Deconvolution in the class of non-stationary repetitive signals

A multipath propagation system excited by a repetitive signal is described. The complete medium transfer function is considered as a parallel combination of paths having transfer functions with the same magnitude and shape but different linear phase functions. The total transfer function strongly depends on the phase assumptions and on the scaling of the component paths. Different echo (delay) structure is produced at the output for different path transfer functions. Simulation of this system with repetitive excitation shows that a slight change in the fundamental excitation frequency can cause large changes in the system output. The advantages and disadvantages of homomorphic deconvolution of multipath repetitive signals are discussed, and results of deconvolving real data (vehicle exhaust sounds) are presented