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Many analog processes take “infinite” frequency range for granted, but they can’t do the same in the digital domain. For example, a standard analog peaking EQ has a bell curve that is symmetrical around the center frequency; one side slopes to 0 Hz, and the other slopes toward infinite Hz.
You can implement the same EQ in the digital domain, but infinity is suddenly much closer. In fact, what was infinite Hz is now the Nyquist frequency (half the sampling rate) or 22.05 kHz at a sampling rate of 44.1 kHz. This difference in the proximity of infinity results in an EQ curve with a dramatically lopsided shape (see Fig. 6).
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FIG. 6: With an analog peaking EQ, the bell curve is symmetrical around the center frequency; one side slopes to 0 Hz, and the other slopes toward infinite Hz (top). If a digital EQ is uncorrected for digital’s closer infinite frequency, the curve’s top part becomes mapped into a much smaller frequency space, resulting in a lopsided shape (bottom). |
Those problems can be avoided or at least minimized by clever programming. The degree to which the programmer is successful defines, to a great extent, the differences between good and bad digital EQs.
Besides the creation of a more-or-less correct EQ curve, there are also matters of taste and personality, just as in analog EQs. The way a programmer chooses to approach these infinite-frequency quandaries affects the overall sound. Moreover, some products emulate the more esoteric sonic distinctions among classic analog EQs, such as slope and overshoot characteristics.
Compressors and limiters also have frequency-related issues. You’re probably familiar with aliasing—it causes audio artifacts when sampled audio contains frequencies higher than the Nyquist frequency. Aliasing doesn’t occur only during sampling, however; it can also happen entirely within the digital domain.
For instance, compression and limiting work by modulating one audio-rate signal (the input) with another audio-rate signal (the compressor or limiter’s automatic gain control, which operates in the audio range when the attack and release envelope times are fast). When you modulate one audio-rate signal with another, it has the effect of adding the two signals’ frequencies; if the total exceeds the Nyquist frequency, you’ll get some aliasing.
A full-bandwidth audio signal processed with a limiter or a compressor with fast attack or decay times falls into that category; the faster the attack or release and the greater the compression or limiting amount, the more aliasing you hear. That is the cause of the crunchiness many people hear in digital-dynamics processors. Again, clever programming, especially oversampling, can minimize these aliasing artifacts.
You’ll find similar predicaments in synths. Resonant filters suffer from the same infinity-is-much-too-close syndrome as digital EQs, and various synths differ widely in their success at addressing the problem. For instance, standard Chamberlin digital filters (the most common type) only work correctly to about one-sixth of the sampling rate. For a synthesizer running at 44.1 kHz, that means the resonance tops out at about 7 kHz.
Oscillators have problems similar to compressors. For example, a square wave at, say, 4 kHz is actually generating frequencies well above the Nyquist limit, because of the waveform’s sharp edges. Untamed, that can cause excruciating aliasing, especially toward the top of the keyboard (as you can hear in some popular products). Similar aliasing can also happen when samples are transposed above their original pitches. Techniques for dealing with these complications vary and account for some of the sonic differences among synthesizers.
Finally, it’s worth noting that some solutions are common knowledge and in the public domain, whereas many others are protected by patents or kept close to the vest as trade secrets. In short, different products use different techniques for dealing with frequency-related obstacles, and some are simply more successful and pleasant sounding than others.
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Reprinted with permission from
Magazine, May, 2001© 2000, Intertec Publishing, A Primedia Company All Rights Reserved
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