On FIR delta modulation digital filters

The performance of a finite impulse response (FIR) delta modulation digital filter (DMDF) that requires no multiplication operations has been studied in two important aspects. First, an analytical expression for the threshold word length at which the DMDF performance begins to deteriorate rapidly has been obtained explicitly in terms of sampling frequency and input signal level. Second, three approximate formulas for the optimum LDM step size of DMDF in the region where the word length is greater, equal to, or less than the threshold word length, respectively, have been obtained. These analyses have been done assuming a band-limited Gaussian input, and have been verified by computer simulation. A design example of an FIR DMDF is also given.