The convolution theorem for the continuous wavelet tranform
Signal Processing
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The purpose of this paper is to develop a new approach-time-frequency deconvolution filter-to optimally reconstruct the nonstationary (or time-varying) signals that are transmitted through a multipath fading and noisy channel. A deconvolution filter based on an ambiguity function (AF) filter bank is proposed to solve this problem via a three-stage filter bank. First, the signal is transformed via an AF analysis filter bank so that the nonstationary (or time-varying) component is removed from each subband of the signal. Then, a Wiener filter bank is developed to remove the effect of channel fading and noise to obtain the optimal estimation of the ambiguity function of the transmitted signal in the time-frequency domain. Finally, the estimated ambiguity function of the transmitted signal in each subband is sent through an AF synthesis filter bank to reconstruct the transmitted signal. In this study, the channel noise may be time-varying or nonstationary. Therefore, the optimal separation problem of multicomponent nonstationary signals is also solved by neglecting the transmission channel