Analysis of multiexponential transient signals using interpolation-based deconvolution and parametric modeling techniques

Previous work has shown that the deconvolution technique is one of the most effective procedures for analyzing transient exponentially decaying signals. Direct deconvolution approach often leads to poor resolution of the estimated decay rates since the fast Fourier transform (FFT) algorithm is used to analyze the resulting deconvolved data. One of the most promising approaches is based on optimal inverse filtering followed by fitting an autoregressive moving average (ARMA) model to the deconvolved data so that its AR parameters are determined by solving high order Yule-Walker equations (HOYWE) via the singular value decomposition (SVD) algorithm. Many desirable results have been obtained by using this technique for both dean and noisy signals. However, the real-time implementation of this algorithm poses some difficulties since nonlinear transformation is involved in such analysis. One method of overcoming this difficulty is by incorporating the spline interpolation algorithm into the nonlinear preprocessing procedure. The performance of the proposed algorithm in accurately estimating the number of exponential signals and their corresponding exponential constants for both simulated and real data is investigated in this paper. Results of analysis have shown that high-resolution estimates of decay constants are obtained when the proposed algorithm is used to analyze multiexponential signals with varied signal-to-noise (SNR) ratio.