Patent US3638004A successfully refreshed from Google Patents.
US3638004A
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Fourier transform computer
Assignee: TIME DATA CORP
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Filing: 1968-10-28
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Granted: 1972-01-25
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Expires: 1988-10-28
Abstract
Abstract A digital computer for rapidly determining the Fourier transform of a real input signal is disclosed. The computer utilizes the symmetries of sinusoidal functions to reduce the computations required to determine the Fourier transform. Simultaneous addition, multiplication and memory accessing are performed by the computer thereby reducing the time normally required to compute a Fourier transform.
Inventors
- 👤 Edwin A Sloane
- 👤 Bruce T Mckeever
- 👤 Burtis W Meyer
Bibliographic Details
Application Number
—
Jurisdiction
US
Data Source
google_patents
Last Synchronized
2026-11-05 23:05
CPC Classifications
G; G06; G06F; G06F17/00; G06F17/10; G06F17/14; G06F17/141; G06F17/142
Claims Analysis
Total Claims: 17
Claim 1
Independent Claim
187 words
A method for computing the Fourier transform of a real signal, where the said signal is represented by N number of amplitude sample, (An) of said signal, in a computer comprising a memory means, arithmetic means, trigonometric means and accumulation means comprising the following steps: a. performing a first fold of said amplitude samples to form the quantities (An+AN n) Sigma n and (An-AN n) Delta n with said arithmetic means; b. performing a second fold on said quantities Sigma n and Delta n to form the quantities: ( Sigma n+ Sigma N n), ( Sigma n- Sigma N n), ( Delta n+ Delta N n) and ( Delta n- Delta N n) with said aRithmetic means; c. multiplying with said arithmetic means the results of said second fold by trigonometric functions generated by said trigonometric means; d. adding and subtracting the results of each of said multiplications with the accumulated results of the prior multiplication for each frequency generated by said trigonometric means with said accumulation means; whereby the results of said method will be the even frequency coefficients of a Fourier transform of said signal.
Claim 2
Independent Claim
187 words
A method for computing the Fourier transform of a real signal, where the said signal is represented by N number of amplitude sample, (An) of said signal, in a computer comprising a memory means, arithmetic means, trigonometric means and accumulation means comprising the following steps: a. performing a first fold of said amplitude samples to form the quantities (An+AN n) Sigma n and (An-AN n) Delta n with said arithmetic means; b. performing a second fold on said quantities Sigma n and Delta n to form the quantities: ( Sigma n+ Sigma N n), ( Sigma n- Sigma N n), ( Delta n+ Delta N n) and ( Delta n- Delta N n) with said aRithmetic means; c. multiplying with said arithmetic means the results of said second fold by trigonometric functions generated by said trigonometric means; d. adding and subtracting the results of each of said multiplications with the accumulated results of the prior multiplication for each frequency generated by said trigonometric means with said accumulation means; whereby the results of said method will be the even frequency coefficients of a Fourier transform of said signal.
Claim 3
Dependent Claim
24 words
The method defined by claim 1 wherein said trigonometric functions include a trigonometric function of a fundamental frequency and harmonics of said fundamental frequency.
Claim 4
Dependent Claim
22 words
The method defined by claim 2 wherein said amplitude samples (An) of said signal are taken at substantially equally spaced time intervals.
Claim 5
Dependent Claim
27 words
The method defined by claim 3 wherein the period of said fundamental frequency is approximately equal to the time interval between the first and last amplitude samples.
Claim 6
Dependent Claim
60 words
The method defined in claim 1 wherein the results of the first fold are multiplied by trigonometric functions generated by said trigonometric means with said arithmetic means, and the results of said multiplication are accumulated for each frequency generated by said trigonometric means with said accumulation means to yield the odd frequency coefficients of a Fourier transform of said signal.
Claim 7
Independent Claim
109 words
A method for computing the Fourier transform of a real signal, where the said signal is represented by N number of amplitude samples, (An) of said signal, in a computer comprising a memory means, arithmetic means, trigonometric means and accumulation means comprising the following steps: a. performing a first fold of said amplitude samples to form the quantities (An+AN n) Sigma n and (An-AN n) Delta n with said arithmetic means; b. folding the quantities Sigma n and Delta n and the results thereof in a complex fold forming the quantities Xp q and Yp q until p log2 N/2 with said arithmetic means trigonometric means and accumulation means;
Claim 8
Independent Claim
109 words
A method for computing the Fourier transform of a real signal, where the said signal is represented by N number of amplitude samples, (An) of said signal, in a computer comprising a memory means, arithmetic means, trigonometric means and accumulation means comprising the following steps: a. performing a first fold of said amplitude samples to form the quantities (An+AN n) Sigma n and (An-AN n) Delta n with said arithmetic means; b. folding the quantities Sigma n and Delta n and the results thereof in a complex fold forming the quantities Xp q and Yp q until p log2 N/2 with said arithmetic means trigonometric means and accumulation means;
Claim 9
Dependent Claim
71 words
The method defined by claim 6 wherein said quantities Sigma n and Delta n are folded in a complex fold to form the quantities Xp q and Yp q where p log2 N/2 includes at least one double complex fold where the quantities Xp q and Yp q are converted to the Xp 2 q and Yp 2 q stage without computing the quantities Xp 1 q and Yp 1 q.
Claim 10
Dependent Claim
22 words
The method defined by claim 7 wherein said amplitude samples (An) of said signal are taken at substantially equally spaced time intervals.
Claim 11
Independent Claim
134 words
A method for computing the Fourier transform of a real signal, where said signal is represented by N number of amplitude samples, (An) of said signal, in a computer comprising an arithmetic means, trigonometric means and accumulation means comprising the following steps: a. performing a first fold of said amplitude samples to form the quantities (An+AN n) Sigma n and (An-AN n) Delta n with said arithmetic means; b. multiplying with said arithmetic means the results of said first fold by trigonometric functions generated by said trigonometric means; c. accumulating the results of each of Said multiplications with the accumulated results of the prior multiplications for each frequency generated by said trigonometric means with said accumulation means; whereby the results of said method will be the coefficients of a Fourier transform of said signal.
Claim 12
Independent Claim
134 words
A method for computing the Fourier transform of a real signal, where said signal is represented by N number of amplitude samples, (An) of said signal, in a computer comprising an arithmetic means, trigonometric means and accumulation means comprising the following steps: a. performing a first fold of said amplitude samples to form the quantities (An+AN n) Sigma n and (An-AN n) Delta n with said arithmetic means; b. multiplying with said arithmetic means the results of said first fold by trigonometric functions generated by said trigonometric means; c. accumulating the results of each of Said multiplications with the accumulated results of the prior multiplications for each frequency generated by said trigonometric means with said accumulation means; whereby the results of said method will be the coefficients of a Fourier transform of said signal.
Claim 13
Dependent Claim
24 words
The method defined by claim 9 wherein said trigonometric functions include a trigonometric function of a fundamental frequency and harmonics of said fundamental frequency.
Claim 14
Dependent Claim
22 words
The method defined in claim 10 wherein said amplitude samples (An) of said signal are taken at substantially equally spaced time intervals.
Claim 15
Independent Claim
183 words
A method for computing the Fourier transform of a real signal, where the said signal is represented by N number of amplitude samples, (An) of said signal, in a computer comprising a memory means, arithmetic means, trigonometric means and accumulation means comprising the following steps: a. performing a first fold of said amplitude samples to form the quantities (An+AN n) Sigma n and (An-AN n) Delta n with said arithmetic means; b. folding the quantities Sigma n and Delta n in complex folds forming the quantities Xp q and Yp q until p log2 N/4 with said arithmetic means, trigonometric means and accumulation means; c. solving the eight resulting simultaneous equations equal to 2Naq; 2Nbq; 2Na(N/2) q; 2Nb(N/2) q; 2Na(N/4) q; 2Nb(N/4) q; 2Na(N/4) q and 2Nb(N/4) q for each of said values of a and b where said sine and cosine values are generated by said trigonometric means and said accumulation means accumulates the terms of said equations; whereby the values of a and b will be representative of the real and imaginary coefficients of the Fourier transform of said real signal.
Claim 16
Independent Claim
183 words
A method for computing the Fourier transform of a real signal, where the said signal is represented by N number of amplitude samples, (An) of said signal, in a computer comprising a memory means, arithmetic means, trigonometric means and accumulation means comprising the following steps: a. performing a first fold of said amplitude samples to form the quantities (An+AN n) Sigma n and (An-AN n) Delta n with said arithmetic means; b. folding the quantities Sigma n and Delta n in complex folds forming the quantities Xp q and Yp q until p log2 N/4 with said arithmetic means, trigonometric means and accumulation means; c. solving the eight resulting simultaneous equations equal to 2Naq; 2Nbq; 2Na(N/2) q; 2Nb(N/2) q; 2Na(N/4) q; 2Nb(N/4) q; 2Na(N/4) q and 2Nb(N/4) q for each of said values of a and b where said sine and cosine values are generated by said trigonometric means and said accumulation means accumulates the terms of said equations; whereby the values of a and b will be representative of the real and imaginary coefficients of the Fourier transform of said real signal.
Claim 17
Dependent Claim
61 words
The method defined by claim 12 wherein the folding of the quantities Sigma n and Delta n to form the eight simultaneous equations includes at least one double complex fold where the quantities Xp q and Yp q are converted to the Xp 2 q and Yp 2 q stage without computing the quantities Xp 1 q and Yp 1 q.
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USPTO Annuity & Maintenance Windows
| Annuity Stage | Window Opens | Payment Deadline | Surcharge Period Until | Estimated Fee | Status |
|---|---|---|---|---|---|
| 3.5 Years (Year 4) | 1975-01-24 | 1975-07-26 | 1976-01-25 | $2000.00 | Window Closed / Lapsed |
| 7.5 Years (Year 8) | 1979-01-24 | 1979-07-26 | 1980-01-25 | $3760.00 | Window Closed / Lapsed |
| 11.5 Years (Year 12) | 1983-01-24 | 1983-07-26 | 1984-01-25 | $7700.00 | Window Closed / Lapsed |