The most striking advantage of FIR filters is that they can be designed to have exact linear phase. In situations where linearity of phase is not important, it is sometimes preferable to use IIR filters because an IIR filter usually requires a much lower order for the same set of magnitude response specifications. This implies fewer multipliers and adders.
For various reasons, a comparison of IIR and FIR filters is more involved than the above remark appears to imply. First, there exist techniques (which are perhaps less readily available), for the design of nonlinear phase FIR filters. For a given magnitude response specification, such FIR filters are less expensive than the linear phase versions. Second, there are some commercial signal processing chips, specifically tailored for the implementation of FIR filters. In these chips, the implementation of IIR filters is not necessarily more efficient. Finally, there exist multistage design techniques for the design of narrowband FIR filters which are sometimes more efficient than IIR filters. It is, therefore, difficult to provide a comparison that is fair under all contexts. In this text, we will merely compare the number of multiplications and additions. It should be cautioned that in many cases these do not provide a good measure of complexity.
— P.P. Vaidyanathan, “Multirate systems and filter banks” (1993). Page 60.
Again: It is, therefore, difficult to provide a comparison that is fair under all contexts. In this text, we will merely compare the number of multiplications and additions. It should be cautioned that in many cases these do not provide a good measure of complexity.