Generation of All Radix-2 Fast Fourier Transform Algorithms Using Binary Trees and Its Analysis (original) (raw)

2012

Abstract

ABSTRACT In this work a systematic method to generate all possible fast Fourier transform (FFT) algorithms is proposed based on the relation to binary trees. The binary tree is used to represent the decomposition of a discrete Fourier transform (DFT) into sub-DFTs. The radix is adaptively changed according to compute sub-DFTs in proposed decomposition. In this work we determine the number of possible algorithms for 2 n -point FFTs with radix- 2 butterfly operation and propose a simple method to determine the twiddle factor indices for each algorithm based on the binary tree representation. I. I NTRODUCTION In many DSP algorithms the discrete Fourier transform (DFT) and inverse DFT is used. Examples include orthogo- nal frequency-division multiplexing (OFDM) communication systems and spectrometers. An N-point DFT is expressed as

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