ABSTRACT
This chapter discusses some illustrative examples of wavelets. It describes the Shannon wavelet, Meyer wavelet, and spline-based wavelets. Shannon wavelets are also called sinc wavelets. Shannon wavelets are named in honor of C. E. Shannon. Recall that as per Shannon’s sampling theorem a band-limited function can be expanded in terms of sinc functions. Shannon wavelets use sinc functions as scaling functions. Unlike Haar wavelets, sinc wavelets are spread out in time, but are discontinuous in the frequency domain. The Shannon scaling function and wavelets have sharp discontinuities in the frequency domain. Therefore, these functions have poor localization properties in the time domain. Splines are piecewise polynomials, with smooth conjunctions between the pieces.
