Fast Fourier Transform

The split-radix approach for computing the discrete Fourier transform (DFT) is extended for the vector-radix fast Fourier transform (FFT) to two and higher dimensions. It is obtained by further splitting the ( N /2× N /2) transforms with twiddle factors ...

In this paper for certain long transform lengths, Winograd's algorithm for computing the discrete Fourier transform (DFT) is extended considerably. This is accomplisbed by performing the cyclic convolution, required by Winograd's method, with the ...

An efficient algorithm for computing the one-dimensional partial fast Fourier transform $$f_j=\sum _{k=0}^{c(j)}e^{2\pi ijk/N} F_k$$fj=?k=0c(j)e2?ijk/NFk is presented. Naive computation of the partial fast Fourier transform requires $${\mathcal O}(N^2)$$...