The Complete Guide To Linear Phase Equalization/EQ

Linear phase EQ is a powerful audio effect/process that deserves to be understood by audio professionals and hobbyists alike. This tool can be used to great benefit regardless of how experienced we are with EQ.

In this article, we'll learn all there is to know about linear phase EQ and how it compares to the other types of EQ. We'll consider the pros and cons of linear phase EQ processing and look at various examples to solidify our comprehension.

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A Primer On EQ & Phase

Before getting into linear phase EQ specifically, I think it's important to go over the basics of typical equalization and its relationship to phase in order to set the stage, so to speak, about how powerful linear phase EQ actually is.

Feel free to skip ahead to the section What Is Linear Phase Equalization? by clicking the link.

What is audio equalization? EQ is the process of adjusting the balance between frequencies within an audio signal. This process increases or decreases the relative amplitudes of some frequency bands compared to other bands with filters, boosts and cuts.

Using EQ, we can effectively alter the frequency content of a signal to best suit the mix. We can accentuate important/characteristic frequencies and reduce or even eliminate problem frequencies (noise, interference, resonances, sibilance, etc.).

EQ is used in mixing, tone shaping, crossovers, feedback control and many more applications. It is easily one of the most important audio processes there is.

However, with equalization comes phase shift (generally speaking).

Equalization largely relies on filters to adjust (boost, cut or completely eliminate) frequencies within the audio signal.

Typical audio filters in analog and digital systems will introduce some amount of phase shift to the signal.

With analog circuits, there will be 90º of cumulative maximum phase shift one way or another for every reactive electrical component (generally a capacitor) in the circuit.

The number of reactive components in a simple filter circuit also determines the order of the filter and, therefore, the roll-off/slope of that filter (generally measured in decibels per octave or decibels per decade).

With typical minimum phase EQ plugins, the latency or delay of the frequencies affected by EQ filters causes phase shift.

Many EQ plugins are designed to emulate specific analog minimum phase EQs, which would require phase shift to be part of the programming if the emulation was to be precise.

In this section, we'll consider three different EQ filter types (high-pass, low-pass and band-pass) and how they affect the phase of the processed signal.

High-Pass Filters & Phase Shift

A typical first-order high-pass filter will extend to a positive 90º maximum phase-shift as the filter extends to the stopband. The cutoff frequency will mark the halfway point of the phase-shift (in this case, it'll be +45º). This can be visualized in the following graphs:

If we were to look at a basic first-order analog high-pass filter circuit, we'd see a single reactive component (the capacitor C_HP):

Here is a table relating the order; frequency roll-off rate/slope; maximum phase shift, and cutoff frequency phase shift of high-pass filters:

Order	Roll-Off Rate/Slope	Maximum Phase Shift	Phase Shift At Cutoff Frequency
First Order	6 dB/octave 20 dB/decade	+90º	+45º
Second Order	12 dB/octave 40 dB/decade	+180º	+90º
Third Order	18 dB/octave 60 dB/decade	+270º	+135º
Fourth Order	24 dB/octave 80 dB/decade	+360º	+180º
Fifth Order	30 dB/octave 100 dB/decade	+450º	+225º
Sixth Order	36 dB/octave 120 dB/decade	+540º	+270º

Low-Pass Filters & Phase Shift

A typical first-order low-pass filter will extend to a negative 90º maximum phase-shift as the filter extends to the stopband. The cutoff frequency will mark the halfway point of the phase shift (in this case, it'll be -45º). This can be visualized in the following graphs:

If we were to look at a basic first-order analog low-pass filter circuit, we'd see a single reactive component (the capacitor C_LP):

Here is a table relating the order; frequency roll-off rate/slope; maximum phase shift, and cutoff frequency phase shift of low-pass filters:

Order	Roll-Off Rate/Slope	Maximum Phase Shift	Phase Shift At Cutoff Frequency
First Order	6 dB/octave 20 dB/decade	–90º	–45º
Second Order	12 dB/octave 40 dB/decade	–180º	–90º
Third Order	18 dB/octave 60 dB/decade	–270º	–135º
Fourth Order	24 dB/octave 80 dB/decade	–360º	–180º
Fifth Order	30 dB/octave 100 dB/decade	–450º	–225º
Sixth Order	36 dB/octave 120 dB/decade	–540º	–270º

Band-Pass Filters & Phase Shift

A typical second-order band-pass filter will extend to a positive 90º maximum phase-shift at the low-end stopband and a negative 90º maximum phase-shift at the high-end stopband. The cutoff frequencies will mark the halfway point of the phase shift. This can be visualized in the following graphs:

Below is a basic second-order band-pass filter (essentially a first-order high-pass filter combined with a first-order low-pass filter). Here, we see two reactive electrical components: the capacitor for the high-pass portion (C_HP) and the capacitor for the low-pass portion (C_LP):

Here is a table relating the order; frequency roll-off rate/slope; maximum and minimum phase shift, and the phase shift at the cutoff frequencies of band-pass filters:

Order	Roll-Off Rate/Slope	Maximum Phase Shift	Phase Shift At Low-End Cutoff Frequency	Minimum Phase Shift	Phase Shift At High-End Cutoff Frequency
Second Order	6 dB/octave 20 dB/decade	+90º	+45º	–90º	–45º
Fourth Order	12 dB/octave 40 dB/decade	+180º	+90º	–180º	–90º
Sixth Order	18 dB/octave 60 dB/decade	+270º	+135º	–270º	–135º
Eighth Order	24 dB/octave 80 dB/decade	+360º	+180º	–360º	–180º
Tenth Order	30 dB/octave 100 dB/decade	+450º	+225º	–450º	–225º
Twelfth Order	36 dB/octave 120 dB/decade	+540º	+270º	–540º	–270º

Other EQ Filters & Phase Shift

Let's look at a few more amplitude-frequency and phase-frequency graphs of typical EQ filters to further solidify the fact that typical EQ causes phase shift.

A typical second-order band-stop filter will extend to a negative 90º maximum phase-shift at the low-pass stopband side of the filter and a positive 90º maximum phase-shift at the high-end stopband side of the filter. The cutoff frequencies will mark the halfway point of the phase shift, and the centre frequency will have a full 180º swap. This can be visualized in the following graphs:

Here are a couple of graphs showing the typical frequency response and phase shift of an analog bell/peak filter. Remember that, by increasing the Q, we would narrow the bandwidth and steepen the roll-offs. If we increased the gain (boosting or cutting), we would increase the phase shift. In these examples, the slope is about 12 dB/oct with a Q of about 1.7:

Here are examples of amplitude-frequency and phase-frequency graphs for first-order low shelf boost and low shelf cut filters. The phase shift is at a maximum (negative) at the centre frequency of the low shelf boost and a maximum (positive) at the centre frequency of the low shelf cut. The phase-shift is not quite 90º either way:

Here are examples of amplitude-frequency and phase-frequency graphs for first-order low shelf boost and low shelf cut filters. The phase shift is at a maximum (negative) at the centre frequency of the high shelf boost and a maximum (positive) at the centre frequency of the high shelf cut. The phase-shift is not quite 90º either way:

Many manufacturers try to minimize the effects of phase-shift with “minimum phase” designs. However, as we've discussed, only linear phase EQ does away with all of this phase-shifting completely.

Before we move on, I should note that, in some cases, phase-shifting may produce sonically pleasing effects on the audio. However, in many other cases, it has the opposite effect. Therefore, it's useful to be able to rid of the potential for phase-shift-induced distortion altogether with a linear phase EQ.

I have a video detailing EQ's side effect of phase shifting. Check it out here:

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What Is Linear Phase Equalization?

Linear phase equalization is EQ that does not cause any phase shift in the signal it processes. It can effectively filter out, boost and/or cut frequency bands without causing any difference in phase between the input and output signals.

Since there is no change in the phase of the output versus the input, the phase relationship is said to be linear, hence the name “linear phase EQ”.

Linear phase EQs have been made possible thanks to digital signal processing (DSP). Plugin programming and computer processing power have become powerful enough to do away with the phase shift that comes with altering the amplitude of defined frequency bands.

Therefore, we'll only ever see linear phase EQ software, which means linear phase EQ will typically only be available in plugins.

The filters of linear phase EQ plugins analyze the frequency content of a signal and apply gain (positive or negative) to the appropriate frequencies via FIR (finite impulse response) filters. This effectively eliminates any phase-shifting that arises.

What are finite impulse response filters, you may ask?

As the name suggests, FIR filters are conceptually based on the idea of a filter with an impulse response that has a finite duration.

In signal processing, the impulse response of a dynamic system (like EQs that process audio signal) refers to the output of the system when presented with a short burst of a signal at the input, known as an “impulse”.

In most analog systems, the impulse response time theoretically goes on forever, though the response itself is often relatively brief in reaction to the impulse. An analog filter may achieve an FIR with complex designs, though this is rather cumbersome for EQ designers.

In digital systems, an impulse response time can be more easily designed with a finite duration. Within this defined response time, the impulse response will settle to zero.

FIR filters are preferred over their infinite impulse response (IIR) filter counterparts as they do not require feedback in their designs (which can exacerbate any distortion within the system). They're also always stable and do not behave differently at extreme cutoff frequencies.

FIR filters are also required if linear phase EQ is to be achieved. A linear phase filter can create equal delay (equal response time) across all frequencies and eliminate phase shift with finite impulse response filters.

Due to the processing required of FIR filters, linear phase EQ plugins will be rather CPU intensive. They will cause latency in the signal path as the computer processes the digital information.

To further this issue, the fact that a linear phase EQ will delay all frequencies by the same time to eliminate phase differences causes even more “latency” in the form of actual delay.

To make up for this latency, many linear phase EQs will shift the output signal earlier in time. Though this can drastically reduce the overall delay in the signal path, there is a downside in the “pre-ringing” that happens to the output.

Pre-ringing is where an echo of the signal will precede the intended output signal. This occurrence is particularly noticeable (and mostly undesirable) if the processed signal has strong/sharp transient information. It is less noticeable on “smoother” signals.

So then, linear phase EQ trades the potential of phase-shifting artifacts for the potential of pre-ringing artifacts.

This makes linear phase EQ a great choice for surgical/narrow filtering (like notch filtering) where the slope(s) of the filter(s) are very steep and the resulting phase-shift of a minimum phase EQ would be rather extreme.

However, it also means that linear phase EQ is likely not the best choice for gentler equalization or as the EQ for signals with strong transients.

Linear phase EQs lend themselves incredibly well to parallel processing. Because they don’t introduce any phase-shift, there will be no unnatural phase-cancellation when the dry (no EQ) and processed (with EQ) tracks are mixed back together.

Parallel processing with EQ is an invaluable tool in a mixing engineer's arsenal and can be used in combination with other effects to achieve a wide variety of results.

Remember that linear phase EQ is typically only achievable in plugins, which are limited only by the coding/programming that goes into them. Therefore, most linear phase EQs are designed to be fully parametric (why not go all out when designing the plugin?).

A parametric EQ offers full customization of a set number of EQ filters. Each frequency band/filter may have the choice of filter type, centre/cutoff frequency, Q factor/bandwidth, and relative gain (boost/cut). It is the most flexible and powerful type of EQ.

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Examples Of Linear Phase Equalizers

Before we wrap things up, it’s always a great idea to consider some examples. Let’s look at 2 different linear phase equalizers to help solidify our understanding of this EQ type.

Blue Cat's Liny EQ

The Blue Cat’s Liny EQ is an awesome low-latency linear phase graphic equalizer plugin.

This plugin features 8 bands with fixed centre frequencies at 120, 330, 640, 2.5k, 5k, 10k and 16k Hertz. Each band can offer a wide ±40 dB of cutting or boosting without affecting the phase of the affected frequencies and can be shaped between normal/notch and smooth/sharp characters for up to 4 different shapes.

The dual channels version offers independent settings for the left/right or mid/side channels along with a stereo-linked option.

FabFilter Pro-Q 3

The FabFilter Pro-Q 3 is a powerful equalization plugin that offers everything we could want in an EQ, including dynamic, parametric, stereo, mid-side and, of course, linear phase EQ functionality.

Up to 24 bands can be easily added or removed from the Pro-Q 3 plugin. In addition to the wide variety of filter types (including brickwall), the Pro-Q 3 also offers customization of the order (dB/octave slope), centre or cutoff frequency, gain (±30 dB), and Q factor (0.025 to 40) of each band. Each band can also be set to act upon the left, right, or both stereo channels or on the mid or side channels.

More importantly, in the context of this article is the fact that all of this functionality can be achieved with linear phase. In fact, users can choose between Zero Latency, Natural Phase and Linear Phase modes in this uber-powerful EQ plugin.

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Related Questions

What are the different types of EQ? When it comes to audio equalization, there are several types of EQ to be aware of. They are as follows:

• Graphic EQ
• Parametric EQ
• Semi-Parametric EQ
• Dynamic EQ
• Linear Phase EQ
• Passive EQ
• Shelving EQ
• Stereo EQ
• Mid-Side EQ

What is dynamic EQ? Dynamic EQ is a type of equalization where the EQ of certain frequencies is triggered dynamically as those frequencies surpass a set amplitude threshold in the audio signal. Dynamic EQ, like a compressor, will have threshold, attack and release settings to alter the EQ of a signal dynamically.