Spectral root homomorphic deconvolution system

In this paper, we develop a new homomorphic deconvolution system that is useful when the signal to be deconvolved is a convolution of two components one of which is a train of pulses and about the other we have some a priori information on its approximate number of poles and zeros. The system that we develop is essentially the same as the logarithmic homomorphic deconvolution system (1,2,3) except that the logarithmic and exponential operations are replaced with ( )^γand ( )^1/γoperations. By theoretical and/or empirical results, we illustrate that under appropriate conditions, the new system with the proper choice of γ can potentially yield a better result than the logarithmic homomorphic deconvolution system and that the results obtained by the new system with the value of γ close to zero are essentially the same as those obtained by the logarithmic homomorphic deconvolution system.