Abstract
This chapter describes wavelet analysis in the spaces of discrete splines whose spans are powers of 2. This wavelet analysis is similar to wavelet analysis in the polynomial-spline spaces. The transforms are based on relations between exponential discrete splines from different resolution scales. Generators of discrete-spline wavelet spaces are described. The discrete-spline wavelet transforms generate wavelet transforms in signal space. Practically, wavelet transforms of signals are implemented by multirate filtering of signals by two-channel filter banks with the downsampling factor 2 (critically sampled filter banks). The filtering implementation is accelerated by switching to the polyphase representation of signals and filters.
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Notes
- 1.
Here \(U_{[m]}^{4r}(\omega ) \) is the characteristic function of the space \({}^{4r}\mathscr {S}_{[m]}\).
References
A.B. Pevnyi, V. Zheludev, On the interpolation by discrete splines with equidistant nodes. J. Approx. Theory 102(2), 286–301 (2000)
A.B. Pevnyi, V. Zheludev, Construction of wavelet analysis in the space of discrete splines using Zak transform. J. Fourier Anal. Appl. 8(1), 59–83 (2002)
W. Sweldens, The lifting scheme: a custom-design construction of biorthogonal wavelets. Appl. Comput. Harmon. Anal. 3(2), 186–200 (1996)
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© 2016 Springer International Publishing Switzerland
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Averbuch, A.Z., Neittaanmäki, P., Zheludev, V.A. (2016). Non-periodic Discrete-Spline Wavelets. In: Spline and Spline Wavelet Methods with Applications to Signal and Image Processing. Springer, Cham. https://doi.org/10.1007/978-3-319-22303-2_10
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DOI: https://doi.org/10.1007/978-3-319-22303-2_10
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