Overview of digital filter design

Advantages of fir filters

• Straight forward conceptually and simple to implement
• Can be implemented with fast convolution
• Always stable
• Relatively insensitive to quantization
• Can have linear phase (same time delay of all frequencies)

Advantages of iir filters

• Better for approximating analog systems
• For a given magnitude response specification, IIR filters often require much less computation than an equivalent FIR,particularly for narrow transition bands

Generic filter design procedure

• Choose a desired response, based on application requirements
• Choose a filter class
• Choose a quality measure
• Solve for the filter in class 2 optimizing criterion in 3

Perspective on fir filtering

Most of the time, people do $L^{}$ optimal design, using the Parks-McClellan algorithm . This is probably the second most important technique in "classical"signal processing (after the Cooley-Tukey ( radix-2 ) FFT).

Most of the time, FIR filters are designed to have linear phase. The most important advantage of FIR filters over IIRfilters is that they can have exactly linear phase. There are advanced design techniques for minimum-phase filters,constrained $L^2$ optimal designs, etc. (see chapter 8 of text).However, if only the magnitude of the response is important, IIR filers usually require much fewer operations and aretypically used, so the bulk of FIR filter design work has concentrated on linear phase designs.