A real-time Spline/Wavelet Signal Analyzer

Abstract

Splines and Spline-Wavelets of order m differ from any other functions in that they are uniquely determined by their (mlist order derivatives that are staircase waveforms (piecewise constants) of finite length. Through this important observation, we are able to build a general purpose spline/wavelet signal analyzer. A patent application which includes this class of analyzers hais been filed with the U.S. government recently [ 11. Since the mth order 13-spline and splinew,avelet (B-wavelet) have compact supports (i.e., finite duration) andthe B--wavelets are symmetric or antisymmetric depending on m being even or odd [2,3], our signal analyzer is essentially distortion free. An input analog signal is digitized and mapped into a spline: signal space (a subspace of L2 in which signals are represented by spline functions) of specific order and sulfficiently fine grid. This mapping is done by using an FIR filter based on a local cardinal interpolation method developed in [4,5]. Accordingly, the wavelet decomposition and reconstruction algorithms [2,3,6] can be applied in parallel to separate the signal into different filequency bands for different processing purposes. The result is similar to one obtained by the multi-channel filter bank method.