Relations between sensitivity of moment and root in cascade form FIR filters

In practical realizations, because the coefficients and state variables of filters are represented as a fixed word length, discrepancy between the idealized and actual performances of digital filters resulting from coefficient quantization will occur. A concept of moment of impulse response has been proposed as a measure to describe such signals in the time domain. In this paper, the authors discuss the moment and its coefficient sensitivity in FIR filters realized in both direct and cascade second order stages; introduce the concept of root coefficient sensitivity; derive relations of them; and give an example of simulation to illustrate the evaluation method that they proposed