6533b7dcfe1ef96bd12728dd

RESEARCH PRODUCT

Periodic Discrete and Discrete-Time Splines

subject

description

Periodic discrete splines with different periods and spans are introduced in Sect. 3.4 of Volume I (Averbuch, Neittaanmaki 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.