FAST FOURIER ANALYZER

• US 3,581,078 A
• Filed: 11/24/1967
• Issued: 05/25/1971
• Est. Priority Date: 11/24/1967
• Status: Expired due to Term

• Current Assignee: George H. Robertson
• Original Assignee: George H. Robertson
• Inventors: Robertson, George H.
• Application Number:
  US04/685,648
• Time in Patent Office: 1,278 Days
• US Class Current: 708/821
• CPC Class Codes: G06G 7/1921 for forming Fourier integrals, harmonic analysis and synthesis spectrum analysis G01R23/00

Abstract

The recursive equations of the Cooley-Tukey algorithm are implemented in analog form, thereby significantly decreasing the time needed to compute either the Fourier transform or the inverse Fourier transform of a signal segment, relative to the time needed for the same computation by a digital implementation of these equations.

Claims

1. Apparatus which comprises:

means for modulating a complex sinusoid with N sets of samples representative of a waveform, thereby producing an input set of N modulated sinusoids, m processors 1,...,M,...,m, where M and m are integers and M equals 1Mm, each processor containing arrangements of conducting paths and combining nodes, with selected conducting paths including specified phase-shifting networks, the first processor selectively combining the sinusoids in said input set of N modulated sinusoids after phase-shifting selected ones, to produce a first set of processed sinusoids, the Mthprocessor selectively combining the sinusoids in the (M1)thset of processed sinusoids after phase-shifting selected sinusoids in said (M1)thset, to produce an Mthset of processed sinusoids, and the mthprocessor selectively combining the sinusoids in the (m1)thset of processed sinusoids after phase-shifting selected sinusoids in said (m1)thset, to produce an output set of N modulated sinusoids.

2. Apparatus as in claim 1 in which said means for modulating comprises:

means for storing said N sets of samples, and means for individually modulating said sinusoid with each sample of said N sets of samples to produce said input set of N modulated sinusoids.

3. Apparatus as in claim 1 in which said means for modulating comprises means for modulating the complex sinusoid with the amplitudes of said N sets of samples of said waveform.

4. Apparatus as in claim 1 in which said means for modulatinG comprises means for modulating the complex sinusoid with the amplitude of the DC component and the amplitude and initial phases of selected harmonically related frequency components of said N sets of samples representative of said waveform.

5. Apparatus as in claim 1 in which said means for storing includes means for storing complex samples possessing both amplitude and phase information, and in which said means for individually modulating said sinusoid with each of said samples includes means for both amplitude and phase modulating said sinusoid with each of said samples to produce said input set of N modulated sinusoids.

6. Apparatus which comprises:

a source of a first complex sinusoid ei twhere omega is a selected frequency, means for storing N complex samples, each sample in general containing both amplitude and phase information, means for amplitude and phase modulating each of N identical complex sinusoids derived from said first complex sinusoid with a corresponding one of said N complex samples, to produce an input set of N complex sinusoids, and means for processing said input set of N complex sinusoids to produce an output set of N amplitude and phase modulated sinusoids representing a selected transformation of said N complex samples.

7. Apparatus which comprises:

means for modulating each of N samples with a corresponding one of N identical sinusoids, where N equals rmboth r and m being positive integers greater than unity, to produce an input set of N modulated sinusoids, m means 1,...,M, ..., m, for processing said input set of N modulated sinusoids, where M and m are integers, M being given by 1 Mm, to produce an output set of N modulated sinusoids representing a selected transformation of said N stored samples, the Mthof said m means for processing comprising;

means for producing an Mthset of sinusoids, each sinusoid in said Mthset being produced by summing r selected sinusoids from the (M1)thset of N sinusoids, the (M1)thset of N sinusoids being said input set of N modulated sinusoids when M equals 1, each sinusoid from said (M1)thset contributing to r sinusoids in said Mthset, selected sinusoids from said (M1)thset being phase shifted by selected amounts prior to being combined in selected combinations, and said Mthset of N sinusoids being said output set of N modulated sinusoids when M equals m.

8. Apparatus as in claim 7 in which r equals 2.

9. Apparatus as in claim 8 in which m equals 3.

10. Apparatus as in claim 7 in which r equals 3.