The homomorphic analytic signal
This paper introduces an alternative form of analytic signal that is formed using homomorphic signal processing techniques. It may be generated for signals that demonstrate redundancy in their pole-zero distributions, such as phase signals and real signals. The analytic signal is formed by manipulating the positions of the signal's nonminimum phase poles and zeros to create a minimum phase signal. A factorization of real signals is presented that demonstrates the properties of the homomorphic analytic signal, and a new definition of instantaneous frequency is developed. Examples are given to verify the theory and comparisons with the linear analytic signal, and instantaneous frequency are made.