In this paper, we examine the FFT of sequences x„ = xN + „ with period N that satisfy certain symmetric relations. It is known that one can take advantage of these relations in order to reduce the computing time required by the FFT. For example, the time required for the FFT of a real sequence is about half that required for the FFT of a complex sequence. Also, the time required for the FFT of ...

We provide a polymorphic framework for radix-n Fast Fourier Transforms (FFTs) where all known kinds of monomoporhic radix-n algorithms can be obtained by specialization. The framework is mathematically based on the Cooley-Tukey mapping, and implemented as a C++ template meta-program. Avoiding run-time overhead, all specializations are performed statically.

We define the notion of the Fourier transform for the rook monoid (also called the symmetric inverse semigroup) and provide two efficient divideand-conquer algorithms (fast Fourier transforms, or FFTs) for computing it. This paper marks the first extension of group FFTs to non-group semigroups.

In this paper, we proposed an variable length FFT processor architecture which could be used in multi-mode and multi-standard OFDM communication system. Based on radix-2 single-path delay feedback architecture, FFT is implemented with the aid of LUT and control logic. The expected architecture would complete FFT ranging 2048/1024/512point. Keywords-FFT; Radix-2 FFT; variable length FFT;

The chirplet transform is the generalization form of fast Fourier Transform, short-time Fourier transform, and wavelet transform. It has the most flexible time frequency window and successfully used in practices. However, the chirplet transform has not inherent inverse transform, and can not overcome the signal reconstructing problem. In this paper, we proposed the improved chirplet transform (...

We propose an algorithm that uses the discrete wavelet transform (DWT) as a tool to compute the discrete Fourier transform (DFT). The Cooley-Tukey FFT is shown to be a special case of the proposed algorithm when the wavelets in use are trivial. If no intermediate coeecients are dropped and no approximations are made, the proposed algorithm computes the exact result, and its computational comple...