Finite impulse response digital filters

The recursive filters of Chapter 5 are very efficient structures for achieving steep-sided filter designs, with low transition bandwidth. However, in many situations, their poor phase response is a severe limitation. Finite impulse response (FIR) filters are nonrecursive, making them unconditionally stable, and further they offer the possibility of achieving a linear phase characteristic. However they will require more stages of delay and multiply than an infinite impulse response (IIR) filter with a similar passband magnitude specification. In this chapter both time and frequency descriptions of FIR transversal filters will be examined. Symmetry conditions, to ensure linear phase response, will be outlined and design techniques for linear phase FIR filters will be presented. Finally, there will be a discussion of the effects of finite precision arithmetic on the filter performance and the major applications for FIR filters will be outlined.