Phase One

Contrary to popular belief, phase and polarity are not the same thing.In the audio world, you often see the words polarity and phase used interchangeably,
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Contrary to popular belief, phase and polarity are not the same thing.

In the audio world, you often see the words polarity and phase used interchangeably, which might lead you to believe that they mean the same thing. However, these terms refer to two different concepts. I'll look at each concept, discuss how they relate to one another, and give you some examples that illustrate them in terms of music production.

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FIG. 1: Sine waves a and b have the same amplitude and frequency, but their polarities are reversed. When they are added together, they cancel each other out.

POLAR REGIONS
Polarity refers to the positive and negative values of a signal voltage. Consider the sine wave in Fig. 1a. This waveform, like all analog audio signals, is an alternating-current (AC) signal, which means that the signal voltage repeatedly alternates from positive to negative. The voltage starts at 0V, goes positive, then negative, then back to 0. This completes 360 degrees of the waveform, or one cycle.

Now look at the sine wave in Fig. 1b, which is a copy of the first. The voltage starts at 0, goes negative, then positive, and ends up back at 0. This waveform is like a mirror image of the original, because its polarity is reversed, or inverted, with respect to the original. Whenever the first sine wave's voltage values are positive, the second wave's voltages are negative, and vice versa.

If you add these signals together, perhaps by summing them in a mixer, the two signals cancel each other out, as illustrated in Fig. 1. At every point in time, you are adding equivalent positive and negative voltages, and the result always equals 0V. If the signals have different amplitudes, they will only partially cancel each other. This makes sense, because at every point in time, you are subtracting the lesser voltage of one sine wave from the greater voltage of the other. The signal that remains is the difference in voltage between them.

The situation is the same with all signals, not just sine waves. For example, if you mix a trumpet recording with an inverted copy of itself, the two signals cancel out, just as with the sine waves. Again, at every point in time, equivalent positive and negative voltages are added together, regardless of the complexity of the signal. The result is always 0V.

Obviously, the result is different when you sum two different signals. If you are mixing a recording of a flute with a recording of a trumpet, inverting the polarity of the flute track might give the mix a slightly different timbre or tone. However, the signals are not identical, so they won't cancel each other out.

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FIG. 2: Sine waves a and b have the same amplitude and frequency, but they are 90 degrees out of phase. When they are added together, a single sine wave with greater amplitude is created.

PHASE OUT
Whereas polarity refers to the values of a signal voltage, phase concerns the time relationship between identical signals. The sine waves in Fig. 2a and Fig. 2b are exactly alike, but the second signal begins a quarter of a cycle later than the first. Whenever two identical signals begin their cycles at different points in time, they're out of phase. The time difference between them is called the phase shift, and it is measured in degrees. In Fig. 2, the two signals are 90 degrees out of phase. If you add these signals together, they won't cancel each other out. Instead, the voltages add up at each point in time to create an output waveform with a greater amplitude than the original's.

Sine waves are great for illustrating these concepts, because they have only one frequency component: the fundamental. Musical tones are more complex and interesting, because they contain a fundamental frequency plus many overtones. These frequency components are called partials. Each partial is really a sine wave at a particular frequency, and the combination of the partials creates the timbre of the sound.

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FIG. 3: When a complex signal is added to an out-of-phase copy of itself, comb filtering results. The term comb filtering stems from the appearance of the spectrum that is produced.

When you combine a complex signal, such as a trumpet recording, with a copy of it that has been shifted in phase, the partials add to and subtract from each other in several ways. Depending on the amount of phase shift, some partials cancel completely, some partials are only reduced a bit, and others reinforce each other and increase in amplitude. This phenomenon of cancellation and reinforcement at different frequencies is called comb filtering, because a graph of the areas of cancellation and reinforcement resembles a comb (see Fig. 3).

If the phase relationship between the two signals changes, the comb filtering changes as well. The comb filtering can change even more if the phase-shifted signal is reversed in polarity, changing all the cancellations and reinforcements accordingly. The comb filtering also changes if the phase-shifted signal is greater or lesser in amplitude than the original.

CROSS RELATIONS
Now I'll look at how phase and polarity are related. Go back to Fig. 1 to see a sine wave and a polarity-reversed copy of it. Imagine that instead of being polarity-reversed, the copy was delayed by half a cycle, or 180 degrees. The result is unchanged. Because sine waves have only one partial, inverting the polarity of a sine wave produces the same result as shifting it 180 degrees out of phase.

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FIG. 4: Complex tones, such as musical sounds, contain many partials. Here, the first four partials of a simple musical tone are shown. You can see that each partial''s cycle is a different length.

This isn't true with complex signals, because they contain many partials at different frequencies. As a result, each partial's cycle has a different length, which means they can't all be shifted by half of a cycle at the same time. For example, Fig. 4 shows the components of a complex tone with a fundamental frequency of 100 Hz and other partials at 200 Hz, 300 Hz, and 400 Hz. The partials have been graphed separately to illustrate the different cycle lengths.

Suppose you make a copy of this signal and shift the copy's phase by 180 degrees at the fundamental. The copied signal would be moved in time by one-half of the fundamental's cycle. If you then combine the original and the copy, the fundamentals cancel each other out. Just as in Fig. 1, the voltages would always add up to 0V.

However, the next partial, 200 Hz, has a cycle that is only half as long as the fundamental's cycle. When the fundamental is shifted by 180 degrees, the second partial is shifted by one full cycle, or 360 degrees. Therefore, the second partial retains the same polarity in both signals (offset by one cycle), and its amplitude doubles instead of getting canceled out. The phase shift of the third partial is 540 degrees, or one cycle (360 degrees) plus 180 degrees more, so it's canceled out. At 400 Hz, there's 720 degrees of phase shift. Because 720 degrees is twice 360 degrees, or two complete cycles, the 400 Hz partial also doubles in amplitude. In this simple example, the odd-numbered partials are canceled out, and the even-numbered partials double in amplitude. The result is comb filtering.

The bottom line is this: applying a phase shift of 180 degrees to a complex signal is not the same thing as reversing its polarity, as it is with sine waves. Nevertheless, identical signals with opposite polarities are often referred to as being "out of phase." For example, on many mixing consoles, each input has a switch labeled "Phase," and the user manual might say that the switch "puts the signal 180 degrees out of phase." This switch doesn't really shift the signal in time; it simply inverts the signal's polarity.

Why the "Phase" label? Well, in the early days of electronics, the term phase was used to refer to the polarity of audio signals, and the word polarity was reserved for describing power signals. Technically, this terminology isn't correct for complex signals, but the industry still uses this convention.

FIX IT IN THE MIX
Proper handling of signal polarity and phase is an important part of audio production, because unintended comb filtering can ruin a project. However, we can apply these concepts in creative ways as well.

For example, critical analysis of music mixes is an excellent way to learn new ideas and techniques for your own work. Manipulation of signal polarity can be a useful tool in such analysis. Think of a stereo mix as having three basic components: sounds in the left channel (A), sounds in the right channel (B), and sounds common to both channels. We can often learn how music is mixed by listening to these components separately. One way to do this is to cancel out the sounds common to both channels and listen critically to the remaining sounds. This technique sometimes called A-B listening.

To analyze music through A/B listening, connect the outputs of your source, such as a CD player, to two channels of a mixer. Pan both channels to the center, and then reverse the polarity on one of the channels. Any sounds that are equal in both channels of the mix are canceled out, because their polarities in one channel are inverted with respect to the same sounds in the other channel. The mono signal that remains contains the sounds that were panned to the left or right channel, but not both. (Sounds that are more pronounced in one channel than in the other in the stereo mix are reduced in volume in this inverted mono mix, but they are not eliminated completely.) Comparing this signal with the stereo mix, as well as with the complete (noninverted) mono signal, helps you learn more about the reverbs, backing parts, stereo spreads, and other details that are often masked by the more prominent parts of the mix.

Manipulating signal polarity can help fix problems as well. For example, suppose you do a multitrack recording of a band, and you send each instrument to a separate track. Later, while listening to the playback, you discover that you mistakenly sent some of the guitar signal to the synth track.

You may be able to fix the synth track. First mute everything but the synth and guitar tracks. Reverse the polarity of the guitar track and mix it in with the synth track. Change the level of the inverted guitar track until you find one that removes most of the guitar sound, leaving just the synth part. Bounce the result to an open track, and the problem is solved! This technique doesn't work in all cases, but it might get you out of a tough situation now and then.

Creative use of phase shift is another powerful tool in music production. For example, a common technique for recording a guitar amp is to place one mic right up to the speaker cabinet and a second mic just a foot or so behind the first. The mics pick up the sound from the amp at different times, which means the signals are out of phase. When you mix these signals together, some frequencies cancel each other out, and some reinforce each other. The resulting comb filtering often creates a guitar timbre that a single mic can't capture. If you don't like the sound, move the second mic back and forth until you find just the right spot where the comb filtering creates an interesting and useful sound.

The same technique can also be employed in mixing. Suppose you are mixing a tune, and something isn't quite right about the bass track. The performance is great, but the tone just isn't cutting it. You've fiddled with EQ and compression, but the right sound eludes you. Split the track into another mixer input and insert a delay on it. Set a delay time of less than a millisecond, as low as 0.1 ms, with no feedback. By adding the two inputs together, you create a comb-filter effect for the bass track, again generating tones that might not be achievable with simple EQ.

By using different delay times and adjusting the balance between the original signal and the copy, you can create many different timbres. Don't forget that you can also reverse the polarity of the delayed signal, which gives you even more tonal variations. This approach works great for lots of sounds, particularly snares, kick drums, basses, and guitars.

FINAL CYCLE
Manipulating signal phase and polarity can be a powerful tool in audio production, in subtle and dramatic ways. Once you understand the difference between these concepts - and know what to expect - you will find other interesting techniques for your work. Just remember to check your mixes in mono!