showstack

First

Sampling, and the one rule about it

A microphone produces a continuously varying voltage — see transducers. A converter measures it at fixed intervals and writes down a number each time. Everything digital that follows is operations on that list of numbers.

The rule is Nyquist: to represent a frequency you must sample at more than twice it. 44.1 kHz — the rate AES3 and consumer digital audio were built around — gets you just past 22 kHz, which is past the top of human hearing, which is why that number exists. Sample below twice a frequency and it does not simply vanish — it comes back as a different, lower frequency that was never in the original. That is aliasing, it is unrecoverable once it has happened, and it is why every converter has an anti-aliasing filter in front of it removing anything above half the sample rate before it gets a chance.

Two pieces of hardware sit behind that sentence and are worth naming, because they are the join between this page and the analogue one. The anti-aliasing filter is a real low-pass circuit, and a steep one at 44.1 kHz is hard to build without audible side effects near the top of the band — which is the actual engineering argument for higher sample rates, since sampling at 96 kHz lets the filter be gentle and lets it start well above anything you can hear. Behind it, a sample-and-hold stage catches the voltage and freezes it, because a converter cannot measure a value that is still moving while it is measuring it. Everything digital rests on a capacitor holding a charge steady for a few microseconds.

Higher sample rates buy headroom above hearing, gentler filters, and less latency in block-based processing. They do not buy detail inside the audible band that 48 kHz was missing.

The one that matters more

Bit depth is resolution, and 6 dB per bit

Each sample has to be written down as a whole number, and bit depth decides how many distinct values are available. 8 bits gives 256. 16 bits gives 65,536. 24 bits gives about 16.7 million.

The gap between one available value and the next is an error, and that error is noise. Add a bit, halve the gap, drop the noise by about 6 dB. So 16-bit gives roughly 96 dB of dynamic range and 24-bit roughly 144 dB — which is more than any converter, room or microphone on earth can actually deliver. 24-bit is not there because you can hear the bottom of it; it is there so that you can record conservatively, leave headroom, and still have a noise floor below the room.

Drag the depth down and watch the staircase appear.

The same idea, other side of the building

Why a moving light has a fine channel

DMX gives each channel 8 bits — 256 steps. On a dimmer that is mostly acceptable and visibly not enough at the bottom of a slow fade, which is why fixtures apply dimming curves and better ones dim in 16 bits.

On a moving head it is a real problem. A fixture that pans through 540° over 256 steps moves about 2.1° per step. At the end of a long throw that is a beam jumping across the stage in visible increments, and no amount of console smoothing invents positions that the protocol cannot express.

So fixtures offer 16-bit control: two channels for one parameter, a coarse and a fine, combined as coarse × 256 + fine. 65,536 steps, and the same 540° now resolves to about 0.008° — below anything an audience could see.

It costs you a channel per parameter, which is why a fixture's extended mode has a much larger footprint. And it introduces a failure everyone meets once: if coarse and fine arrive from different sources, or one is patched and the other is not, the light jitters — because the fine channel is chasing a coarse value that keeps changing underneath it.

The one that confuses people

What 32-bit float actually buys

Fixed-point formats have a hard ceiling. Reach the largest number the format holds and there is nothing above it, so the waveform is cut flat — clipping, permanently, in the data.

32-bit floating point stores a value and a separate exponent, so the scale moves with the signal. There is no fixed ceiling in any practical sense. Inside a mixing engine that means an internal gain stage can go far above nominal and come back down with nothing lost, which is why every modern DAW and digital desk works in float internally, whatever Dante or MADI is carrying between them.

What it does not do is protect the input. The converter in front of it is fixed-point and has a real, physical ceiling. Overload that and it clips before the number is ever created — and no float format downstream can invent back a peak that was never captured.

A 32-bit float recorder is a slightly different claim: those use two converters at different gains and combine them, so the recorder genuinely does have enormous usable range. That is a hardware trick, not a property of the number format, and worth knowing which one a spec sheet is selling you.

Now the fun part

DSP is arithmetic on a list of numbers

Every effect on every processor you have used is built from a very short list of operations. There is nothing else in there.

Two of them in detail

What "fuzzy" is, and what reverb is doing

Distortion. A clean amplifier is linear: double the input, double the output. Push it past what it can do and the peaks flatten. Those flattened peaks are mathematically identical to the original wave plus a set of harmonics at multiples of its frequency — harmonics that were not in the source and that your ear reads as brightness, grit, warmth or harshness depending on which ones appeared.

How the curve bends decides the character. A soft knee rounds the peaks and generates mostly low-order harmonics, which sit close to the original and sound like fullness. Hard clipping — a brick wall, which is what digital does natively — generates high-order harmonics that sound aggressive and, worse, land above half the sample rate and fold back down as inharmonic aliasing. That specific ugliness is the sound of digital distortion done without oversampling, and it is why good plug-ins run their non-linear stage at a multiple of the session rate.

Reverb. A real room gives you the direct sound, then a handful of distinct early reflections off nearby surfaces, then an increasingly dense tail as reflections of reflections pile up. Algorithmic reverbs recreate that with networks of delays and all-pass filters — the classical Schroeder designs and modern feedback delay networks are both doing this.

Convolution reverb takes another route: record a real space's response to an impulse, and mathematically apply that recording to your signal. It is exact for the space it was measured in, and it is fixed — you cannot make the hall bigger, because you did not model a hall, you photographed one.

The through line

Why this page sits where it does

A sensor turns the world into a voltage — that is the previous page. A converter turns that voltage into numbers. Everything after it, in every department, is arithmetic on numbers: a filter, a delay, a fade, a pan value, a pixel.

And at the end of that chain the numbers become a voltage again, and something physical moves — a cone, a yoke, an LED. The digital part of a show is a long detour between two analogue events, and the only questions that matter along it are how often you wrote the value down, how precisely, and what arithmetic you did in between.