Analysis and design of fir delta modulation digital filters

Abstract

An FIR delta modulation digital filter (DMEF) employs a simple linear delta modulation (LDM) as a means for A/D conversion of input signal, and accordingly it requires no multiplication operations. This aspect is an important advantage for cost reduction, hardware simplicity, and reduced size. When a DMDF is realized, its actual performance deviates from the ideal case due to quantization effects which consist of DM quantization of input signal and A/D conversion of coefficients. In this thesis an extensive study on the performance of an FIR DMDF has been done in two aspects that previously have not been investigated. First, an error analysis of DMDF has been done, in which we have focused on two import ant parameters. i.e., LDM step size and word length of filter coefficients. For a band-limited Gaussian input, an expression for the threshold word length at which the performance of DMDF begins to deteriorate rapidly has been obtained explicitly in terms of sampling frequency and input signal level. This result has been verified by computer simulation. From the analysis we have found that the threshold word length decreases by one bit for each doubling of signal level and increases by two or three bits for each doubling of sampling frequency. Second, optimization of DMDF performance has been studied. It has been found that the optimum LDM step size of DMDF shifts as the word length decreases (i.e., as the coefficient quantization effect increases). For a band-limited Gaussian input three approximate formulas for the optimum LDM step size of DMDF in the regions where a word length is greater than, equal to, and less than the threshold word length, respectively, have been obtained, and verified by computer simulation. In addition, computer simulation results for the effect of DMDF bandwidth on performance, variation of frequency response due to quantization effects, and variation of optimum DMDF performance for different values of filter parameters such as word l...