A question of phase

If you’ve paid attention for long enough, you’ve seen heated debate in online forums and letters to the editor in magazines. One side will claim that it has been proven that people can’t hear the effects of phase errors in music, and the other is just as adamant that the opposite is true.

Much of the confusion about phase lies with the fact that there are several facets to this issue. Narrow arguments on the subject can be much like the story of the blind men and the elephant—one believes that the animal is snake-like, while another insists that it’s more like a wall. Both sides may be right, as far as their knowledge allows, but both are equally wrong because they’re hampered by a limited understanding of the subject.

What is phase?

Phase is a frequency dependent time delay. If all frequencies in a sound wave (music, for instance), are delayed by the same amount as they pass through a device, we call that device “phase linear.” A digital delay has this characteristic—it simply delays the sound as a whole, without altering the relationships of frequencies to each other. The human ear is insensitive to this kind of phase change of delay, as long as the delay is constant and we don’t have another signal to reference it to. The audio from a CD-player is always delayed due to processing, for instance, but it has no effect on our listening enjoyment.

Relative phase

Now, even if the phase is linear (simply an overall delay), we can easily detect a phase difference if we have a reference. For instance, you can get closer to one of your stereo speakers than the other; even if you use the stereo balance control to even the relative loudness between speakers, it won’t sound the same as being equidistance between them.

Another obvious case is when we have a direct reference to compare to. When you delay music and mix it with the un-delayed version, for instance, it’s easy to hear the effect; short delays cause frequency-dependent cancellation between the two signals, while longer delays result in an obvious echo.

If you connect one of your stereo speakers up backwards, inverting the signal, you’ll get phase cancellation between many harmonic components simultaneously as they cancel in the air. This is particularly noticeable with mono input and at low frequencies, where the distance between the speakers has less effect.

The general case

Having dispensed with linear phase, let’s look at the more general case of phase as a frequency-dependent delay.

Does it seem likely that we could hear the difference between a music signal and the same signal with altered phase?

First, I should point out that phase error, in the real world, is typically constant and affects a group of frequencies, usually by progressive amounts. By “constant”, I mean that the phase error is not moving around, as in the effect a phase shifter device is designed to produce. By “group of frequencies”, I mean that it’s typically not a signal frequency that’s shifted, or unrelated frequencies; phase shift typically “smears” an area of the music spectrum.

Back to the question: Does it seem likely that we could hear the difference between an audio signal and the same signal with altered phase? The answer is… No… and ultimately Yes.

No: The human ear is insensitive to a constant relative phase change in a static waveform. For instance, you cannot here the difference between a steady sawtooth wave (which contains all harmonic frequencies) and a waveform that contains the same harmonic content but with the phase of the harmonics delayed by various (but constant) amounts. The second waveform would not look like a sawtooth on an oscilloscope, but you would not be able to hear the difference. And this is true no matter how ridiculous you get with the phase shifting.

Yes: Dynamically changing waveforms are a different matter. In particular, it’s not only reasonable, but easy to demonstrate (at least under artificially produced conditions) that musical transients (pluck, ding, tap) can be severely damaged by phase shift. Many frequencies of short duration combine to produce a transient, and phase shift smears their time relationship, turning a “tock!” into a “thwock!”.

Because music is a dynamic waveform, the answer has to be “yes”—phase shift can indeed affect the sound. The second part is “how much?” Certainly, that is a tougher question. It depends on the degree or phase error, the area of the spectrum it occupies, and the music itself. Clearly we can tolerate phase shift to a degree. All forms of analog equalization—such as on mixing consoles—impart significant phase shift. It’s probably wise, though, to minimize phase shift where we can.

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5 Responses to A question of phase

  1. This article is a worthwhile read. Chamberlin’s “Musical Applications of Microprocessors” gave a similar point of view but I initially got from the text that phase doesn’t matter very much. He mentions that in the case of additive synthesis, morphing from one set of harmonics to another can be done with a weighted average of the two waveforms at each sample as long as the phases are the same. From this it would seem like a good idea to always use zero phase for additive synthesis. And if you cannot hear the difference, then why not ignore or use zero phase for all synthesis?

    But when I tried zero (instead of random) phase with PadSynth there was an audible whack with each repetition of the array of samples. Of course this amplitude beat shows up in a graph of sin(t) + sin(t*2) + sin(t*3) + …, which is something I had not considered. sin(t + r1) + sin(t*2 + r2) + sin(t*3 + r3) + … with random phases smooths out the amplitude over the several-second loop.

    • Nigel Redmon says:

      Thanks for the comment and ideas! BTW, one place that static phase differences can make a difference is when using non-linear processing. The most obvious is that the relative phase of harmonics can affect the peak amplitude—so that you might have clipping in one case but not another, despite having the sample amplitudes of individual harmonics for both cases.

  2. martin says:

    I have a phase control on an Alpine car eq. Is it best to have it set to zero?

    • Nigel Redmon says:

      In a sound system, a phase switch is usually there to compensate for a wiring error, or for an amp (say, for a subwoofer) that inverts the phase relative to the other amps. So yes, usually, you’ll leave the switch at “normal”. If you switch it, expect the sound to be less “full”, due to the phase cancellation. It should be very easy to tell if your phase switch is in the correct position.

  3. Simon Hawkins says:

    The audible effect you have described above, where random phasing smoothes out the amplitude, is due to the behaviour of the digital filter in the DAC or possibly in the software that you are using. The interpolation algorithm, however it is implemented, will perform differently (and I would expect ‘better’) if the wave forms are out of phase, because it can obtain more ‘information’ if each one is slightly different. But the ear does not ‘hear’ phase difference, although it does detect it and our brain uses it to determine position, distance, movement and possibly velocity. Which is pretty clever when you think about it.

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