Linear Phase vs. Minimum Phase EQ

Linear Phase EQ

I have been doing a lot of study about linear-phase versus minimum-phase equalization. I wanted to really understand the differences and possible advantages/disadvantages one may have over the other in particular situations. I found that I was not alone in my search. However, there is very little actual documentation on linear-phase filters and how a linear-phase relationship is structured or relates to audio processing.

There are some very basic questions that should be answered that almost seem hidden from any product descriptions or message boards.

  • “What is the reason for linear-phase EQ?
  • “What is linear phase, and how does it relate to a minimum-phase EQ?
  • “Why are linear-phase EQs so directed toward mastering?”
  • “Can there be a hardware linear-phase EQ? Why or why not?”

One of the most popular searches relating to linear-phase EQ on Google is “linear-phase explained,” which still holds very poor results. After the search, I was still grasping at straws. I said “to hell with it,” and held my own experimentation.

I created a new Pro Tools session with an oscillator at 1 kHz and line level running separately through a minimum-phase EQ plug-in and a linear-phase EQ plug-in. I recorded the results and was astounded by the differences when I boosted or cut frequencies at any bandwidth or frequency.

The linear-phase equalizers and minimum-phase equalizers will produce different results despite the same sound source every time. Here’s what I found:

Analog EQ

With any analog equalizer, the bands being boosted or cut are subject to phase-shifts due to the latency created by the change in amplitude within that band in relation to unaffected bands. This is unavoidable, but manufacturers try to reduce the amount of phase-shift as much as possible (unless it produces a pleasing or characteristic sound), thereby calling these sets of equalizers ‘minimum-phase.’

Digital EQ

Most digital equalizers have algorithms that are modeled after minimum-phase equalizers, due to their prominence in the analog world, their lack of plug-in latency issues, and in the big market for analog replication. These algorithms are digital, so obviously different from the get-go, but are meant to mirror the process of the analog latency and wide bands, and then its subsequent recovery, thus keeping with the minimum-phase concept.

Linear Phase EQ

The way that the equalizer algorithms are configured are completely different for linear-phase equalizers.

Linear-phase is exactly how it’s described: linear. For the varying wavelengths of varying frequencies, linear-phase equalizers adjust phase accurately to the degree of zero phase-shift. This can only be achieved digitally with such accuracy. This non-existent phase shift, leaves the actual amplitude of the waveform almost unchanged in many instances where a minimum-phase equalizer may cause drastic amplitude changes (depending upon the degree of phase shift).

This outcome allows linear-phase equalizers to affect the harmonic character without much change in overall level, making them ideal for mastering practices (which is why they tend to be marketed toward mastering engineers).

Here is a video I made comparing linear phase EQ to minimum phase EQ:

Chime in with your own thoughts on linear phase EQ in the comments below.

Sam O'Sullivan

Sam O'Sullivan

Samuel O'Sullivan has been playing various instruments and composing within the bounds and mixtures of multiple genres for more than 10 years. Samuel, first established as a drummer/percussionist, has made his mark as a guitarist, vocalist, pianist, violinist, composer, and recording engineer. In addition to producing albums for various bands, Samuel produces his own music under the name 'A Mess of a Mind'.
  • Ciaran

    Nice Post …. always wondered about this

  • http://www.inaudible.org.uk inaudible

    That was really helpful.

    nice one

  • http://www.lsbaudio.com Chris Santoro

    There’s actually a lot of literature out there on linear and minimum phase systems, you just have to know where to look. A signal processing textbook would be a good place to start, but I can understand if that’s not up everyone’s alley.

    A good way to think about it is this: a linear phase eq has a constant time delay (latency), independent of frequency. If the latency of the EQ is T ms, then a 40Hz tone will be delayed by T ms just the same as a 1kHz tone. It’s called linear phase because the phase shift (delay) is a linear function of frequency.

    In contrast, an EQ with non-linear phase will introduce delay that is frequency dependent. A 40Hz tone might be delayed by one amount while a 1kHz tone will be delayed by some other amount, depending on the response of the EQ.

    The big take away is that a linear phase eq preserves the phase relationships between all frequencies, because it delays them all by the same amount, so you won’t have phasing issues (radical changes in the waveform shape and sound). You might encounter these phasing issues when mixing a non-linear phase EQ’d signal back in with a dry/unprocessed signal.

    So why would you ever use a filter that’s not linear phase? Well, for one, linear phase filters tend to have higher overall latency and much higher computational cost than minimum phase filters. Secondly, depending on what type of content you’re trying to filter and how steep you want your filter to be, the phasing issues may not actually be an issue.

    • http://www.deluxemastering.com.au Adam Dempsey

      Minimum-phase EQ (as opposed to linear phase) tends to be best for correcting for minimum phase issues (ie most of them).
      One of the best sounding analogue EQ’s I’ve ever used sounds so “musical” largely due to its broad Q & phase shift.

    • http://www.facebook.com/danny.blume.92 Danny Blume

      Thanks for the excellent explanation. I’ve been using linear EQ a lot lately to good effect, just didn’t fully understand what it was!

  • matucha

    Linear phase EQ have pre-ring and post-ring (because of time-symetrical impulse), minimum phase have only post-ring. Post-ring is easily masked and sometimes even beneficial, because it can create something from nothing. Like some kick drums where you can get longer/heavier response from the ring.
    Pre-ring can be hardly detectable or quite unnatural in some cases. IMO the lower you go, the better minimum phase works.

    Sometimes you really want to shift the phase so minimum phase EQ is the right type to use. Sometimes you don’t want to make your instruments asymetrical so using lin-phase hipass works the best. For example some voices get very asymetrical after minimal phase HP filtering and lowshelving.

    Mastering engineers don’t use linear phase EQs as much as you’d think. Minimum phase is more natural in many cases.

  • http://www.jonasr.com Jonas R. Kirkegaard

    Hello, just came across this article and was reminded that I wrote a small school assignment about this a few years ago… In the assignment I put a screenshot of the waveform of an impulse (1 sample at zero dB) going trough TC Electronic’s Dynamic EQ which has a “linear phase” enable option. It can be seen here

    http://www.jonasr.com/pics/Billede%2016.png

    (dont mind the danish nonsense in the middle… Its just a screenshot from an old assignment…)

    The upper waveform is the Dynamic EQ with minimum phase and it only has a post-ring. The lower has the symmetrical linear phase waveform with identical pre- and post ring as stated in the post above…

    Hmm… no point really… Just a picture…

  • Steve Denheyer

    I’m confused – how would a phase shift cause a drop in amplitude?

    • http://arguments.callee.info/ HB

      You probably know this part, but waveforms typically bounce up and down between positive and negative values. So if the shift causes positive values to be aligned with negative values, the sum would be smaller than the original signal if it was positive+positive or negative+negative before the phase shift.

      It’s easier to understand with a picture, but I don’t have one handy… If you’re familiar with phase cancellation caused by microphones recording one source from two different distances, it’s the same idea. Adding does not always mean louder since the signal may be positive or negative at a given point in time.

  • Jean-Francois Guay

    This article (mostly in the video) doesn’t measure or show the difference between linear vs non linear phase filter. This article merely show difference between frequency response of different filter design technique that are not related to the phase linearity, such as elliptic IIR filter (that are non linear) that exhibit oscillation in the pass and stop band compared to other filter design technique such as Butterworth IIR filter (that are also non linear) but have a flat frequency response in the pass and stop band but to the cost of a slower attenuation in the stop band…

  • http://www.masteringmastering.co.uk/onlinemastering.html online mastering studio

    I do not think I have used a linear phase EQ in 3 years. Ever since I exaggerated the transient adjusting effect, it turned me off. I am normally battling to retain punch rather than reduce it. Horses for courses as always though.

  • Garry burke

    IS 63 millisecond difference in time between min/lin CORRECT

  • mastermat

    today I had a very bad experience using a linear phase EQ that I will probably never will use one again: I mastered a track using a linear phse EQ, together with other processing (analog and digital) and after I listened and someting sounded strange….I tested all the analog instances first and then the digital instances….the problem was the linear phase EQ I use, it had a very nasty pre ringing….you could really hear the pre ringing as an actual ringing sound. it was maybe the track, that brought this phenomenon to light, very minimal an stripped down, everything that I did in mastering was very easy to detect…this was my first experience of pre ringing in linear phase EQs but it will keep me away of these types of EQs for the future…

    • Judea

      “ill never use a linear eq again!” is pretty harsh. The problem was the EQ or The Mix or Your Setup, not the fact that it was “Linear” ….just sounds kinda ignorant sorry. Like “Ill never wear ‘sneakers’ again cause i got a huge blister!” …..maybe dont run so hard! lol

    • Bill

      Linear phase is unnatural and produces unnatural pre-ringing.

      If linear phase is better than minimum-phase, are negative phase filters better than linear phase?

  • travelergtoo

    Good article. The comments were as good as the article too.

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  • Bill

    “but manufacturers try to reduce the amount of phase-shift as much as possible”

    Nah. Analog electronic filters are naturally minimum-phase. The term “minimum-phase” is just used in marketing materials to make this sound like something special. See MYTH #2: http://www.rane.com/note115.html