Abstract

We describe a new algorithm for mixed-phase deconvolution. It is valid only for pulses whose Z-transform has no zeros on the unit circle. That is, the amplitude spectrum cannot be zero for any frequency. Using the Z-transform of a discrete-time signal, and assuming that the signal has alpha zeros inside the unit circle, the inverse of its minimum-delay component may be estimated by solving the extended Yule-Walker (EYW) system of equations with the lag alpha of the autocorrelation function (ACF) on diagonal of the coefficient matrix. This property of the solution of EYW equations is exploited to derive mixed-phase inverse filters and their corresponding mixed-phase pulses. For different values of alpha , a suite of inverse filters is generated using the same ACF. To choose the best decomposition and its corresponding mixed-phase inverse filter, we have used the value of alpha which gives the maximum value of the LP norm of the filtered signal. The optimal value of alpha does not seem to be very sensitive to the choice of norm as long as p>2. In the numerical examples, we have used p = 5. The mixed-phase deconvolution filter performs better than minimum-phase deconvolution on the synthetic and real data examples shown.

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