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Fast Fourier Transform

2018
As was defined in a previous chapter, the discrete Fourier transform (DFT) is the sampled version of the discrete-time Fourier transform (DTFT), with a finite number of samples taken around the unit circle in the Z-domain. DFT is very useful in the analysis of discrete-time signals and linear time-invariant discrete-time systems.
Brian E. Dalrymple, E. Jill Smith
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Fast Fourier Transform

2021
In this chapter we learn radix-2 decimation-in-time fast Fourier transform algorithm—the most important algorithm in DSP. We understand the divide-and-conquer philosophy of all FFT algorithms in which inputs samples are recursively divided into smaller and smaller groups, finally the DFT is calculated upon very small data vectors, e.g.
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Fast Fourier Transforms

Proceedings of the November 7-10, 1966, fall joint computer conference on XX - AFIPS '66 (Fall), 1966
The "Fast Fourier Transform" has now been widely known for about a year. During that time it has had a major effect on several areas of computing, the most striking example being techniques of numerical convolution, which have been completely revolutionized. What exactly is the "Fast Fourier Transform"?
W. M. Gentleman, G. Sande
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Fast Fourier Transform

2020
The fast Fourier Transform (FFT) is an algorithm that increases the computation speed of the DFT of a sequence or its inverse (DFT) by simplifying its complexity. This is because by computing the DFT and IDFT directly from its definition is often too slow to be practical.
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The fast Fourier transform

2004
Abstract This chapter demonstrates the use of different data distributions in different phases of a parallel fast Fourier transform (FFT), which is a regular computation with a predictable but challenging data access pattern. Both the block and cyclic distributions are used and also intermediates between them.
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Fast Fourier Transform

2012
In the computation of classical Discrete Fourier Transform (DFT), the computational complexity is huge especially for complex multiplication and complex addition the processor takes large amount of time cycles. In the present chapter faster methods of doing DFT are discussed. As we know, to expedite any algorithm, parallel processing is required.
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Fast Fourier transform

2014
The digital Fourier transform (DFT) pair introduced in Chap. 4 is a very useful formula for numerical operations of the Fourier transform. However, if one tries to perform the calculation, it requires a large number of computations.
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