stated that “Benson applied the established rule that a law of nature cannot be the subject of a patent.” 437 U.S. at 589, 98 S.Ct. at 2525. Characterizing its decision in Flook, the Court said: “To a large extent our conclusion is based on reasoning derived from opinions written before the modern business of developing programs for computers was conceived.” Id. at 595, 98 S.Ct. at 2528.
. The “point of novelty” approach would condemn the claim in Mackay Radio as nonstatutory. The Supreme Court there noted that the invention “was achieved by the logical application of a known scientific law [the formula recited in the claim] to a familiar type of antenna,” 306 U.S. at 94, 59 S.Ct. at 431 (emphasis ours), thus recognizing that the formula was at the “point of novelty.” See In re Sherwood, 613 F.2d 809, 817 n.11, 204 USPQ 537, 545 n.11 (Cust. & Pat.App. 1980). According to the authority cited in note 5, supra, this claim is statutory; the formula is applied in a specific manner to specific structure to determine physical characteristics of the structure — the spatial relationship between the antenna elements.
The same is true of the claim at issue in Eibel Process Co., supra. The “point of novelty” there was the application of the law of gravity to an otherwise well-known machine. The fact that the Supreme Court found the claim valid serves to demonstrate the unworkability of the “point of novelty” approach.
The requirement that, the underlying subject matter which has been improved must be statutory is amply illustrated by Flook. Since a method of calculation is nonstatutory, it follows that any improvement thereon would likewise be nonstatutory.
. Flook requires that the § 101 analysis be performed on the claim as a whole. 437 U.S. at 594 & n.16, 98 S.Ct. at 2528.
. See note 8, supra.
. In Johnson, a seismic trace containing superimposed noise was subjected to signal processing by computer. As a result of the processing the unwanted noise component was removed from the trace. In order to make a trace palatable to a computer, it must sometimes be converted to a computer-compatible format. One method of doing this is to sample the amplitude of the signal at regular intervals and convert the resulting amplitude value to a binary equivalent form. The resulting noiseless trace may also appear in binary form. It nevertheless is the same signal as the “wiggle trace” which it represents, and is not a pure number, and unless form is to control over substance, the fact that a process result is stated in computer-compatible form should not be the basis for holding an invention to be nonstatutory.
. Ex parte Jepson, 1917 C.D. 62, 243 O.G. 525.