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Algorithms for Discrete Fourier Transform and Convolution pp 132–175Cite as

Linear and Cyclic Convolution

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Part of the book series: Signal Processing and Digital Filtering ((SIGNAL PROCESS))

Abstract

Linear convolution is one of the most frequent computations carried out in digital signal processing (DSP). The standard method for computing a linear convolution is to use the convolution theorem which replaces the computation by FFT of correspondingsize. In the last ten years, theoretically better convolution algorithms have been developed. The Winograd Small Convolution algorithm [1] is the most efficient as measured by the number of multiplications.

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References

  1. Winograd, S. “Some Bilinear Forms Whose Multiplicative Complexity Depends on the Field of Constants”, Math. Syst. Theor. 10(1977):pp. 169–180.

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  2. Agarwal, R. C. and Cooley, J. W. “New Algorithms for Digital Convolution”, IEEE Trans. on ASSP, 25(1977): pp. 392–410.

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  3. Auslander, L., Cooley, J. W. and Silberger, A. J. “Number Stability of Fast Convolution Algorithms for Digital Filtering”, VLSI Signal Proc, IEEE Press, (1984):pp. 172-213.

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  4. Blahut, R. E. Fast Algorithms for Digital Signal Processing, Chapter 3 and 7. Addison-Wesley, 1985.

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  5. Nussbaumer, H. J. Fast Fourier Transform and Convolution Algorithms, Second Edition, Chapter 3 and 6. Springer-Verlag, 1981.

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  6. Burrus, C.S. and Parks, T.W. DFT/FFT and Convolution Algorithms, New York: John Wiley and Sons, 1985.

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  7. Oppenheim, A.V. and Schafer, R.W. Digital Signal Processing, Englewood Cliffs, NJ: Prentice-Hall, 1975.

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Author information

Authors and Affiliations

  1. Center for Large Scale Computing, City University of New York, New York, NY, 10036-8099, USA

    R. Tolimieri, Myoung An & Chao Lu

Authors
  1. R. Tolimieri
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  2. Myoung An
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  3. Chao Lu
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Editor information

Editors and Affiliations

  1. Department of Electrical and Computer Engineering, Rice University, Houston, TX, 77251-1892, USA

    C. S. Burrus (Professor and Chairman) (Professor and Chairman)

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© 1989 Springer Science+Business Media New York

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Tolimieri, R., An, M., Lu, C. (1989). Linear and Cyclic Convolution. In: Burrus, C.S. (eds) Algorithms for Discrete Fourier Transform and Convolution. Signal Processing and Digital Filtering. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-3854-4_6

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  • DOI: https://doi.org/10.1007/978-1-4757-3854-4_6

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4757-3856-8

  • Online ISBN: 978-1-4757-3854-4

  • eBook Packages: Springer Book Archive

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