Open AccessJournal Article
FFT pruning
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TLDR
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.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.read more
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References
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An algorithm for the machine calculation of complex Fourier series
J.W. Cooley,John W. Tukey +1 more
TL;DR: Good generalized these methods and gave elegant algorithms for which one class of applications is the calculation of Fourier series, applicable to certain problems in which one must multiply an N-vector by an N X N matrix which can be factored into m sparse matrices.
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An algorithm for computing the mixed radix fast Fourier transform
TL;DR: This paper presents an algorithm for computing the fast Fourier transform, based on a method proposed by Cooley and Tukey, and includes an efficient method for permuting the results in place.
Proceedings ArticleDOI
Fast Fourier Transforms: for fun and profit
W. M. Gentleman,G. Sande +1 more
TL;DR: The "Fast Fourier Transform" has had a major effect on several areas of computing, the most striking example being techniques of numerical convolution, which have been completely revolutionized.
Journal ArticleDOI
System for automatic formant analysis of voiced speech.
TL;DR: A system for automatically estimating the lowest three formants and the pitch period of voiced speech is presented, based on a digital computation of the cepstrum (defined as the inverse transform of the log magnitude of the z‐transform).
Journal ArticleDOI
Short‐Time Spectrum and “Cepstrum” Techniques for Vocal‐Pitch Detection
TL;DR: Cepstral techniques appear to be even more reliable and efficient than visual methods for pitch detection, and to produce high‐resolution spectra without utilizing either heterodyning methods or bandpass filter banks.