Linear and Cyclic Convolution

  • R. Tolimieri
  • Myoung An
  • Chao Lu
Part of the Signal Processing and Digital Filtering book series (SIGNAL PROCESS)


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.


Digital Signal Processing Polynomial Ring Toeplitz Matrix Circulant Matrix Convolution Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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

Copyright information

© Springer Science+Business Media New York 1989

Authors and Affiliations

  • R. Tolimieri
    • 1
  • Myoung An
    • 1
  • Chao Lu
    • 1
  1. 1.Center for Large Scale ComputingCity University of New YorkNew YorkUSA

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