Tech Focus

Inside Audio Filtering Part 1: Fundamental FIR Filter Concepts & Applications In Loudspeakers

What is FIR filtering and how does it compare to ubiquitous IIR filtering? This article aims to answer these questions.

FIR Vs IIR Filters

So how do IIR and FIR filters compare? Let’s take a look at some common filter types. Figure 12 shows the frequency responses of 1st order Butterworth IIR LP and HP filters along with FIR filters of various lengths that are designed to approximate the IIR filters. (The FIR design method used involves sampling the IIR filter impulse response and applying DC correction.)

Figure 12

Here the FIR filters need to be ~40 taps or longer to begin to accurately approximate the IIR filters. The 10, 20 and 30 tap FIR filters have significant ripple and deviate from the IIR, in magnitude, by up to ~6 dB.

Figure 13 offers a view of the frequency response of a 1 kHz parametric IIR filter along with FIR filters of various lengths that are designed to approximate the IIR filter. Each plot shows a different FIR design method.

Figure 13

The first method has more error toward DC but a slightly better match near 1 kHz. The second method matches the IIR better above and below 1 kHz but has a slightly worse match around 1 kHz. Using either method, the FIR filter needs to be ~40 taps or longer to begin to accurately approximate the IIR parametric filter.

FIR Filter Length

Because FIR filters don’t have feedback, their ability to affect low frequencies is directly proportional to their length. The longer the filter, the lower the frequencies that can be adjusted; either in magnitude, phase or both. Higher Q adjustments – sharper magnitude and phase transitions – also require longer FIR filters.

Figures 14 and 15 provide examples of 384 and 3072 tap FIR filters; the filter responses are the dark blue and dark red lines. Both FIR filters are attempting to match the desired EQ for a loudspeaker – the light blue and light red lines. The difference plots show the difference in magnitude and phase between the desired ideal filter frequency response and the frequency responses of the FIR filters.

Figure 14
Figure 15

Note:

• The longer the filter, the more effective FIR filtering is at achieving EQ, particularly toward low frequencies.

• Even the 3072 tap FIR filter can’t achieve the high-Q magnitude change desired at ~65 Hz. (It actually takes more than 10,000 taps at 48 kHz for the FIR filter to match the desired EQ.)

In my next article, we’ll look at computational complexity relative to IIR filtering and key FIR filter benefits, including independent control of magnitude and phase.

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