Section 6.9.  A BRIEF COMPARISON OF IIR AND FIR FILTERS

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6.9. A BRIEF COMPARISON OF IIR AND FIR FILTERS

The question naturally arises as to which filter type, IIR or FIR, is best suited for a given digital filtering application. That's not an easy question to answer, but we can point out a few factors that should be kept in mind. First, we can assume that the differences in the ease of design between the two filter types are unimportant. There are usually more important performance and implementation properties to consider than design difficulty when choosing between an IIR and an FIR filter. One design consideration that may be significant is the IIR filter's ability to simulate a predefined prototype analog filter. FIR filters do not have this design flexibility.

Table 6-1. IIR and Nonrecursive FIR Filter Characteristics Comparison

Characteristic

IIR

FIR (nonrecursive)

Number of necessary multiplications

Least

Most

Sensitivity to filter coefficient quantization

Can be high.[*] (24-bit coefficients needed for high fidelity audio)

Very low (16-bit coefficients satisfy most FIR filter requirements)

Probability of overflow errors

Can be high[*]

Very low

Stability

Must be designed in

Guaranteed

Linear phase

No

Guaranteed [**]

Can simulate prototype analog filters

Yes

No

Required coefficient memory

Least

Most

Hardware filter control complexity

Moderate

Simple

Availability of design software

Good

Very good

Ease of design, or complexity of design software

Moderately complicated

Simple

Difficulty of quantization noise analysis

Most complicated

Least complicated

Supports adaptive filtering

Yes

Yes




[*] These problems can be minimized though cascade or parallel implementations.

[**] Guaranteed so long as the FIR coefficients are symmetrical.

From a hardware standpoint, with so many fundamental differences between IIR and FIR filters, our choice must to be based on those filter characteristics that are most and least important to us. For example, if we needed a filter with exactly linear phase, then an FIR filter is the only way to go. If on the other hand, if our design required a filter to accept very high data rates and slight phase nonlinearity is tolerable, we might lean toward IIR filters with their reduced number of necessary multipliers per output sample.

One caveat though: just because an FIR filter has, say, three times the number of multiplies per output sample relative an IIR filter does not mean the IIR filter will execute faster on a programmable DSP chip. Typical DSP chips have a zero-overhead looping capability whose parallelism speeds the execution of multiply and accumulate (MAC) routines, with which FIR filtering is included. The code for IIR filtering has more data/coefficient pointer bookkeeping to accommodate than FIR filter code. So, if you're choosing between an IIR filter requiring K multiplies per output sample and an FIR filter needing 2K (or 3K) multiplies per output sample, code both filters and measure their execution speeds.

Table 6-1 presents a brief comparison between IIR and FIR filters based on several performance and implementation properties.

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