Like you might noticed, I’m a big fan of digital domain audio. That said, this does not mean that I am not aware of its weaknesses. In fact, it’s quite the opposite. I think, the best way to enjoy digital, it’s by knowing its limits. Welcome to my world !

Let’s go trashy: Discrete versus Continuous

Switching from analog to digital world can be overwhelming. I mean, nothing will be as big, in terms of change, than switching from the tape to the hard drive. Sound engineers (or most often, their assistant!) could spent hours cutting the tape with scissors to put scotch tape on it, in order to replace a snare hit! From that point of view, digital is definitely wonderful. That is one of the main reason why we all work with computer now: We spend less time on stupid things, and more on what matters, which is the sound.

It is true, however, that digital at its beginning was not wonderful at all. The first A-D converters sounded disguistings (literally!) and digital compressors were victims of aliasing since it processed the sampled point only and not the intersampling data !  Why is that ? Let’s go with some theory here…

Analog domain is continuous, every instants you have current passing. It is smooth, there is no aliasing possible. However, in digital domain, the information we got is an instantaneous value at a very specific time, then no info for few milliseconds. So, if a compressor is treating only the information he has, like if it was linear between point, then you’re find yourself with aliasing phenomenon… Why ? Because signal between sampled point can trepass the threshold without ever been treated !

Why the sampling frequency is not higher then?

At the beginning of digital, memory capacities were incredibly low. For this reason, they set the sampling rate standard for compact disc at its minimum. But, at this point, according to there mathematics, it was suppose to be lossless… How do they chose the minimum do you think ???  Check it out… you’re going to find it funny…

Nyquist-Shannon sampling and reconstruction theorem

The actual theorem affirm that it is possible to recovery entirely a signal if the sampling rate is at least two times the highest frequency present in the recording. But the part that most engineers tend to forget is the following: Yes, it is possible to recover entirely the signal if we use the SINC function to recover the sample. Since you’re probably not a DSP engineer, I think it’s not a luxury to specify more clearly what a SINC function is… Sinc function can be described as follow: y =Sin(x) / x. In other word, a very complex function that as to take into account every point that came before and after that actual event. No real time processing could ever do that!

Okay, so what’s the problem ?

Do you really think that every cheap cd player tries to interpolate between points by applying a complex sin(x)/x form on the entire song before even playing it ?? The answer is : depends on the daw and its settings. Even in professional software, during playback, the sound you hear is sometimes linealy interpolated ! That is why we are so tempted by 96kHz sampling rates ! It’s not because 44.1kHz is bad, it simply because it takes to much resources to interpolate following a sin(x)/x form! Let’s take a look at the following cheap figures:

Do you really think that every cheap cd player tries to interpolate between points by applying a complex sin(x)/x form ?? The answer is : HELL NO!

So, what is the moral of this story ?

1. Never turn your back on digital. In order to use it efficiently, you need to know its strenghts as well as its weaknesses.
2. People who are complaining that digital sounds cold, ironically, they usually the same people that are claiming that is no difference between 44.1kHz and 96kHz… Those people are also often interpolating linearly in order to save CPU.
3. You can achieve very continuous waves in digital domain, without the analog drawbacks simply by either working at very high sampling rate  or by working at high sinc interpolation quality.
4. If you’re working at 44.1kHz, the loss that you get from linear interpolation is in the high frequencies. If you want to hear the difference, that’s were you have to focus your listening.
5. Every time you use a compressor, make sure it oversamples at least by a factor of 4 to make sure to avoid aliasing caused by intersample overshoot.
6. There is no need to buy summing analog gear ! Simply work at smart digital settings, it will do the same, or even better !
7. A-D/D-A conversions are the most degrading part of a studio… if you can avoid it… do it.

I hope you appreciated that article, and that will be useful to your future digital audio projects !

Sincerly

Chris.