WAVEFORM SIGNAL SHAPING USING WAVELET PARAMETERIZATIONS

Abstract

We explore the idea of matching a scaling function - the basic building block of a wavelet function - to a desired spectrum. This would allow the scaling function to be used as the signal pulse for a digital communication system that is matched to the channel, avoiding problems such as energy loss or noise amplification due to spectral nulls. An unconstrained parameterization of the scaling function coefficients represents the scaling functions. This parameterization is adapted using gradient descent. Tests indicate that the adaptation is able to capture major features of a desired spectrum, including spectral nulls and major lobes.