Moulton Laboratories
the art and science of sound
About Comb Filtering, Phase Shift and Polarity Reversal
By Dave Moulton
August 1993
1. Generating a comb filter response

The phenomena of comb filtering, phase shift and polarity reversal are surrounded in myth and are a bedrock topic for audio engineers.

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The View from 2005: Nothing’s changed! We’re still as confused as ever!

About Comb Filtering, Phase Shift and Polarity Reversal

There's a lot of loose language around the recording industry and some of the least understood and most abused of such jargon has to do with "being out of phase" and "comb filtering." Now, these terms represent some really important concepts that are central to recording craft, but the mythology surrounding them is so loaded with misconceptions and misstatements that a careful and thorough understanding of what they actually are and mean is vital to your recording success. So button down your brain cells, campers! We're goin' thinkin'!

We’ll start by considering an audio signal and a single delayed reiteration of it. We’ll treat these as a monaural signal, with the original and delayed components mixed together through the system shown in Figure 1.
  
Electronic equivalent of the flow of a signal and its delayed iteration, recombined into a single signal. In the case we will be looking at, the delay line has a delay of 1 millisecond, the levels of both the original and delayed signals going into the mixer are equal, and the signal is a 1 KHz. sine wave.

The simplest case in audio is a sine wave. Let’s pick one with a frequency smack in the middle of the audio spectrum, say, 1 KHz. And let’s set the delay line to a 1 millisecond delay time. In this case there are a thousand cycles of the wave each second, and we are delaying the sound in time by exactly one-thousandth of a second, so that the sound and its delayed iteration have the following relationship:
  
A sine wave of 1 KHz. frequency (1 ms. period) and its delayed iteration, at 1 ms. delay. The resulting mixed signal will be a 1 KHz. sine wave 6 dB louder.

When you sum or mix these two signals, the result is a 1 KHz. sine wave that is 6 decibels louder than the original sound by itself. Because the phase shift is exactly 360°, which is functionally equivalent to a 0° phase shift, the original signal and the delayed signal overlay exactly and their amplitudes added together result in a doubling of overall amplitude at each point in the waveform (which results in an overall increase in amplitude of 6 dB). Because it results in a signal that is louder than the original, this is called constructive interference. By the same token, if we use the 1 millisecond delay with a signal of 2 KHz. we get the same constructive interference, because now the phase shift is 720°, which is also equivalent to 0°:
  
A sine wave of 2 KHz. frequency (.5 ms. period) and its delayed iteration, at 1 ms. delay. The resulting mixed signal will be a 2 KHz. sine wave 6 dB louder.

However, when we delay a sine wave signal of 500 Hertz by 1 millisecond, the phase shift is only 180°, so we get the infamous “180° phase-shift cancellation.”
  
A sine wave of 500 Hz. frequency (2 ms. period) and its delayed iteration, at 1 ms. delay. The resulting mixed signal will be (in theory) a signal with no amplitude, or a complete cancellation of signal.

One more illustration should fill in the picture and then we can talk about this. If we have a signal of 1500 Hz. (or 2500 Hz., or 3500, or any other frequency some multiple of 1000 Hz. above 500 Hz.), we will also get a complete cancellation.
  
A sine wave of 1500 Hz. frequency (.67 ms. period) and its delayed iteration, at 1 ms. delay. The resulting mixed signal will be (in theory) a signal with no amplitude, or a complete cancellation of signal.

Several things should be apparent.

First, the amount of phase shift varies for a given delay time as a function of frequency, so that lower frequencies have less phase shift, higher frequencies have more phase shift, and each frequency has a unique amount of phase shift. One quirky part of this is that for any repeating wave shape, 360° of phase shift is the functionally the same as 0° of phase shift, so we usually don't worry about the multiples of 360°, just the number of degrees between 0 and 360.
  
The phase shift for any frequency with a delay of 1 millisecond. The diagonal line represents the increasing phase shift as a function of frequency. Note that we can think of 540° as being effectively the same as 180°.

Second, all whole number multiples of the frequency whose period is the same as the delay time (1 KHz. in this case, so we are talking about 2 KHz., 3 KHz., 4 KHz., etc.) will have delayed iterations that will be “in phase” with the original.

Third, the frequency whose period is twice as long as the delay time (500 Hz. in this case) will have a delayed iteration that will be “out of phase” with the original. All frequencies that are above that frequency by the amount of the original frequency (as noted above) will also be “out of phase” with their original signals.

Boiled down, this means that the broad-band frequency response of the mixed result of a signal and its delayed version will be extremely lumpy, with 6 dB boosts interspersed with total cancellations (also called “nulls”) at frequencies across the spectrum that are related to the period of the delay time. For the example we have been using, the response curve will look like this:
  
Frequency response curve resulting from the mix of a signal at 0 dB and a 1 ms. delayed iteration of that signal at 0 dB. Peaks will be at +6 dB and nulls will be <-100 dB. The graph is drawn with a linear horizontal axis for frequency, as opposed to the more conventional logarithmic or octave-based scale.

This frequency response curve is the famous “comb-filter” response. Obviously, it is dramatically different from the response of the original signal, which is represented by the dotted line at 0 dB. It is very audible(!) and, interestingly, has a pretty obvious pitch, which in this case is the pitch of a 1 KHz tone. This pitch will impose itself on whatever material is playing through our little single-delay circuit. When we do effects like phasing and flanging (see my article on Early Delays for more information of this), the whooshing sound is due to the frequency of the comb filter being varied, which in turn is done by varying the delay time.
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COMMENTS

Kansas City, MO     Aug 25, 2006 12:17 AM
So why is it that my turbosound TMS-3 rig calls to invert the polarity of the mid and high drivers? I thought it was because of the phase problems of analog crossovers but when i spoke with them they said that I could achive the same results by wiring my system in phase at all points and placing a 1ms delay on the mids and highs. So now that we all have digital crossovers should everything be wired in phase and not delayed to preserve the phase coherent design of the box or should we use the delays availible in modern crossovers to more acurately time-allign the box OR should it be left alone and wired out of phase and not delayed? I suppose my question is why were they designed to run mid/high out of phase and would that change when switching to a 4 way system.
Ryan Chamberlain 
     Aug 25, 2006 11:13 AM
Your initial assumption is, so far as I know, correct.

The inverting of polarity is intended to reduce destructive interference at the crossover frequencies, while ignoring the compartively minor issues of polarity in the driver's passband.

I wouldn't be so casual about simply applying a 1 ms. delay. However, if you are triamping and have DSP/xovers prior to the amps you can certainly do a nicer job of cleaning up the driver interactions than can be done with passive crossovers. To get it relly good, you are going to need some pretty good measurement instrumentation.

As for the last part of your question, I don't know why they were designed as they were, or what assumptions they are making. Unfortunately, it sounds like they aren't being entirely clear with you.

I hope this helps.

Dave
DaveMoulton 
Budapest, Hungary     Jan 15, 2007 09:13 AM
Hello! I've found in some articles that phase shifting in EQ'ing can really affect the attack of the sound... Having known this, I've got to ask whether it could be a problem when you are setting up your amplifiers at a concert hall or a rehearsal room. I'm a guitarist and I started to wonder the thing I've mentioned before.
There are tips and tricks to avoid that phase shifting effect (using broad Q's for boosting, using only a small amount, and cutting with narrow Q's) in mixing, that I know, but is this useful for a rock band, setting up their amplifiers? (2 guitars, 1 bass)
Andras Toth 
     Feb 08, 2007 03:39 PM
For anyone's interest, a similar article on this topic can be seen over at Whalco Development:

http://www.whalco.ca
Webmaster 
     Jul 13, 2007 04:33 AM
In your tutorial explained polarity change of one of srereo signal and given that to chnge the pola rity if one channel for the solution for this If same frequency components in both channels this is ok But if same frequency component not totally in both channel this solution some time give wrong solutions. But phase correlation meter indicate phase out please give explaination about this also from your tutorial
Asoka 
Groton, MA     Jul 17, 2007 01:33 PM
I'm not sure I completely understand your comment/question. Any "difference" components in a stereo signal will NOT be cancelled when polarity is inverted for one channel and the signals are summed to mono, while all the identical components will be cancelled. See my pieces on A+B/A-B listening and analysis techniques.

The phase correlation meter simply indicates the relative amplitude of the "sum" and "difference" components (the in-polarity vs. out-of-polarity parts) of a stereo signal. It's a simplified view of what is going on in a stereo signal that has some limited usefulness.

I hope this helps.

Best,

Dave
Dave Moulton 
     Sep 22, 2010 03:18 PM
Dear Dave,

FYI at the following link:  http://www.ultrabitplatinum.com/?page_id=725   .  If you find that interesting, I can send you a text only version sans commercial references.  You may also find my think piece about polarity at http://www.ultrabitplatinum.com/?page_id=88 interesting as well, or not. 

If you'd help me sort out the mistakes, when and if they're corrected, you just might become an instant overnight music-lovers' folk hero. Or on the other hand be tarred and feathered and have your ears cut off and served up to you on a silver platter for your last meal as an audiophile guru.  I invite you to visit so that I can take you out for a meal on me and then we can share some of your music and mine on my custom built (by me) audio system on a CD player with a digital domain remote controlled polarity switch.  My system is the best I've heard so far for discerning polarity which still must be done by ear. Those who hear CDs played over my system don't usually have much trouble hearing polarity.  But whatever happens it will be just between the two of us, if that's what you prefer. It'll be attorney client privilege, or Perfect Polarity Pundit privilege, you decide.

Besides email may also call me 7 days a week at 619-401-9876 or toll free at 888-588-9542 between 9AM and 11:45PM Pacific Time.

Best regards.

George S. Louis, Esq., CEO
Digital Systems & Solutions
Email: gslouis@gslouis.com
Website: www.UltraBitPlatinum.com
Phone: 619-401-9876
1573 Kimberly Woods Drive
El Cajon, CA 92020-7261

P.S. How difficult would it be for companies' voice menus instead of saying "Please listen to the entire announcement because our menu has changed recently before making your selection" to "Our announcement was last changed on such and such date?
georgelouis 
France     May 30, 2013 03:38 PM
This is great ! I've been looking for this for ages.
Thx again for the explanation.
capillotraktor 

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