David Lamkins picked up his first guitar a long time ago. As best he can recall the year was 1967: the year of the Summer of Love. Four decades later David has conjured up an amalgam of folk, rock and jazz solo guitar music for the occasional intimate Portland audience.
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location: Portland, OR USA

Facets: digital, physics, technology, @musings info

Anti-digital myths busted

A lot of anti-digital arguments are made by people who understand only the quantization portion of the A/D/A process. I'm sure you've seen the diagrams: a smooth analog waveform is sampled at a regular interval to produce a stairstep approximation of the original signal. If this is all you know about, it's easy to argue convincingly (although incorrectly) that the original waveform is not preserved and that the accuracy of phase information suffers as the input frequency approaches the Nyquist limit, which is one-half of the sampling frequency.

People who know a little bit more about sampling will talk about aliasing. When the input frequency exceeds the Nyquist frequency you get a "reflection" in the frequency domain. For example, if you're sampling at 44 KHz, then any input frequency from 0 to 22 KHz will be properly sampled. But a 22.1 KHz input sampled at 44 KHz will register as a 21.9 KHz signal. Needless to say, such behavior would be extremely nonmusical if it was allowed to occur.

The reality is that sampling is not used as described above (the stairstep representation) and aliasing is not allowed to occur.

It's true that the samples in their digital form do take the appearance of a stairstep waveform. However, there is always filtering involved as part of the sampling and reconstruction process. Without getting into technical details, the original waveform is preserved in a properly-designed A/D/A chain. Also, the sampling and filtering is designed in such a way that aliasing is for all practical purposes impossible to invoke. (For a very well-written article on the subject please see Dan Lavry's "Sampling Theory for Digital Audio". This is the most accessible, complete and accurate article I've read on the subject. Although some math is required, Lavry's article is the best explanation I've read outside of an engineering text.)

There is one gotcha w.r.t. aliasing in the world of the guitarist, and that involves nonlinear (i.e. "distortion") processing of the digital representation of the signal. When you introduce distortion you create the possibility of creating frequencies _above the Nyquist limit_ in the digital domain. It takes extra care in algorithm design - and extra processing power - to prevent this from being a problem. Inexpensive multi-FX units tend to not do a great job of preventing internal aliasing. Cliff has demonstrated that he understands and has mastered that problem in the Axe-FX.

BTW, high sampling rates are not inherently necessary for good performance. 44 KHz is sufficient for high-quality audio reproduction, and more than adequate for MI usage.

Bit depth is a different matter. More bits will give you a higher S/N ratio. Until such time as analog circuit design gets an order of magnitude or two better in its noise performance, you really don't need more than 20 to 24 bits resolution. In theory, anyhow...

In practice, A/D and D/A converters are imperfect. They may not (read that: they usually don't) give you the full theoretical range of accuracy once you get down to extremely low signal levels, causing noise above the theoretical floor implied by the bit depth.

D/A and A/D converters are rated by linearity and montonicity. The better the converter, the closer its actual behavior matches the ideal behavior. Less expensive converters have deviations from the ideal behavior at very low signal levels. This causes increased distortion and noise.

Sampling rates that are higher than necessary tend to produce better performance because the surrounding circuitry must be designed to higher standards. In other words, there's really no need to store or process all those extra bits so long as the designer exercises due diligence in the analog circuit design around the A/D and D/A converters.

Sometimes vendors find it less expensive to create a marketable product at a certain price point through overspecifying the converters and relaxing the analog design. The sampling and reconstruction filters that I mentioned earlier need to have fairly exacting tolerances for best results. High-accuracy analog filters are more expensive to build. A designer can spec converters at higher resolution and bit depth to gain a bit of leeway on the analog design. It'd be much more expensive to design the analog signal path to work well up to the actual Nyquist frequency. However, holding the maximum frequency closer to 20 KHz while increasing the sampling rate gains a bit of performance through a rather simple and inexpensive design tweak while holding the line on the cost of analog circuitry.

Higher bit rates mask some of the problems caused by less-accurate filters and converters. It's a neat marketing ploy, actually. It's far less expensive for the vendor to build gear which samples at higher bit rates than it is to improve the quality of the converters and filters to perform properly at normal bit rates. The vendor wins by being able to charge significantly more for a minor engineering tweak. The customer loses by having to upgrade CPU, memory and disk to handle increased processing and storage requirements.

December 28 2008 23:32:46 GMT