Fast digital convolution using p-adic transforms

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Fast digital convolution using p-adic transforms

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© The Institution of Electrical Engineers
Published

A transform, with similar properties to number theoretic transforms, is defined in a finite segmented p-adic field. It is shown that such a transform has a larger dynamic range than the ordinary number-theoretic transform for a given prime p. In addition any rational number may be represented in this field exactly, leading to error-free arithmetic.

Inspec keywords: signal processing; transforms

Other keywords: number theoretic transforms; p-adic transforms; error-free arithmetic; fast digital convolution

Subjects: Signal processing and detection; Integral transforms

References

    1. 1)
      • I.S. Read , T.K. Troung . Complex integer convolution over a direct sum of Galois fields. IEEE Trans. , 657 - 661
    2. 2)
      • R.C. Agarwal , C.S. Burrus . Fast convolutions using format number transforms with applications to digital filtering. IEEE Trans. , 87 - 97
    3. 3)
      • G. Buchmann . (1964) , Introduction to .
    4. 4)
      • K. Mahler . , -adic numbers and their functions.
    5. 5)
      • E.V. Krishnamurthy . Matrix processors using p-adic arithmetic for exact linear computations. IEEE Trans. , 633 - 639
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