New Deconvoluation Method for a Time Series Using the Discrete Wavelet Transform

Abstract

In this paper, we present a new deconvolution method for digital signals, which is distorted by the characteristics of the transfer system. First we show how to decompose the transfer system into subsystems using the discrete wavelet transform, and show that the unstable behavior of the inversion of the narrow bandpass system can be mitigated by removing subsystems which correspond to the stopband. Then we derive the regularized inverse system that estimates the wavelet coefficients of the input data series. Since the sampling interval of the wavelet coefficients are 2^j-times longer than that of the original signals, the proposed method can reduce the computational cost significantly.