A new homomorphic deconvolution system

It is shown in this paper that under the assumption that the data sequence x(n) is formed by convoluting a sample white random sequence p(n) with a minimum-phase sequence h(n) the homomorphic system for deconvoluting x(n) can be realized as a simple system in which the linear processing network of the homomorphic system is merely a (-1) multiplier network. This makes the homomorphic system very simple in both design and implementation. Also given in this paper are the experimental results obtained in applying this new method to several test systems. The deconvolved results exhibit good conformity with the original white sample sequence p(n) and the original minimum-phase sequence h(n). The rationale of this deconvolution system also provides an insight relating the homomorphic method to the spectrum estimation method, the latter being practicable only on the same basis that the assumptions mentioned above are being satisfied.