Prime-factor FFT algorithm

About: Prime-factor FFT algorithm is a research topic. Over the lifetime, 2346 publications have been published within this topic receiving 65147 citations. The topic is also known as: Prime Factor Algorithm.

Using discrete Tchebichef transform on speech recognition

Abstract: Speech recognition is becoming popular in current development on mobile devices. Presumably, mobile devices have limited computational power, memory size and battery life. In general, speech recognition is a heavy process that required large sample data within each window. Fast Fourier Transform (FFT) is the most popular transform in speech recognition. In addition, FFT operates in complex field with imaginary numbers. This paper proposes an approach based on discrete orthonormal Tchebichef polynomials as a possible alternative to FFT. Discrete Tchebichef Transform (DTT) shall be utilized here instead of FFT. The preliminary experimental result shows that speech recognition using DTT produces a simpler and efficient transformation for speech recognition. The frequency formants using FFT and DTT have been compared. The result showed that, they have produced relatively identical output in term of basic vowel and consonant recognition. DTT has the potential to provide simpler computing with DTT coefficient real numbers only than FFT on speech recognition.

Double factors algorithm for computing DFT

Abstract: A fast Fourier transform algorithm for computing N=N 1 ×N 2 -point DFT, where both factors N 1 and N 2 are smaller positive integer, said to be a double factors algorithm(DFA), is developed. The DFA subdivides a DFT of length N=N 1 ×N 2 into smaller transforms of length N 1 and N 2 and takes the following steps:(1) computes N 1 N 2 -point DFTs , (2) multiplies the values of DFT by twiddle factors, (3) computes N 2 N 1 -point DFTs. The structure of the DFA is similar to those of the most simple PFA and WFTA, but N 1 and N 2 are not necessarily relatively prime. When N=2M or 4M, the total number of computations of DFT in the DFA is less than those in the radix-2 and radix-4 FFT algorithm but slightly more than that in the split-radix FFT algorithm. When N is other values, the total number of computations of DFT in the DFA is less than those in the PFA and WFTA.

On computing the 2-D FFT

Abstract: A a new implementation of the two-dimensional FFT (2-D FFT) is proposed. Compared with the usual separable solution, the new realization of the 2-D FFT has reduced arithmetic complexity. Computational savings are achieved because the 2-D case enables, after some modifications of the basic separable algorithm, scaling and inverse scaling of butterfly operators. The new improvement is also applied to other 2-D transforms: DCT-IV, DCT, and lapped transforms.

A generalized FFT algorithm on transputers

Abstract: A generalized algorithm has been derived for the execution of the Cooley-Tukey FFT algorithm on a distributed memory machine. This algorithm is based on an approach that combines a large number of butterfly operations into one large process per processor. The performance can be predicted from theory. The actual algorithm has been implemented on a transputer array, and the performance of the implementation has been measured for various sizes of the complex input vector. It is shown that the algorithm scales linearly with the number of transputers and the problem size.

Index transforms forn-dimensional DFT's

Abstract: In this paper fundamental theorems are proved for computing the so called index transforms which mapm-dimensional discrete Fourier transform operator (DFT) ton-dimensional one. These transforms are based on mapping indexes of input and output sequences of DFT operators. The general form of these transforms is found and the necessary and sufficient conditions of their existence are described.