ON THE DESIGN OF LOWPASS DIGITAL FIR FILTER COEFFICIENTS

Abstract

In this dissertation, designing of two types of digital FIR filters are studied using three techniques. Firstly, analysis of response-error due to finite precision is considered. Then different types and structures of FIR filters are given. Different approximation criteria used for FIR filter designing are also discussed. In the first technique, equispaced samples of desired frequency response are taken. From these samples of frequency response, the filter coefficients are calculated. In second technique, algorithm is presented to minimize the error in frequency response when finite precision filter coefficients are evaluated by rounding-off the infinitely precision coefficients. At last, maximally flat passband linear phase FIR -filters are considered. In this technique, designing of linear phase FIR digital filter having symmetric impulse response is formulated as a constrained minimization problem. The constraints express the maximal flatness of the frequency response at the origin. The objective function, which is quadratic in filter coefficients, is formed as a convex combination of two objective functions. The two objective functions represent the energy of the error between the frequency response of the designed filter and a scaled version of the frequency response of the ideal filter in both stop and passbands.