Performance evaluation of the deconvolution techniques used in analyzing multicomponent transient signals

Deconvolution is an important preprocessing procedure often needed in the spectral analysis of transient exponentially decaying signals. Three deconvolution techniques are studied and applied to the problem of estimating the parameters of multiexponential signals observed in noise. Both the conventional and optimal compensated inverse filtering approaches produce data which are further analyzed by SVD-based autoregressive moving average (ARMA) modeling techniques. The third procedure is based on homomorphic filtering and it is implemented by the fast Fourier transform (FFT) technique. A comparative study of the performance of the above deconvolution techniques in analyzing multicomponent exponential signals with varied signal-to-noise ratio (SNR) is examined. The results of simulation studies show that the homomorphic deconvolution technique is most computationally efficient, however, it produces inaccurate estimates of signal parameters even at high SNR, especially with closely related exponents. Simulation results show that the optimal compensation deconvolution technique is indeed a generalized form of the conventional inverse filtering and has the potential of producing accurate estimates of signal parameters from a substantial wide range of SNR data.