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Understanding Relationships: Bringing Clarity To Phase, Frequency And Time
The path to making optimal choices with sound reinforcement systems...
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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 measureable 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. (Again, refer to the sidebar.)

Figure 2: An example of a simple PEQ boost.

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.

Ken DeLoria is senior technical editor for Live Sound International and ProSoundWeb, and has had a diverse career in pro audio over more than 30 years, including being the founder and owner of Apogee Sound.

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