Abstract
Periodic discrete splines with different periods and spans are introduced in Sect. 3.4 of Volume I (Averbuch, Neittaanmäki and Zheludev, Spline and Spline Wavelet Methods with Applications to Signal and Image Processing, Springer, Berlin, 2014) [2]. In this chapter, we regard periodic discrete splines as a base for the design of periodic discrete-time wavelets, wavelet packets and wavelet frames. Therefore, only the discrete splines whose spans are 2 are outlined. These discrete splines are linear combinations of the discrete B-splines. So also, the so-called discrete-time splines are discussed in the chapter that are linear combinations of the discrete-time B-splines. The discrete-time B-splines are defined by the polynomial B-splines sampling. Utilization of the Fast Fourier transform (FFT) provides a fast explicit way to implement all the computations.
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Averbuch, A.Z., Neittaanmäki, P., Zheludev, V.A. (2019). Periodic Discrete and Discrete-Time Splines. 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_3
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DOI: https://doi.org/10.1007/978-3-319-92123-5_3
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