6 - Finite impulse response filter design

Abstract

Linear systems are characterized by their impulse responses, which can either have a finite or an infinite duration. A finite impulse response (FIR), h(n), has its non-zero values extending over a finite time interval and is zero beyond that interval. FIR filters are also known as non-recursive filters. One of the major advantages of FIR filters is the ease with which exact linear phase filters can be designed. A filter with linear phase characteristics will not distort the input signal and is desirable in a number of applications such as digital communications. Design methods for FIR filters are generally linear and efficient. Another important property of FIR filters is that they are guaranteed to be stable. Furthermore, they can be efficiently realized on general and special purpose hardware such as most digital signal processing (DSP) chips have special instructions to facilitate the implementation of an FIR filter. One of the most recent approaches to linear phase FIR filter design makes use of the well known linear programming method. In this case, the desired frequency response is composed of two parts: the upper limit function and the lower limit function.