Method of and arrangement for calculating the discrete Fourier t

Details Method of and arrangement for calculating the discrete Fourier t Method of and arrangement for calculating the discrete Fourier t

1981-03-13

1984-03-06

Malzahn, David H.

Boots, shoes, and leggings

G06F 15332

Patent

active

044357745

ABSTRACT:
Method of a N-point discrete Fourier transform. The original set, consisting of N input signal values {a(k)}k=0,1,2, . . . N-1 is converted into two sets of signal values {b.sub.1 (q)}q=1,2, . . . M and {b.sub.2 (q)}q=1,2, . . . M, which each comprise M=(N-1)/2 signal values, each value being a linear combination of two of the original input signal values a(k). These sequences are circularly convolved with the impulse response h.sub.1 (v)=.alpha.cos((2.pi./N) g.sup.V) and h.sub.2 (v)=j.beta.sin ((2.pi./N) g.sup.V), respectively, for generating a set of third data elements y.sub.1 (p) and a set of fourth signal values y.sub.2 (p). Herein N is a prime and .alpha.,.beta. and g represent constants and it holds that p, v=1,2, . . . M, whereas j=.sqroot. -1. The desired output signal value can be obtained by means of a linear combination of the signal values y.sub.1 (p), y.sub.2 (p) and a(0).

REFERENCES:
patent: 4282579 (1981-08-01), Speiser et al.
Agarwal et al., "Fast Convolution Using Fermat Number Transforms with Applications to Digital Filtering", IEEE Trans. on Acoustics, Speech & Signal Processing vol. ASSP-22, No. 2, Apr. 1974, pp. 87-97.
Kolba, "A Prime Factor FFT Algorithm Using High-Speed Convolution", IEEE Trans. on Acoustics, Speech, and Signal Processing vol. ASSP-25, No. 4, Aug. 1977, pp. 281-294.

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