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Real factorisation of noncyclic-convolution operators with application to fast convolution

Real factorisation of noncyclic-convolution operators with application to fast convolution

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A real factorisation of discrete noncyclic-convolution operators is established which yields a fast procedure for performing noncyclic convolutions. The transformations associated with the factorisation need only real summations and subtractions for evaluation purposes, unlike the fast Fourier transform but like the fast Walsh transform.

References

    1. 1)
      • Allwright, J.C.: `Real transformation technique for fast (non-cyclic) convolution', Preprints of the symposium on digital filtering at Imperial College, 31st August–2nd September 1971, London.
    2. 2)
      • Pitassi, D.A.: `Fast convolution using Walsh transforms', Proceedings of the conference on applications of Walsh functions, April 1971, Washington.
    3. 3)
      • Rayner, P.J.W.: `A fast cyclic convolution algorithm', Reserve paper for the symposium on digital filtering at Imperial College, 31st August–2nd September 1971, London.
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