Linear Phase EQ Explained

Linear phase EQ is the most transparent sounding type of equalization, however, it can create some very undesirable side effects, namely increased latency and pre-ringing. In this article we'll take an in-depth look at linear phase EQ and provide some valuable tips on how to minimize pre-ringing.

Linear Phase EQ is Transparent

Linear phase EQ is perfectly transparent because, as the name implies, there are no differences in the phase of the audio across the frequency spectrum. Phase changes introduce coloration which is usually not a problem, but if phase coloration is unwelcome in your audio then linear phase EQ will provide the transparency you need.

Linear phase EQ Introduces Latency

Linear phase EQ can introduce noticeable latency which means it is not suitable for scenarios where latency is an issue such as live performances.

Linear Phase EQ Produces Pre-Ringing

The biggest drawback to linear phase EQ is pre-ringing which is highly undesirable in audio. The amount of pre-ringing is governed by the shape of the EQ curve (in fact there is a precise mathematical relationship between the EQ curve and the amount of pre-ringing for linear phase EQ). This means pre-ringing can be controlled by changing the EQ curve. Some plugins attempt to suppress pre-ringing for you, but as a result you're not getting the curve (or phase) you think you are.

In the rest of this article we'll give you some crucial information about the relationship between EQ curves and pre-ringing so you can apply linear phase EQ like a seasoned pro.

What is Pre-Ringing?

Pre-ringing is a backwards echo. It sounds like a strange sucking sound. It is most noticeably heard on transients. Technically speaking the only way to get perfect linear phase is to apply an EQ twice: once forwards in time and once backwards in time. The application of an identical backwards in time EQ cancels out any phase changes. The latency introduced in linear phase EQ is the result of the backwards in time portion of the EQ nullifying the phase.

As a side note, all EQ suffers from post-ringing but our auditory senses don't notice it nearly as much. Linear phase EQ effectively halves the post-ringing and instead provides an equal and opposite amount of pre-ringing.

Typically, the longer the pre-ringing, the more noticeable it is.

Avoiding Pre-Ringing

It is possible to enjoy the transparency of linear phase EQ while avoiding pre-ringing. Once you understand what causes pre-ringing you should have the knowledge to apply linear phase EQ judiciously.

The shape of an EQ curve is entirely responsible for how much pre-ringing you'll get from a perfectly linear phase EQ. Note the word "perfectly" in the last sentence: to suppress pre-ringing, you either need to change the EQ curve, or allow the phase to be non-linear. The general rule is: cutting leads to less audible side effects, whereas if you are boosting then gentler EQ curves (lower Q, gain and order) and higher corner/center frequencies provide less pre-ringing. Let's look at some examples.

Visualizing Pre-Ringing

To see the effects of pre-ringing, we're going to apply different EQ curves to a test signal specially crafted to exaggerate ringing artefacts.

The test signal we're going to use is a 20 millisecond square pulse:

The closest you're likely to get to a square pulse in audio is a transient which explains why transients tend to generate the most ringing (often called transient smearing). Transients only occur for a fraction of the time of our test signal and so produce a much smaller amount of ringing than in our tests.

Linear phase EQ will display equal amounts of pre-ringing and post-ringing. The pre-ringing will show up as a ripple over the left hand side of the square pulse and the post-ringing will show up as a ripple over the right hand side of the square pulse.

Effect of EQ Boosts and Cuts on Pre-Ringing

We'll fix the frequency of a peaking EQ at 400Hz and use a constant Q of 1 to show that boosting produces more noticeable ringing than cutting.

Peaking EQ with a gain of 20dB:

Peaking EQ with a gain of 10dB:

Peaking EQ with a gain of -20dB:

Peaking EQ with a gain of -10dB:

Comparing the above parametric EQ cuts with their equivalent parametric EQ boosts shows that an EQ cut produces ringing of a shorter duration and decreased amplitude than an equivalent boost.

Effect of Frequency on Pre-Ringing

We'll fix the gain of a peaking EQ at 15dB and use a constant Q of 1 to show that lower frequencies produce more noticeable ringing.

Peaking EQ at 100Hz:

Peaking EQ at 500Hz:

Peaking EQ at 2500Hz:

From the diagrams above we can see that the amplitude of the ringing is the same at all frequencies, however, the duration of the ringing is considerably shortened at higher frequencies.

Effect of Q on Pre-Ringing

We'll fix the gain of a peaking EQ at 15dB and use a constant frequency of 200Hz to show that higher Q values produce more noticeable ringing.

Peaking EQ with a Q of 5:

Peaking EQ with a Q of 1:

Peaking EQ with a Q of 0.2:

The relationship between Q and pre-ringing is complex. Increasing Q lengthens the duration of pre-ringing, but reduces the amplitude. The duration of ringing is typically more of a problem but you should audition Q carefully around material rich in transients.

Linear Phase EQ Cheat Sheet

We've only looked at peaking EQ in depth, but here's a full cheat sheet for applying linear phase EQ for all filter types:

Peaking EQ

  • Prefer cutting to boosting.
  • Prefer lower orders.
  • Prefer higher frequencies.
  • Higher Q at higher frequencies is fine.
  • Watch your Q at lower frequencies (avoid high Q values, but audition any changes around transient rich material).

Low Pass

  • Keep Q at 1 (below 1 is acceptable, above 1 is to be avoided).
  • Prefer lower orders.
  • Prefer higher frequencies.

High Pass

  • Q values less than 1 are acceptable (above 1 is to be avoided).
  • Prefer lower orders.
  • Prefer higher frequencies.

Notch

  • Prefer lower orders.
  • Prefer higher frequencies.
  • It's likely you'll be using high Q values. It's worth auditioning against minimum phase EQ as a notch naturally masks its phase changes which are highest in the cut out region.

High/Low Shelf

  • Keep Q at 1 (below 1 is acceptable, above 1 is to be avoided).
  • Prefer lower orders.
  • Prefer higher frequencies.
© 2024 Crave DSP Limited