Orthonormal wavelets with simple closed-form expressions

Abstract

Two classes of orthonormal wavelets that have simple closed-form expressions are derived from pulses with the raised-cosine spectrum. These wavelets, which are bandlimited and polynomial-decaying in time, are found to be particular examples of the Lemarie-Meyer (1992, 1993) wavelets. The derivation reveals interesting connections between wavelet construction and intersymbol interference (ISI)-free signaling for digital communications.