Patent US2343999A successfully refreshed from Google Patents.
US3584781A
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Fft method and apparatus for real valued inputs
Assignee: AT&T Inc
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Filing: 1968-07-01
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Granted: 1971-06-15
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Expires: 1988-07-01
Abstract
Abstract Methods and apparatus for generating Fourier series coefficients by fast Fourier transform techniques are disclosed. When the input sequence to be transformed includes only real-valued signals, important savings of storage and computation time are realized through the elimination of conjugate results. Instead, only one of a pair of conjugate final results, and the intermediate results leading to them, are explicitly generated; the remaining results are derived by selective conjugation. Techniques for facilitating the computing methods by selective reordering and accessing are also described.
Inventors
- 👤 James O Edson
Bibliographic Details
Application Number
—
Jurisdiction
US
Data Source
google_patents
Last Synchronized
2026-10-23 13:01
CPC Classifications
G; G06; G06F; G06F17/00; G06F17/10; G06F17/14; G06F17/141; G06F17/142
Claims Analysis
Total Claims: 34
Claim 1
Independent Claim
89 words
In a machine having a memory, the method of generating signals representing a complete set of Fourier series coefficients corresponding to a sequence of real-valued input signals comprising the following automatically performed steps of 1. performing successive iterations of a Cooley-Tukey transform based on said input signals, including at each iteration only the first of each pair of intermediate sets of operations which would otherwise yield complex conjugate signals as results, and 2. generating signals representing complex conjugates of the complex results of the final iteration of said transform.
Claim 2
Dependent Claim
89 words
In a machine having a memory, the method of generating signals representing a complete set of Fourier series coefficients corresponding to a sequence of real-valued input signals comprising the following automatically performed steps of 1. performing successive iterations of a Cooley-Tukey transform based on said input signals, including at each iteration only the first of each pair of intermediate sets of operations which would otherwise yield complex conjugate signals as results, and 2. generating signals representing complex conjugates of the complex results of the final iteration of said transform.
Claim 3
Dependent Claim
23 words
generating first and second sequences of binary signals by appending to said reference binary signals signals representing a binary 1and a binary 0respectively,
Claim 4
Dependent Claim
23 words
generating first and second sequences of binary signals by appending to said reference binary signals signals representing a binary 1and a binary 0respectively,
Claim 5
Dependent Claim
16 words
generating signals representing complex conjugates of the complex results of the final iteration of said transform.
Claim 6
Dependent Claim
16 words
generating signals representing complex conjugates of the complex results of the final iteration of said transform.
Claim 7
Dependent Claim
34 words
The method of claim 1 wherein said step of performing successive iterations comprises the step of operating on all exponential operands having a given argument before proceeding to such operands having a different argument.
Claim 8
Dependent Claim
14 words
generating a reversed signal representing in digits-reversed order said signal representing said harmonic number,
Claim 9
Dependent Claim
14 words
generating a reversed signal representing in digits-reversed order said signal representing said harmonic number,
Claim 10
Dependent Claim
20 words
generating Signals representing complex conjugates of at least some of the complex results of the last iteration of said transform.
Claim 11
Dependent Claim
20 words
generating Signals representing complex conjugates of at least some of the complex results of the last iteration of said transform.
Claim 12
Dependent Claim
36 words
storing said signal corresponding to said one of said binary integers in a first memory location when no 1''s are identified in digit positions other than the least significant digit position in said binary integer, and
Claim 13
Dependent Claim
36 words
storing said signal corresponding to said one of said binary integers in a first memory location when no 1''s are identified in digit positions other than the least significant digit position in said binary integer, and
Claim 14
Dependent Claim
26 words
generating a memory identification signal by deleting the digit following the first 1 and complementing the digits following said first 1 in said reversed signal, and
Claim 15
Dependent Claim
26 words
generating a memory identification signal by deleting the digit following the first 1 and complementing the digits following said first 1 in said reversed signal, and
Claim 16
Dependent Claim
20 words
accessing said stored signals in pairs from memory locations identified with said first and second sequences of binary signals, and
Claim 17
Dependent Claim
20 words
accessing said stored signals in pairs from memory locations identified with said first and second sequences of binary signals, and
Claim 18
Dependent Claim
28 words
The method of claim 1 wherein said step of performing successive iterations comprises the step of operating on all real-valued operands before proceeding to operands having complex values.
Claim 19
Dependent Claim
34 words
storing said signal corresponding to said one of said binary integers in a memory location identified with a modified binary integer formed by masking the digit following the most significant in said binary integer.
Claim 20
Dependent Claim
34 words
storing said signal corresponding to said one of said binary integers in a memory location identified with a modified binary integer formed by masking the digit following the most significant in said binary integer.
Claim 21
Dependent Claim
19 words
The method of claim 1 wherein said step of generating signals representing complex conjugate signals comprises the steps of
Claim 22
Dependent Claim
13 words
selectively combining said accessed signals with each other and with selected exponential signals.
Claim 23
Dependent Claim
13 words
selectively combining said accessed signals with each other and with selected exponential signals.
Claim 24
Dependent Claim
21 words
generating a signal representing the conjugate of the signal stored in a memory location uniquely corresponding to said memory identification signal.
Claim 25
Dependent Claim
21 words
generating a signal representing the conjugate of the signal stored in a memory location uniquely corresponding to said memory identification signal.
Claim 26
Dependent Claim
55 words
In a method for the machine processing of real-valued data in accordance with iterative fast Fourier transform techniques on a machine having memory and computational facilities, the improvement comprising the step of selectively deleting from memory at intermediate iterations those results which represent complex conjugate values of a previously generated one of said intermediate results.
Claim 27
Dependent Claim
55 words
In a method for the machine processing of real-valued data in accordance with iterative fast Fourier transform techniques on a machine having memory and computational facilities, the improvement comprising the step of selectively deleting from memory at intermediate iterations those results which represent complex conjugate values of a previously generated one of said intermediate results.
Claim 28
Dependent Claim
29 words
In a machine having a memory, the method of generating signals representing Fourier series coefficients corresponding to a sequence of real-valued input signals comprising the following automatically performed steps:
Claim 29
Dependent Claim
29 words
In a machine having a memory, the method of generating signals representing Fourier series coefficients corresponding to a sequence of real-valued input signals comprising the following automatically performed steps:
Claim 30
Dependent Claim
30 words
The machine method of storing in a plurality of machine memory locations a sequence of signals having a unique correspondence to a sequence of binary integers comprising the steps of
Claim 31
Dependent Claim
30 words
The machine method of storing in a plurality of machine memory locations a sequence of signals having a unique correspondence to a sequence of binary integers comprising the steps of
Claim 32
Dependent Claim
43 words
The method of claim 7 comprising the additional step of storing said signal corresponding to said one of said binary integers in a portion of said memory location identified with said modified binary integer, which portion is identified with said masked binary digit.
Claim 33
Dependent Claim
28 words
The machine method of generating a sequence of signals representing Fourier series coefficients corresponding to a sequence of signals stored in a machine memory comprising the steps of
Claim 34
Dependent Claim
28 words
The machine method of generating a sequence of signals representing Fourier series coefficients corresponding to a sequence of signals stored in a machine memory comprising the steps of
References Cited (Backward Citations)
No citation records indexed.
USPTO Annuity & Maintenance Windows
| Annuity Stage | Window Opens | Payment Deadline | Surcharge Period Until | Estimated Fee | Status |
|---|---|---|---|---|---|
| 3.5 Years (Year 4) | 1974-06-14 | 1974-12-14 | 1975-06-15 | $2000.00 | Window Closed / Lapsed |
| 7.5 Years (Year 8) | 1978-06-14 | 1978-12-14 | 1979-06-15 | $3760.00 | Window Closed / Lapsed |
| 11.5 Years (Year 12) | 1982-06-14 | 1982-12-14 | 1983-06-15 | $7700.00 | Window Closed / Lapsed |