Strengths and Weaknesses

Because an IIR filter uses both a feed-forward polynomial
zeros as the roots) and a feedback polynomial (poles as the
roots), it has a much sharper transition characteristic for a
given filter order. Like analog filters with poles, an IIR filter
usually has nonlinear phase characteristics. Also, the
feedback loop makes IIR filters difficult to use in adaptive
filter applications.
Due to its all zero structure, the FIR filter has a linear phase
response when the filter’s coefficients are symmetric, as is
the case in most standard filtering applications. A FIR’s
implementation noise characteristics are easy to model,
especially if no intermediate truncation is used. In this
common implementation, the noise floor is at - 6.02 B + 6.02
log2NdB where B is the number of actual bits used in the
filter’s coefficient quantization and N is again the filter order.
This is why most Intersil filter ICs have more coefficient bits
than data bits.
An IIR filter’s poles may be close to or outside the unit circle
in the Z plane. This means an IIR filter may have stability
problems, especially after quantization is applied. An FIR
filter is always stable. FIR filters also allow development of
computationally efficient architectures in decimating or
interpolating applications, which will be described in more
detail later.