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 for 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 (LHDS) [1]-[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 LHDS and that the results obtained by the new system with the value of γ close to 0 are essentially the same as those obtained by the LHDS. As a potential area of practical application, a new speech analysis/ synthesis system is developed based on the new homomorphic deconvolution system discussed in this paper. Some preliminary results on the performance of such a system are also discussed.