Because designing digital filters involves making compromises to emphasize characteristics you want over characteristics you do not want, comparing FIR and IIR filters can help guide you in selecting the appropriate filter design for a particular application.
IIR filters can achieve the same level of attenuation as FIR filters but with far fewer coefficients. Therefore, an IIR filter can provide a significantly faster and more efficient filtering operation than an FIR filter.
You can design FIR filters to provide a linear-phase response. IIR filters provide a nonlinear-phase response. Use FIR filters for applications that require linear-phase responses. Use IIR filters for applications that do not require phase information, such as signal monitoring applications.
One difference between FIR and IIR filters is the impulse response, which is finite or infinite, respectively. When you design a filter, you must consider other differences between FIR and IIR filters that might affect the design. For example, FIR filter implementations typically require more multiplications and summations than IIR filters with similar filtering performance. However, because certain computer architectures, for example digital signal processors (DSPs), are frequently better suited to performing FIR filtering, the computation speed of an IIR filter is not necessarily faster than an FIR filter. The following table compares the attributes of causal FIR and IIR filters.
| Attribute | FIR Filter | IIR Filter |
|---|---|---|
| Exact linear phase response | Possible | Not possible |
| Stability | Always stable | Conditionally stable |
| Computational complexity | More computations | Fewer computations |
| Data path precision typically required | Less precision required | Greater precision required |
| Zero-input limit cycles1 | Cannot produce limit cycles | Might produce limit cycles |
| 1 "Zero-input limit cycle behavior refers to the effect that the output may continue to oscillate indefinitely with a periodic pattern while the input remains equal to zero. And it is a consequence either of the nonlinear quantizers in the feedback loop of IIR filter or of overflow of additions." (Oppenheim and Schafer) | ||