Showing papers on "Split-radix FFT algorithm published in 1971"

FFT pruning

Abstract: There are basically four modifications of the N=2Mpoint FFT algorithm developed by Cooley and Tukey which give improved computational efficiency. One of these, FFT pruning, is quite useful for applications such as interpolation (in both the time and frequency domain), and least-squares approximation with trignometric polynomials. It is shown that for situations in which the relative number of zero-valued samples is quite large, significant time-saving can be obtained by pruning the FFT algorithm. The programming modifications are developed and shown to be nearly trivial. Several applications of the method for speech analysis are presented along with Fortran programs of the basic and pruned FFT algorithm. The technique described can also be applied effectively for evaluating a narrow region of the frequency domain by pruning a decimation-in-time algorithm.

Kronecker Product Factorization of the FFT Matrix

Abstract: A method is presented which utilizes the results of the Glassman paper [1] to factor the FFT matrix in terms of Kronecker product expansions [2], [3]. The method clarifies the Glassman results and presents them in an elegant and compact format.

Fast fourier transform computer and method for simultaneously processing two independent sets of data

Abstract: Special purpose computing equipment is utilized to perform the Fast Fourier Transform algorithm. The computing equipment utilizes serial access memory for storing coefficients during interim periods between calculations and by properly alternating between two clock rates for the serial memory, the computer allows the processing of two Fast Fourier Transform algorithms simultaneously when the input data for the two algorithms is in different binary order.

Digital filters with poles via the FFT

Abstract: A method is presented that uses the fast Fourier transform (FFT) to compute the output of an infinite-impulse-response digital filter. This method uses the summability of infinite-length geometric sequences to account for the aliasing that is inherent in using the discrete Fourier transform (DFT) to calculate convolutions. Previous procedures that use the FFT to realize recursive digital filters require that the filter have a large number of poles and zeros before the FFT method offers a computational advantage over the direct implementation of the filter. The technique presented here is competitive with direct filter implementation.

An Algorithm for the Machine Computation of Partial-Fractions Expansion of Functions Having Multiple Poles

Abstract: The partial-fractions expansion of a function F(s)/(s-a)m, m > 1, involves the computation of m coefficients, namely (1 /i!)(diF(a)/dsi), 0 ≤ i ≤ m-1. Wehrhahn [1] and Karni [3] have provided a method for computing these coefficients algebraically. A new approach is taken here which involves approximating a multiple pole by neighboring simple poles. The theory developed turns out to have a very interesting resemblance to the FFT algorithm. The algorithm is illustrated by several examples. Typical applications are finding the inverse Laplace transform of a function having multiple poles and the evaluation of higher order derivatives of an arbitrary function H(z) at some arbitrary z=z0.

Computation of the Fast Fourier Transform from Data Stored in External Auxiliary Memory for Any General Radix r=2 n , n ≥ 1

Abstract: A general method is presented for the computation of the fast Fourier transform from data stored in external auxiliary memory, for any general radix r = 2nn ≥e external data storage is necessitated whenever the internal computer memory is limited. The general radix requirement arises in the tradeoff in serial FFT processor machines, between the number of passes required to address storage and the number of equivalent sparse matrix multiplicative operations required to compute the fast Fourier transform.