Analytical Insights Into Parameter Estimation for Wiener Deconvolution

All real-time signals observed from various measurement systems require signal-processing techniques like the deconvolution, to compensate for the effect of transfer function of the systems. Wiener deconvolution is a widely used signal-processing technique for signal restoration. Often, if the power spectral density of signal and noise is unknown, the accuracy of the restored signal depends on an unknown filter parameter. In the literature, time-consuming, iterative, computational methods were reported to estimate the parameter. However, many of these methods give a range of optimum values instead of an unique value and often lead to either over-smoothing or under-smoothing. In this paper, novel analytical expressions are presented through which the unknown parameter can be estimated explicitly. The analytical results of this study are compared with the numerical methods, and they are found to be accurate and robust against numerical evaluation. Further, the results are demonstrated for signals obtained experimentally from the pulsed electroacoustic system and a network, in authors' laboratory.