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.
We usually emphasize the requirement for linear phase, because linear phase is not an attribute of recursive analog filters, and is purchased by the use of additional filters known as phase equalizer filters. We know that linear phase shift, a property equivalent to pure time delay, can never be achieved exactly with lumped linear circuit components but can be achieved with distributed components which form transmission lines that respond with solutions to the wave equation. Analog phase equalizers in the analog domain are used to obtain equiripple approximations to linear phase slope.
The attraction, and an often-cited advantage, of nonrecursive filters is the ease with which they can achieve linear phase shift. To achieve linear phase in a FIR filter, its impulse response must exhibit symmetry with respect to its center point. We thus find that linear phase shift, a difficult attribute to achieve in the analog domain, is essentially free in the sampled data domain. For reasons that escape us, additional discussion of distortion effects seems to stop here as if access to linear phase has solved the problem. This is a bit premature since we still have to address the effect of equiripple deviation from constant amplitude gain as well as the effect of the equiripple deviation from uniform phase shift of the phase equalized recursive filter.
—Fred Harris, “Multirate signal processing for communication systems” (2004). Pages 67–68.