XO Wave: Analog vs. Digital EQ

Comparing analog to digital EQ is one of the most contentious subjects in audio. When people in audio circles start to discuss this, the safest action is to run for cover. The bottom line, of course, is that "best" is subjective in this domain like many others, but there are a few real differences between analog and digital EQs:

Design Quality: Digital filter design is a relatively new field and people doing it don't always know what they are doing, so there are many bad digital EQs -- some remarkably bad. Analog filters, on the other hand, are mature enough that bad ones are fairly uncommon.

Design Constraints: Analog filter design is often limited by the cost of the parts, whereas digital filter design is often limited by things like target hardware and available CPU time.

Noise: Most signals to be filtered have some noise in them to begin with. Both analog and digital filters may increase this noise, simply because they are boosting some part of the signal. However, analog filters, like any other analog circuitry, always add noise to signals passing through them simply because of mechanical factors like heat, electrostatic noise, and other things that designers have little control over.

Analog Distortion: Both analog and digital filters introduce distortion. However, the types of distortion introduced by the two types of filters can be very different. Analog electronics are usually slightly non-linear, which creates harmonic distortion. In small amounts, harmonic distortion is usually considered benign or even pleasant, since the frequencies it creates are musically related to the desired frequencies passing through the filter.

Digital Distortion: Digital filters, on the other hand, may introduce truncation distortion. If a digital filter is badly designed this truncation results in non-harmonic (or inharmonic) distortion. That is, the distortion created by a digital filter is not musically related to the frequencies in the signal. Digital equipment with inharmonic distortion is probably the main reason digital audio had such a bad reputation in the early days for sounding "sterile", "cold", and "unnatural". Indeed, no natural system creates this kind of distortion, so our dislike of it is not surprising. (By contrast, every amp, every surface that sound bounces off, our ears, and even the air itself, introduce a bit of harmonic distortion, so we tend not to notice unless it is extreme.)

There are two common ways to avoid truncation distortion: use high-precision math, or use "dither," a type of noise, to distribute the distortion artifacts across the frequency spectrum. Whenever possible, XO Wave takes the former approach; however, dither is still used elsewhere in XO Wave when significant truncation is unavoidable, such as when creating an 8 or 16 bit file. For more on dither, see our article A Bit about Dither.

Uneven High Frequencies: virtually all digital filters behave somewhat differently than analog filters at high frequencies. If you want a more "analog" sound from digital filters, the easiest thing to do is to use shelving filters (such as low shelf and high shelf filters) when working with moderate to extreme high frequencies, because shelving filters are immune to this problem.

Phase: For the most part, both analog and digital filters distort the phase of signals in the same way. For more information on this topic, read why no filter is perfect.

-- Bjorn Roche