Moulton Laboratories

the art and science of sound

About Comb Filtering, Phase Shift and Polarity Reversal

August 1993

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

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.

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:

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°:

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.”

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.

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.

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:

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.
# COMMENTS

#
Post a Comment

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

Third, the frequency whose period is

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 “

NEXT> "Polarity" and "Phase"

SIMILAR ARTICLES

Kansas City, MO Aug 25, 2006 12:17 AM

Aug 25, 2006 11:13 AM

Budapest, Hungary Jan 15, 2007 09:13 AM

Feb 08, 2007 03:39 PM

Jul 13, 2007 04:33 AM

Groton, MA Jul 17, 2007 01:33 PM

Sep 22, 2010 03:18 PM

France May 30, 2013 03:38 PM

Acoustics |
ASA Papers |
Composition |
Copyright |
Digital Audio |
Equipment |
Education |
Hearing |
Humor |
Loudspeakers |
Measurement |
Microphones |
Mixing |
Producing |
Recording Industry |
Software |
Studio Design |
Frequency Range

©1988 - ©2014 David Moulton, All Rights Reserved. Privacy Policy