Peer Reviewed Journal via three different mandatory reviewing processes, since 2006, and, from September 2020, a fourth mandatory peer-editing has been added.
Issue of finding a wavelet matched to signal has been addressed by various researchers in past. This paper presents a new method of estimating wavelet that is matched to a given signal in the statistical sense. The key idea lies in the estimation of analysis wavelet filter from a given signal and is similar to a sharpening filter used in image enhancement. The output of analysis wavelet filter branch after decimation is written in terms of filter weights and input signal samples. It is then viewed to be equivalent to difference of middle sample and its smoother estimate from the neighborhood which then needs to be minimized. To achieve this, minimum mean square error (MMSE) criterion is employed using the autocorrelation function of input signal. Since wavelet expansion acts like Karhunen-Loève type expansion for generalized 1/f processes, it is assumed that the given signal is a sample function of an nth order fractional Brownian motion. Its autocorrelation function is used with MMSE criterion to estimate analysis wavelet filter. Next, a method is proposed to design 2-band FIR perfect reconstruction biorthogonal filter bank. This result in compactly supported wavelet matched statistically to given signal. Further, it is shown that compactly supported wavelet with desired support can be designed from a given signal. The theory is supported with number of simulation examples.
