Distortion Characterization of Exponential Signal Reconstructed by Low-Chirp Signal

This paper is an extension of the procedure pointed out to evaluate the distortion of the exponential signal, modeled as multiexponential signal with different amplitudes and time constants. This procedure evaluates the distortion by applying the Prony-like method to the signal reconstructed by zero-crossing time evaluated on the difference between the exponential original signal and the reference sinusoidal one. The extension proposed in this paper concerns with the use of the low-chirp signal as reference instead of the sinusoidal signal. The low-chirp signal permits to increase the number of the zero-crossing time in the section of exponential signal with the higher slope and decreasing in the section with the lower slope. This setting permits to estimate the distortion of the exponential signal with higher accuracy and precision. The parameters' amplitude, phase, and start frequency of the reference low-chirp signal are used to reconstruct the exponential signal in the zero-crossing time in order to overcome the problem of the high-resolution sampling. Their estimation is carried out by the time-varying sine-fitting algorithm that processes the resulting signal that is the difference between the exponential original signal and the low-chirp signal. Advantages of the proposed extended procedure regard the direct estimation of the reference low-chirp signal parameters from the resulting signal over-sampled at low resolution, and the use of only one input acquisition channel that permits to overcome the synchronization problem between the reference and the resulting signal. The numerical and experimental tests validate the extended procedure.