Digital audio: Nyquist, dither, noise shaping, buffer, clock, Mid/Side, and correlation.

Converting sound into numbers is a resolution decision along two axes: how many times per second it is measured, and how many values each measurement can take. You already know sample rate and bit depth. What follows is the rest of the digital chain: what happens when resolution is reduced, how much delay the computer puts between your hands and the speakers, and how stereo phase decisions are measured.

Specifically: the Nyquist theorem explained for musicians, dither, noise shaping, buffer size, digital clock and jitter, Mid/Side, and phase correlation. Start with the sample rate and bit depth guide.

The Nyquist theorem explained for musicians

The theorem says that representing a signal requires sampling at more than twice its highest frequency. In practice, with 44,100 samples per second, the theoretical ceiling is half that, 22,050 Hz, above what most adults hear.

The practical effect is less the ceiling than the trap around it. Frequencies above half the sample rate are not sampled correctly: they fold down and appear as phantom frequencies absent from the original signal. This phenomenon is aliasing, which is why anti-aliasing filters exist before conversion and reconstruction filters afterwards.

For music and normal hearing, 44.1 kHz is unquestionably sufficient. Working at 48, 88.2, or 96 kHz has other reasons: gentler conversion filters, real-time processes generating harmonics above the ceiling, or video compatibility. Increasing sample rate for “more treble detail” is unnecessary; treble detail depends on correctly taken samples, not more samples per second. Xiph’s sampling and quantisation demonstrations are the best way to see it.

Dither

When reducing bit depth, each sample must be rounded to one of the few available values. Simple rounding produces non-random error: it depends on the signal and becomes high-order harmonic distortion, sounding harsh precisely where the material was gentle. Dither introduces a small, controlled amount of noise before rounding, making the error depend on noise rather than signal: the result is white noise instead of tonal distortion, preferable to hearing the rounding.

When to use it: whenever reducing bits, typically from 24 or 32 bits to 16 bits on export. If the destination retains the same resolution, do nothing. Most applications offer several types; Audacity lists Rectangular, Triangular, and Shaped, describing Shaped as applying noise shaping. The four options are compared in the table following this section.

Noise shaping

Noise shaping is the next step after dither: instead of distributing added noise evenly across the spectrum, it sculpts it towards bands where hearing is less sensitive—the high frequencies. Total noise may be equal or greater, but perceived noise is lower because it lies outside the most audible region.

It comes included with most applications’ shaped dither, and sensible use is the same as for dither: final bit reductions, not a knob to raise routinely. Its effect is more noticeable in very clean masters with little high-end energy; in compressed material with saturated treble, the difference from simple dither is smaller.

If your chain digitises at 24 bits and exports at 24 bits, neither process intervenes. Dither and noise shaping are reduction tools, not enhancement tools.

Buffer size

Buffer size is the number of samples the computer processes in one batch. Smaller buffers wake the CPU more often per second: less delay, more load, and greater risk of audio crackles. Larger buffers let the chain work comfortably but with more latency.

Total round-trip delay—input, processing, and output—is what you feel when playing and monitoring with delays. In practice, the target is around 10-20 milliseconds for real-time work, corresponding at 44.1 kHz to a few hundred samples of margin. Above that range, action and sound separate, making monitored playing uncomfortable.

Decision rule: raise the buffer when mixing or rendering with many tracks and processes; lower it when playing live or recording with monitoring. Buffer size is not a sound-quality parameter: if a large buffer still crackles, the issue is load or drivers, not size.

Digital clock and jitter

The digital world needs a pulse saying “now”. That pulse is the clock, which determines the exact sample-taking instant at a converter. Jitter is deviation from that instant: correctly measured samples placed slightly incorrectly in time.

That temporal drift translates into lost clarity, a less defined stereo image, and, when large, artefacts. Manufacturers know this and publish solutions: RME describes SteadyClock as a stabilisation system reducing jitter both in its own outputs and at digital audio inputs, because clock quality affects conversion.

Where it matters in your chain: input/output interfaces, chains with multiple devices synchronised through S/PDIF or AES, and DJ setups with several digitally connected sources. An often-forgotten detail: more resolution does not fix a cheap clock’s jitter; a better clock does.

Mid/Side

Mid/Side is not exotic capture: it is a mathematical rewriting of what you already have. Mid is what both channels share, their sum; Side is what differentiates them, their difference. Two inverse operations restore them: left is Mid plus Side, right is Mid minus Side.

Its usefulness is control. Separating the common from the different lets you narrow or widen stereo without touching the centre, EQ the centre without moving the sides, or process the sides more aggressively because they do not carry the kick’s impact. It also explains why some sounds disappear in mono: if almost entirely in Side, summing to mono cancels them.

You can encode and decode it manually with a couple of operations, and most width plug-ins and paired microphones work on this same basis.

Phase correlation

Phase correlation measures how similar the two channels are. A typical meter runs from +1 to −1: at +1, channels are identical and material is mono; intermediate values show partial differences and stereo information; near 0, there is little relationship; negative values indicate polarity-inverted components.

Polarity, phase shift, and correlation are different and should not be confused. Polarity inversion changes the signal’s sign; phase shift is a frequency-dependent time displacement; correlation is the measured result. Sustained negative correlation indicates cancellation when summing to mono: an inverted channel, incorrectly wired microphone, or badly applied width process.

Why check it in the booth: before sending to a mono system or ensuring your track survives a single-channel PA, check that the meter does not remain negative. It is the cheapest test of whether stereo is robust or merely sounds good with both channels active.

Common mistakes in the digital chain

Increasing sample rate by habit. It adds no audible detail by itself and multiplies file size. Increase it only for a reason: compatibility, live processing generating harmonics, or delivery requirements.

Exporting 24 to 16 bits without dither. This is precisely when rounding becomes audible as harsh distortion in quiet detail.

Lowering the buffer to “improve the sound”. It only lowers latency; failures with a large buffer mean the load is not being handled.

Blaming software for jitter. Jitter is a clock and conversion problem, not a plug-in problem.

Accepting stereo without checking correlation. Stereo that falls apart in mono is only half-finished. The next chapter covers this territory: what DC offset is and how to choose formats when converting.

Next step

You now know how audio is sampled, quantised, clocked, and measured for phase. The final link remains: file formats, bitrate, detecting transcodes, and the displacement called DC offset. Continue with Formats and bitrate: MP3, AAC, OGG, Opus, CBR, VBR, and DC offset.