Quantization of the impulse response coefficients due to finite word length causes the moments to deviate from their ideal values. This deviation is found to have a linear variation with the output roundoff noise of the filter realized in direct form. Since the zeros and poles of a given filter also move away from their designed locations due to quantization, we show a relation between the zeros and poles and the moments of the impulse response.

The basic definition of moment is extended to define the blockwise partial moments. It has been shown that for a class of ideal bandlimited signals, the blockwise partial moments remain invariant. But in case of the actual bandlimited signals, the values of these partial moments are not identical. The deviation from the ideal values is applied to make an evaluation of the actual signals. Two concrete application examples are described. The first example describes a method for evaluating the performance of digital interpolation filter. The usual performance measure, SNR, and the newly proposed measure, m, based on moment deviation method are found to be closely related. Moreover, the new method uses only the actual interpolation output compared to the SNR method where apriori knowledge of ideal output is a must. The second example concerns with the recovery of missing samples in a given bandlimited signal sequence. The recovery based on moment method leads to a simple linear equation structure and hence is easy to apply in practice. It is shown that excellent recovery is possible even for the nonideal bandlimited signals.

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.

It is known that the moments of the cepstrum of a mixed phase signal sequence can be calculated without directly calculating the cepstrum, avoiding the phase unwrapping algorithm and the aliasing error etc. Using this, moments of cepstrum of the minimum phase sequence are calculated from the linear phase sequence without actually calculating the minimum phase sequence.

Conventional sensitivity measures in the study of quantization effects in digital filters involve cross terms of zeros and poles and are hard to express the effect of individual poles and zeros. We show a linear relation between the zeros and poles and the moments of the impulse response. We also show an interesting condition for the zeros of FIR low pass filter having linear phase and real coefficients.