The waveform moments are used for analyzing the various types of signal waves. The ordinary moments can't properly express the characteristics of the given signal sequence, because they are calculated with simple summation formulas of the original signal values and the positive and negative values may cancel each other. So we define the power moments which utilize the square of signal in order to prevent the above defect. Moreover, the cross moments which evaluate the product of signals are derived as more generalized definitions. The cross moments can evaluate not only the characteristics of signal power but also the relations between two signals. Further, we extend the cross moments to the blockwise cross moments and the multicross moments, and then derive the corresponding expressions in frequency domain. Finally, we illustrate the usefulness of the cross moments with some application examples.

Waveform moment describes one of the characteristics of the given signal wave. Though basic definitions are quite simple, use of waveform moment and extended waveform moment is shown in numerous areas of DSP. Expressions in both time domain and frequency domain are found and using these, criterion for excluding Nyquist filter possibility, evaluation of frequency characteristics for Elliptic filter, method for determining frequency response for not all points etc. are derived. It is shown that analysis using extended waveform moment method becomes simpler than the direct application of known standard methods.