Relations between sensitivity of moment and root for FIR filters

The authors propose a method of using the moment of impulse response to evaluate the deviation of frequency characteristic of an finite impulse response (FIR) filter in coefficient quantization. The moment is defined as a weighted summation of impulse responses. The authors develop the moment coefficient sensitivity and discuss how it is related to the zero of FIR filters. Then they propose a new viewpoint which takes the integral of coefficient sensitivity during a period as a measure to evaluate the effect of coefficient quantization and give a simple formula. The benefits of this method are in estimating the peak of deviation of the frequency characteristic and using zeros of the filter only. Furthermore, the measure is used to reconstruct the FIR filter to a two-stage cascade structure with low sensitivity