Reordering-needless four-point Winograd Fourier transformation device
A Fourier transform and reordering technology, used in instruments, special data processing applications, complex mathematical operations, etc., can solve problems such as increasing control complexity, reducing operation speed, and multi-memory resources, to improve operation speed, reduce Hardware cost, effect of simplified control logic
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[0018] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments, but not as a limitation of the present invention.
[0019] The FFT of the N-point sequence x(n) is
[0020]
[0021] Among them, n,k=0,1,...,N-1,W N = e -j2π / N . The amount of multiplication and addition operations to directly calculate the N-point FFT is proportional to the square of N. When N is large, the computation load is very large.
[0022] In order to reduce the computational complexity, when N is not a power of 2, a nested multidimensional PFA can be used to realize N-point FFT. Assume that N can be decomposed into the product of s pairwise prime factors, that is, N=N 1 N 2 …N s . That is, any two factors N i and N j The greatest common divisor of (i, j=1, 2, . . . , s, and i≠j) is 1. Note, N i Not necessarily a prime number. The basic principle of N-point PFA is to map one-dimensional large-point FFT ...
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