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

Abstract

In this paper, we present a new deconvolution method for a time series, 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 effects of ill-posedness due to the narrow bandwidth of the 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 rate of the wavelet coefficients is coarser than that of the original signal, the proposed method can reduce the calculation cost extremely.