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: Two new fast discrete cosine transform computation algorithms are presented, superior to the conventional radix-3 algorithm, that require less computational complexity in terms of the number of multiplications per point and provide a wider choice of the sequence length for which the DCT can be realized.
Abstract: Presents two new fast discrete cosine transform computation algorithms: a radix-3 and a radix-6 algorithm. These two new algorithms are superior to the conventional radix-3 algorithm as they (i) require less computational complexity in terms of the number of multiplications per point, (ii) provide a wider choice of the sequence length for which the DCT can be realized and, (iii) support the prime factor-decomposed computation algorithm to realize the 2/sup m/3/sup n/-point DCT. Furthermore, a mixed-radix algorithm is also proposed such that an optimal performance can be achieved by applying the proposed radix-3 and radix-6 and the well-developed radix-2 decomposition techniques in a proper sequence. >
38 citations
Patent•
05 Aug 1993TL;DR: The Fast Fourier Transform (FFT) processor includes a plurality of pipelined, functionally identical stages, each stage adapted to perform a portion of an FFT operation on a block of data as mentioned in this paper.
Abstract: The Fast Fourier Transform (FFT) processor includes a plurality of pipelined, functionally identical stages, each stage adapted to perform a portion of an FFT operation on a block of data. The output of the last stage of the processor is the high-precision Fast Fourier Transform of the data block. Support functions are included at each stage. Thus, each stage includes a computational element and a buffer memory interface. Each stage also includes apparatus for coefficient generation.
38 citations
07 Jun 1988
TL;DR: An efficient method for computing the discrete Fourier transform when only a few output points are needed is described, based on a novel factorization of the DFT, where one part is computed using standard power-of-two FFTs and the other uses a technique similar to the Goertzel algorithm.
Abstract: The authors describe an efficient method for computing the discrete Fourier transform (DFT) when only a few output points are needed. The method is shown to be more efficient than either Goertzel's method or pruning, and it allows any band in the output to be computed. It is based on a novel factorization of the DFT, where one part is computed using standard power-of-two FFTs (fast Fourier transforms) and the other uses a technique similar to the Goertzel algorithm. >
37 citations
TL;DR: The conversion of time domain data via the fast Fourier (FFT) and Hilbert-Huang (HHT) transforms is compared and the behavior and flexibility of these two transforms are examined for a number of different time domain signal types.
Abstract: The conversion of time domain data via the fast Fourier (FFT) and Hilbert-Huang (HHT) transforms is compared. The FFT treats amplitude vs. time information globally as it transforms the data to an amplitude vs. frequency description. The HHT is not constrained by the assumptions of stationarity and linearity, required for the FFT, and generates both amplitude and frequency information as a function of time. The behavior and flexibility of these two transforms are examined for a number of different time domain signal types.
37 citations
TL;DR: The complex Fourier transform of a real function and its real Hartley transform are expressed in terms of each other, allowing translation of theorems and computer programs between the two versions, and the FHT can transform one real array of length N in half the time that it takes the FFT to process a complex array.
Abstract: The complex Fourier transform of a real function and its real Hartley transform are expressed in terms of each other, allowing translation of theorems and computer programs between the two versionsAny FFT can thus be converted, by a few indexing changes, into a Fast Hartley Transform which is equally efficient, in terms of floating point operations per real datum transformed The FHT can therefore transform one real array of length N in half the time that it takes the FFT to process a complex array of length N Several tricks to speed up both FHT and FFT are presented and a Fortran version of the FHT is supplied which delivers the result in $75\log _2 N$ multiplications and $175\log _2 N$ additions
37 citations