Root moments: a digital signal-processing perspective

The use of cepstral parameters is gaining importance in many areas. However, their introduction is usually through an approach which often mars their simplicity and beauty. The differential cepstrum is an important variant of this class of signal transformations. It has been defined in terms of the logarithmic derivative of the z transform of a given signal. However, a more useful approach is through the Cauchy residue theorem, which yields additional insight and properties. The entire concept and additional properties may be developed in a way that leads naturally to the celebrated Newton identities. These identities are developed and elaborated in the paper. Furthermore, they are employed innovatively in signal-processing problems, including the determination of the minimum phase component of a signal, a stability test for linear systems and the detection of abrupt changes in a signal