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Filters and You: IIR Filters

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Though they're one of the most basic tools available to audio engineers, we don't often think about filters. At best, we may think about whether to use a low-pass or high-shelf filter. There is a lot more to it than that! In this tutorial, we'll look at the different types of analog filters, and how to better choose them in the mixing process. If you don't know the difference between "Butterworth", "elliptical", "ripple"—read on!


The Ideal Filter

In order to understand the different varieties of filters, we first need to know what an ideal filter would look like. What is an ideal filter? One that we cannot achieve!

Typically, when referring to an ideal filter we are actually talking about an ideal low-pass filter since low-pass filters are the building blocks of all other filters. More specifically, our ideal filter has the following properties:

  • It perfectly passes all frequencies below the cutoff frequency.
  • There is no transition band between the pass and stop bands.
  • There is infinite gain reduction at all frequencies above the cutoff frequency.
  • It does not cause any phase shift in the frequency domain.
  • It induces no delay or latency between the original signal and the processed signal. (It works in real time.)

The problem with the ideal filter is that we cannot achieve the above criteria. With real filters, we need to make compromises, which lead us to various approximations of the ideal filter.  Each of these approximations tries to achieve one or more of the above, and in the process sacrifices another.  

Because of these tradeoffs, some approximations are better than others in different situations. They have a different sounds, as well.


IIR Filters

Infinite Impulse Response Filters (IIR) are the classic examples of filters used in the analog domain (and have since been digitized). These filters are referred to as IIR because of the fact that there is always a signal passing through them no matter how small. Why? Because these filters use feedback!

Since there is always at least a little bit of signal going back to the input, you never really run out of signal. Practically speaking there is a null point where the signal does not matter, but it is still technically there.

The following are some of the more well known IIR filters.

1. Butterworth

Various Orders of Butterworth Filters
Various Orders of Butterworth Filters, Wikipedia

Named after Stephen Butterworth, the purpose of this filter (sometimes also called a Linkwitz-Riley filter) is to be maximally flat in the frequency domain. What does this mean? It means that there is no ripple (variations in gain) in either the pass-band, transition-band, or stop-band.

This feature is good for insuring an accurate frequency response of whatever source signal we feed into it. The tradeoff comes in the form of a gentle slope in the transition-band.

Thus, Butterworth filters are poor at attenuating unwanted frequencies. Like all IIR filters, Butterworths also induce a phase shift, but do so in a very slow and smooth way.

Here is a general usage outline for Butterworth filters:

  • They are commonly used in EQ for their gentle characteristics and no ripple. (They're perfect for peak-notch and shelving.)
  • They are useful for slow and smooth low-pass/high-pass effects on the master channel. (Think EDM swells and breaks.)
  • They are not sharp enough to remove narrow unwanted frequencies.

2. Chebyshev

Chebyshev Type 1 Gain and Phase/Group Delay, Wikimedia Commons
Chebyshev Type 1 Gain and Phase/Group Delay, Wikimedia Commons

Derived from Chebyshev polynomials, these filters are more practical in their features. A Type I Chebychev filter induces ripple in the pass-band, while a Type II induces ripple in the stop-band. However unlike the Butterworth, the transition-band is significantly steeper.

This makes Chebyshev better at knocking out problem frequencies with minimal effect on the frequency response. As for phase shift, the shifts induced by a Chebyshev are somewhat irregular, and can lend themselves to a more unique sound.

Here is a general usage outline for Chebyshev:

  • They're useful for EQs that might need a little more character.
  • They're good at knocking out problem frequencies without killing the character of the original source.
  • Ripple could present problems on some sources, depending on cutoff frequency.

Elliptical

Frequency Response of a Elliptical Filter, Wikipedia
Frequency Response of a Elliptical Filter, Wikipedia

If the Chebyshev is a good all-round filter, then the Elliptical is the king of stopping. At the cost of ripple in both the stop and pass bands, an Elliptical offers a very steep transition band.

This makes Elliptical filters great for brick-wall style filters or super surgical removal of specific frequencies. The phase shift is also going to be colorful with Elliptical filters since the emphasis was on having the sharpest transition possible.

Here is a general usage outline for Elliptical:

  • They're useful for stopping frequencies at a very specific point.
  • They're excellent for getting rid of pure tones that may have made their way into a mix.
  • Lots of ripple and phase shift make it a highly colorful filter, which may or may not be desired.

3. Bessel

Bessel Filter Gain and Group Delay, Wikipedia
Bessel Filter Gain and Group Delay, Wikipedia

For the phase-obsessed, the Bessel filter offers the best phase response of any IIR, given its focus on having a near linear phase response. It additionally has the benefit of being maximally flat in the frequency domain, like the Butterworth. They have minimal ringing to boot!

So why not use it for everything? Because it has the worst transition-band of any filter. This makes it very impractical for focusing in on certain frequencies.

Here is a general usage outline for Bessel filters:

  • They're great for tone shaping wide ranges of frequencies.
  • They leave few additional effects on the sound being filtered.
  • They can't hone in on specific ranges.

Conclusion For Now

As you can see, IIR filters come in many shapes and flavors. While there are more esoteric designs, these are generally the only filters you will see in analog hardware. Even with specialized digital filters (more on those next time) the digital versions of IIR are everywhere.

Assuming they were designed by a competent engineer, there is no reason why a cheaper piece of gear or plugin should sound any different than a more expensive one. Simply pick the right filter for the right job and your workflow will get much easier!

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