Abstract
In this chapter, we discuss how to derive versatile families of periodic discrete-time orthogonal wavelets and wavelet packets from discrete and discrete-time splines outlined in Chap. 3. These wavelets and wavelet packets, although not having compact supports, are well localized in the time domain. They can have any number of discrete vanishing moments. Their DFT spectra tend to have a rectangular shape when the spline order grows and provide a collection of refined splits of the Nyquist frequency band. The wavelet and wavelet packet transforms are implemented in a fast way using the FFT.
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Averbuch, A.Z., Neittaanmäki, P., Zheludev, V.A. (2019). Periodic Orthogonal Wavelets and Wavelet Packets. In: Spline and Spline Wavelet Methods with Applications to Signal and Image Processing. Springer, Cham. https://doi.org/10.1007/978-3-319-92123-5_4
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DOI: https://doi.org/10.1007/978-3-319-92123-5_4
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