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Parallel vector processing of multidimensional orthogonal transforms for digital signal processing applications

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Abstract

This paper presents vector and parallel algorithms and implementations of one- and two-dimensional orthogonal transforms. The speed performances are evaluated on Cray X-MP/48 vector computer. The sinusoidal orthogonal transforms are computed using fast real Fourier transform (FFT) kernel. The non-sinusoidal orthogonal transform algorithms are derived by using direct factorizations of transform matrices. Concurrent processing is achieved by using the multitasking capability of Cray X-MP/48 to transform long data vectors and two-dimensional data vectors. The discrete orthogonal transforms discussed in this paper include: Fourier transform (DFT), cosine transform (DCT), sine transform (DST), Hartley transform (DHT), Walsh transform (DWHT) and Hadamard transform (DHDT). The factors affecting the speedup of vector and parallel processing of these transforms are considered. The vectorization techniques are illustrated by an FFT example.

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Authors and Affiliations

  1. Electrical Engineering Department, Bucknell University, 17837, Lewisburg, PA

    Mohamed El-Sharkawy, Wenlong Tsang & Maurice Aburdene

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  1. Mohamed El-Sharkawy
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  2. Wenlong Tsang
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  3. Maurice Aburdene
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Additional information

This work is supported in part by the National Science Foundation, Pittsburgh Supercomputing Center (grant number ECS-880012P) and by the PEW Science Education Program.

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El-Sharkawy, M., Tsang, W. & Aburdene, M. Parallel vector processing of multidimensional orthogonal transforms for digital signal processing applications. Multidim Syst Sign Process 1, 199–216 (1990). https://doi.org/10.1007/BF01816549

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  • DOI: https://doi.org/10.1007/BF01816549

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