Phase & Polarity
We often hear phase spoken about in a very basic manner, such as “one loudspeaker is either ‘in-phase’ or ‘out-of-phase’ with another.” This is more correctly referred to as the polarity relationship of the loudspeakers. When polarity is reversed, then all of the energy emanating from a loudspeaker – without respect to frequency – is also reversed.
In such a case, two theoretically perfect loudspeakers would perfectly cancel each other’s entire output across the full audible spectrum. However, this won’t actually occur due to the physical imperfection of virtually all known loudspeakers.
What does in fact occur is that the low frequencies will almost totally cancel each other because the physical imperfections of the loudspeakers are relatively minor in relation to the long (and therefore forgiving) LF wavelengths, while the shorter wavelengths of the high frequencies will partially cancel and partially combine, causing havoc with the MF and HF frequency and phase response.
It’s worth noting that a phase offset of multiple sound sources is akin to how a flanger works. The effect of “flanging” was originally created by slowing down a reel of tape on a tape recorder that started out in sync with another tape recorder playing an identical track.
Flanging was accomplished by applying your finger on the edge of the reel to alter the speed of the tape machine (hence the term). The small offset in time created the well-known sonic effect that’s now easily replicated by the use of modern analog and digital electronics.
But it’s also important to note that a flanger is an intended sonic effect.
Conversely, loudspeaker offset – which also creates a form of flanging (albeit not wandering up and down like the tape recorder variety), is rarely intended to be of positive value.
Let’s look again at one of the numerous definitions of phase. Phase-versus-frequency is the relationship of an alternating signal (all sonic energy is comprised of alternating signals) at a given frequency, in relation to the time that it takes the sonic energy to propagate to a given point in space.
When all frequencies arrive at the same time at the same point in space, then the phase response is said to be linear or flat. If some segment of the frequency spectrum arrives earlier or later than another, than the phase response is not flat and phase offset has occurred.
If we were to move one of a pair of matched loudspeakers a few inches rearward while maintaining a fixed listening position, the effect on the phase response of the energy arriving at the listener’s position would be much greater in the higher frequencies than in the lower frequencies, simply because the wavelengths are much shorter in the high-frequency range than in the low-frequency range.
Thus, phase can be said to be wavelength versus time. Once this concept becomes clear, it also becomes easier to understand what’s happening with your sound system on a practical level.
Known & Stable Source
Whenever a signal, musical or otherwise, occurs in time and space, it inherently possesses a measurable frequency response and phase response. A sine wave at a fixed frequency exhibits only a simplex frequency response – that of a single frequency – along with possibly some distortion-related overtones. Therefore, the phase response of a single sine wave is generally considered to be a simplex matter.
But speech and music are different. They inherently comprise a complex series of waveforms which make the picture a lot more complicated. This is why measurement equipment is so valuable, because a good measurement system provides a known and stable source, that when acquired by the measurement engine, is capable of accurately characterizing a sound system in a short time span.
Every time an IIR is introduced into a signal path (PEQ, shelving, HP, LP, crossover, etc.), a corresponding phase lead and lag is introduced as well. Phase and frequency are two sides of the same coin. One cannot exist without the other.
The phase lead, or lag, begins at the lower skirt of the filter and ends at the upper skirt. At the maximum peak or trough of the filter, the phase response is always exactly at zero (Figure 2). Intuitive? Hardly.
But if you spend some time measuring the frequency and phase response of your favorite equalizer as you adjust the settings (highly recommended), you will eventually be able to decipher the response of the acoustic signature of your sound system in a typical venue environment. It takes practice to understand what you’re seeing, but it’s time well spent.
The bottom line is that learning to use measurement equipment, particularly affordable systems like the industry-leading (Rational Acoustics) Smaart package, are essential in developing a solid understanding of what’s really taking place in regard to the system you’re trying to optimize.
While many might argue that “what you hear is more important than what you measure,” this position is usually based on the use of imperfect measuring apparatus—or uninformed interpretation of the measured data.
Peaks & Dips
Offering an alternative perspective, one would need to listen to chromatic scales across the entire audible frequency spectrum, for hours on end, to identify the subtle (and not so subtle) peaks and dips that are always present in the frequency domain.
I sometimes hear about engineers who EQ the system to the tonality of the drums or to the band’s sound check. I then ask what happens if the band decides to play in a different key? Or if the gig is a festival and some acts are playing in, let’s say E Major, while others play in Bb, Ab, or Eb minor – what might have been missed? It’s not far-fetched to imagine that holes or peaks in the spectral response won’t be identified until the next act takes the stage.
But even more so, trying to convert what you hear from the system into making improvements in the time/phase domain is next to impossible without the use of accurate instrumentation.
Sidebar: IIR vs. FIR
As in most aspects of life, there are exceptions to everything. Unlike IIR filters, the relatively new breed of filters known as FIR can alter the frequency response of a system without altering the phase response.
However, there is a price to pay. Since phase and time are impossible to separate, the price you pay is that any change in the frequency domain will result in a corresponding effect in the time domain, i.e., additional signal delay.
For some applications like cinema or AV track playback, this might be perfectly acceptable. For other applications, such as stage monitors or front-fill loudspeakers in small theatres, even a small degree of signal delay may not be appropriate.
Each situation must be carefully considered and addressed in regard to the intended end-result. And that is exactly the approach that helps us all further our craft.