Topic
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.
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TL;DR: A simple FFT-based algorithm for spectrum estimation using a single pass through the FFT is presented and is certainly better than the single pass FFT in separating closely spaced sinusoids.
Abstract: A simple FFT-based algorithm for spectrum estimation is presented. The major difference between this and spectrum estimation using a single pass through the FFT is that the proposed algorithm is iterative and the FFT is used many times in a systematic may to search for individual spectral lines. Using simulated data, the proposed algorithm is able to detect mulitple sinusoids in additive noise. The algorithm is certainly better than the single pass FFT in separating closely spaced sinusoids. Finally the algorithm is applied to some experimental measurements to illustrate its properties. >
123 citations
TL;DR: This article describes a computational method, called the Fourier sampling algorithm, which takes a small number of (correlated) random samples from a signal and processes them efficiently to produce an approximation of the DFT of the signal.
Abstract: This article describes a computational method, called the Fourier sampling algorithm. The algorithm takes a small number of (correlated) random samples from a signal and processes them efficiently to produce an approximation of the DFT of the signal. The algorithm offers provable guarantees on the number of samples, the running time, and the amount of storage. As we will see, these requirements are exponentially better than the FFT for some cases of interest.
122 citations
TL;DR: The method treats Fast Fourier Transforms of multichannel EEGs so that they can be used for intracerebral source localizations and finds the least square deviation sum between the entry positions and their orthogonal projections onto the straight line.
122 citations
TL;DR: A method for the calculation of the fractional Fourier transform (FRT) by means of the fast Fouriertransform (FFT) algorithm is presented and scaling factors for the FRT and Fresnel diffraction when calculated through the FFT are discussed.
Abstract: A method for the calculation of the fractional Fourier transform (FRT) by means of the fast Fourier transform (FFT) algorithm is presented. The process involves mainly two FFT’s in cascade; thus the process has the same complexity as this algorithm. The method is valid for fractional orders varying from −1 to 1. Scaling factors for the FRT and Fresnel diffraction when calculated through the FFT are discussed.
118 citations
TL;DR: In this article, the authors show how discrete Fourier transformation can be implemented as a filter bank in a way which reduces the number of filter coefficients, leading to new forms of FFT's, among which is a \cos/sin FFT for a real signal which only employs real coefficients.
Abstract: The paper shows how discrete Fourier transformation can be implemented as a filter bank in a way which reduces the number of filter coefficients. A particular implementation of such a filter bank is directly related to the normal complex FFT algorithm. The principle developed further leads to types of DFT filter banks which utilize a minimum of complex coefficients. These implementations lead to new forms of FFT's, among which is a \cos/\sin FFT for a real signal which only employs real coefficients. The new FFT algorithms use only half as many real multiplications as does the classical FFT.
112 citations