Vectorized mixed radix discrete fourier transform algorithms
Article Abstract:
The formulation and implementation of an algorithm for the full vectorization of the fast Fourier transform (FFT) that effectively utilizes the potential speed of vector processors and handles the problem of hierarchical storage. Techniques are described for: general mixed radix algorithms; the prime factor algorithm (PFA); the multidimensional discrete Fourier transform (DFT); the rectangular transform convolution algorithms; and the Winograd fast Fourier transform algorithm. Extensive programming, timing, and testing of the radix 4 x 2 FFT algorithm was done for the IBM 3090 Vector Facility, yielding good and consistent performance over a very wide range of transform lengths.
Publication Name: Proceedings of the IEEE
Subject: Electronics
ISSN: 0018-9219
Year: 1987
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Synthesis of high-resolution narrow-band Fourier spectra from low-resolution transforms
Article Abstract:
A new technique enables the coefficients of a large, high-resolution fast Fourier transform (FFT) to be exactly and directly synthesized from the coefficients of low-resolution transforms over the same frequency range. Such a technique bypasses the limits on resolution imposed on FFTs by available computer memory. A described example demonstrates that 16 N-point transforms are sufficient to produce cell-to-cell correspondence with a 4N-point transform over the same time interval. The new technique enables continuous doubling of resolution as needed. The development and validation of the transform conversion equations are described.
Publication Name: Proceedings of the IEEE
Subject: Electronics
ISSN: 0018-9219
Year: 1988
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A new approach to recursive fourier transform
Article Abstract:
A class of windows is introduced which yields the computational invariance property of the recursive Fourier transform (RFT). The proposed class offers spectral resolution enhancement without additional cost in computation. There is an additional memory requirement as the FT block length increases. The use of the proposed windows allows a transform to be updated with a number of computations independent of the transform block length. The introduced property of RFT may be extended to recursive power spectrum estimators where the transform is applied to an autocorrelation function instead of a data sequence.
Publication Name: Proceedings of the IEEE
Subject: Electronics
ISSN: 0018-9219
Year: 1987
User Contributions:
Comment about this article or add new information about this topic:
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