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The discrete W transform. (English) Zbl 0567.65096
Four different versions of the discrete W-transform (DWT) are introduced. The DWT procedure is useful for analyzing integer and fractional harmonics. The version of the DWT is chosen depending on the symmetry of the data sequence in the spatial domain and in the frequency domain. The DWT is decomposed into the discrete cosine transform (DCT) and the discrete sine transform (DST). Eight versions of both DCT and DST are associated with the four versions of the DWT. The relation among different versions of the DWT and that between them and discrete Fourier transform are discussed. Periodic and non-periodic convolutions and cross correlations are given.
Reviewer: Y.Kobayashi

MSC:
65T40 Numerical methods for trigonometric approximation and interpolation
65R10 Numerical methods for integral transforms
42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
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