Showing papers on "Prime-factor FFT algorithm published in 1972"
TL;DR: By eliminating all unnecessary steps and storage locations, and by rearranging the intermediate results and the operation sequence, it is possible to reduce the computation time and the required core storage by a factor of 2 as compared to the case of arbitrary real input.
Abstract: A new algorithm is presented for calculating the real discrete Fourier transform of a real-valued input series with even symmetry. The algorithm is based on the fast Fourier transform algorithm for arbitrary real-valued input series (FTRVI) [1], [2]. By eliminating all unnecessary steps and storage locations, and by rearranging the intermediate results and the operation sequence, it is possible to reduce the computation time and the required core storage by a factor of 2 as compared to the case of arbitrary real input or by a factor of 4 as compared to the general fast Fourier transform for complex inputs.
22 citations
01 Dec 1972
TL;DR: An efficient and accurate method for interpolation of functions based on the FFT is presented and the generation of the characteristic polynomial in the "generalized eigenvalue problem" is considered.
Abstract: The fast Fourier transform (FFT) algorithm has had widespread influence in many areas of computation since its "rediscovery" by Cooley and Tukey [1] An efficient and accurate method for interpolation of functions based on the FFT is presented As an application, the generation of the characteristic polynomial in the "generalized eigenvalue problem" [2] is considered
20 citations
TL;DR: A parallel FFT algorithm is described that segments the fast Fourier transform algorithm into groups of identical parallel operations that can be performed concurrently and independently.
Abstract: For many real-time signal processing problems, correlations, convolutions, and Fourier analysis must be performed in special-purpose digital hardware. At relatively high levels of performance, it becomes necessary for this hardware to perform some of its computations in parallel. A parallel FFT algorithm is described that segments the fast Fourier transform algorithm into groups of identical parallel operations that can be performed concurrently and independently. A hardware implementation of the algorithm is described in the context of the parallel element processing ensemble (PEPE) previously described by Githens [7], [8].
19 citations
01 Jan 1972
TL;DR: In this paper, a method is presented for analyzing the effets of quantization of coefficients on the frequency response of any frequency bin of the fast Fourier transform (FFT) algorithm.
Abstract: A method is presented for analyzing the effets of quantization of coefficients on the frequency response of any frequency bin of the fast Fourier transform (FFT) algorithm. Although more detail is easily obtained, we concentrate on predicting the locations and sizes of all spurious sidelobes in the frequency response which are above any specified level. Certain sidelobes are present due to the particular window or weighting function that is being used. Spurious sidelobes or artifacts are extra sidelobes which are introduced if the FFT coefficients are quantized.
17 citations
TL;DR: A third possibility for hardware implementation of the fast Fourier transform of 2m samples is considered, in which in each pass the multipliers are generated from the values of the multiplier coefficient used in the previous pass.
Abstract: One possible hardware implementation for the fast Fourier transform (FFT) of 2m samples is to have 2m-1 cells, each of which performs two of the necessary computations during each of the m passes through the processor. But in each of these m passes, each of the 2m-1cells may require a different multiplier coefficient for its computations. The two most obvious solutions are costly. The multipliers could be stored in a central memory and sent to each cell when needed; however, it takes time to transmit them and uses many pins, or interconnections between cells. Alternatively, the multipliers could be stored in a ROM in each cell. This makes each cell bigger, and the cells are no longer identical copies of one another. We consider a third possibility in this note. In each pass the multipliers are generated from the values of the multipliers used in the previous pass. This technique requires no increase in the number of pins per cell and little increase in the time required to perform the Fourier transformation.
14 citations
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TL;DR: The possibly unexpected conclusion is made that the FFT implementation using parallel arithmetic units is more efficient in terms of speed and probably design effort and hardware, than one using high radix algorithms.
Abstract: An FFT algorithm is presented that can be implemented with serial-access memory. For clarity and insight the emphasis is upon conciseness and illustration rather than shorthand mathematical notation. The algorithm's potential for high-speed implementation is demonstrated by studying variations on the basic algorithm that include both higher radix algorithms and parallel arithmetic unit algorithms. The fact that these sophisticated variations can be seen and understood by inspection of the basic algorithm emphasizes its simplicity. The algorithm is shown very suitable for efficient special-purpose implementation by the functional independence of the transform node from the particular node in the transform or the number of nodes in the transform, i.e., one node in canonical form (for a given radix) represents the entire FFT algorithm. The algorithm is shown to perform variable length transforms at full operational efficiency with minor modification, thus emphasizing its relative versatility. The possibly unexpected conclusion is made that the FFT implementation using parallel arithmetic units is more efficient in terms of speed and probably design effort and hardware, than one using high radix algorithms.
10 citations