Digital Audio & the DAW: Numbers That Remember a Wave

Press record in any music app and the screen draws a wiggling line. Zoom in far enough and the line turns into dots, one every 0.0227 milliseconds on a CD. Those dots are everything the computer knows about the sound. It never stores the curve between them. Yet when the dots are played back, the curve between them returns, smooth and exact, to the limit of what hearing can tell.

That is odd enough to deserve an explanation, and the explanation is the first half of this piece. The second half is about the practical consequences: why a plug-in that sounds fine can fill a track with a pitch that was never played, why quiet passages get gritty when a file is shortened to 16 bits, why your headphones lag behind your fingers, why an MP3 is a tenth the size of the CD it came from, and why eight tracks added together are louder than any one of them.

Sampling: a wave measured on a clock

An analog-to-digital converter (ADC) does one thing, over and over: it looks at the voltage from the microphone preamp and writes down a number. It does that on a steady clock, the sample rate, and each number is a sample. The digital-to-analog converter (DAC) at the other end reads the numbers back on the same clock and makes a voltage.

Surprisingly, if the original contained no frequencies at or above half the clock rate, nothing was lost. This is the sampling theorem. In Shannon's 1949 wording, a signal with no frequencies higher than B hertz is completely determined by samples spaced less than 1/(2B) seconds apart. The idea has a crowded history: Whittaker published an interpolation formula in 1915, Nyquist's work on telegraph rates in 1924 and 1928 is the usual namesake though it did not state the theorem, Kotelnikov proved it in 1933 and Shannon made it famous to communication engineers in 1948 and 1949.

The commonly quoted upper limit of human hearing is about 20 kHz, and lower for most adults. A clock at 44,100 Hz has a Nyquist frequency of 22,050 Hz, which leaves a little room for the filters that remove everything above. The odd number is a historical accident. Early digital audio was recorded on video recorders, with three samples per video line: PAL gives 294 × 50 × 3 = 44,100, and black-and-white NTSC gives 245 × 60 × 3 = 44,100. Sony's equipment made it the de facto standard, and the compact disc inherited it. The 48 kHz rate came with professional and video work and is the usual choice for anything that goes with picture.

Rate	Nyquist	Where you meet it
44.1 kHz	22.05 kHz	CDs; most music releases
48 kHz	24 kHz	Video, broadcast, film, many DAW defaults
96 kHz	48 kHz	High-resolution releases; some recording and sound design
192 kHz	96 kHz	Archiving; very specialised work

Do higher rates sound better? This is argued. A 2007 blind test by Meyer and Moran passed high-resolution playback through a 16-bit, 44.1 kHz loop and asked listeners to tell the difference: they got 276 right out of 554 trials, 49.8 percent, which is chance. Monty Montgomery of Xiph.Org made the engineering case against 24/192 downloads in 2012. In the other direction, Joshua Reiss's 2016 meta-analysis of 18 published experiments in the Journal of the Audio Engineering Society found a small but statistically significant ability to tell high-resolution from standard audio, larger with trained listeners, and limited to the experiments that could be included. The sensible reading is that 44.1 and 48 kHz are enough for listening to a finished recording, and that higher rates have uses during production (less delay, gentler filters, and more room for processing that adds high frequencies) without being a guarantee of better sound.

Aliasing: the frequency that was never there

What happens when the theorem is broken, and a frequency above the Nyquist frequency gets in? Look at a wagon wheel in a film. The spokes turn forward but the camera takes only 24 pictures a second, so a fast spoke appears to creep backward. The wheel's real speed has been replaced by a false, slower one. In audio, a tone above Nyquist is replaced by a false tone below it. The false tone is its alias: it appears at the distance of the true frequency from the nearest multiple of the sample rate.

This is why real converters put a steep anti-alias filter in front of the ADC, and why many use oversampling, sampling far faster than needed and filtering digitally, which allows a gentle analog filter. Aliasing can also appear inside the computer. Distortion, saturation and some synthesiser waveforms create harmonics at multiples of the input frequency; those that land above Nyquist fold back as inharmonic whistles. Many plug-ins therefore oversample internally. The toy below lets you make an alias on purpose.

Without JavaScript: at 44.1 kHz, a 30 kHz tone is sampled so that it looks exactly like a 14.1 kHz tone. At 8 kHz, a 5 kHz tone looks like 3 kHz.

Quantisation, bit depth and dither

Sampling slices time. Quantisation slices height: each sample is rounded to the nearest of a fixed number of levels. A bit depth of b gives 2^b levels: 65,536 for 16 bits and about 16.8 million for 24. The rounding leaves an error of up to half a step, which sounds like a faint hiss. Each extra bit halves the step, so the error voltage falls by half, 6.02 dB.

The numbers are only for a loud signal. The error is a fixed size, so a quiet passage has less signal above it. And when the signal is only a few steps tall, the error is no longer random hiss. It is a pattern locked to the music, heard as a gritty, buzzing distortion, and a tone smaller than one step can vanish entirely. Dither fixes this by adding a tiny, noise-like signal before rounding, typically triangular noise two steps wide, which scatters the error into a steady, harmless hiss and lets signals below one step survive. The price is about 4.8 dB more noise. You apply it once, at the final reduction in bit depth, not at every stage.

Without JavaScript: a full-scale sine at 16 bits has a signal-to-noise ratio of about 98 dB, at 8 bits about 49 dB, at 4 bits about 23 dB. Triangular dither lowers each by about 4.8 dB.

Inside a DAW the numbers are usually not integers at all. Most mix engines use 32-bit or 64-bit floating point, which spaces its values in proportion to their size. The largest 32-bit float is about 3.4 × 10³⁸, around 770 dB above full scale, so a signal inside the mixer cannot clip in the way a converter can. It still arrives at the output, where the 0 dBFS ceiling is real, so the last gain stage before the converter is the one to watch.

Latency: buffer size against patience

A computer cannot hand audio to the interface one sample at a time; the operating system would never keep up. It works in buffers: blocks of, say, 128 samples. While one block plays, the next is being computed. A bigger buffer makes dropouts less likely and gives plug-ins more time, and delays everything by the length of the buffer.

That matters most when a musician hears themselves through the computer. A singer wearing headphones hears their voice once through the bones of their head and once, late, from the DAW. One study found latency above about 15 ms noticeable to listeners, and broadcast circuits aim for 10 ms or better. People differ. Sound travels 34.3 cm in a millisecond, so a 7 ms round trip is like standing 2.4 m from your own speaker.

The tricks are all about choosing where to pay. Record with a small buffer (64 or 128 samples) and raise it for mixing, when delay does not matter but plug-ins are heavy. Use the interface's direct monitoring, which mixes the input into the headphones in hardware before the computer sees it. Turn off plug-ins on the record-armed track. DAWs also apply plug-in delay compensation: if one plug-in needs 1,024 samples of look-ahead, every other track is delayed by the same amount so they stay in time.

Without JavaScript: 128 samples at 48 kHz is 2.67 ms one way and about 6.8 ms round trip with 1.5 ms of converter overhead. 1,024 samples at 44.1 kHz is 23.2 ms one way, about 47.9 ms round trip.

Lossy codecs: what psychoacoustic coding throws away

CD audio runs at 44,100 × 16 × 2 = 1,411,200 bits per second. Over a phone connection or in a pocket player in the 1990s, that was far too much. The insight of perceptual coding is that the ear has holes. A loud tone masks quieter sounds at nearby frequencies, so they cannot be heard, and above and below a certain range everything is inaudible anyway. A codec splits the sound into frequency bands, works out how much noise each band can hide, and spends bits only where the ear can notice. What is discarded is gone for good; that is what "lossy" means.

MP3, formally MPEG-1 Audio Layer III, was developed mostly at the Fraunhofer Society in Germany under Karlheinz Brandenburg and published in the ISO standard 11172-3 in 1993. At 128 kbit/s it is about 11 times smaller than a CD. Its principal US patent expired in April 2017. AAC, from the same standards family, is a refinement; Opus, specified by the IETF as RFC 6716 in September 2012, works from about 6 to 510 kbit/s with frames as short as 2.5 ms, which makes it suited to calls as well as music. The usual artefacts at low bitrates are a swirly, underwater high end and "pre-echo", a smear before a sharp drum hit.

Two rules follow. Never use a lossy file as a master or a sample source: encoding it again stacks the damage. And "lossless" formats such as FLAC and ALAC are different: they pack the same samples smaller, like a zip file, and return exactly the original.

Without JavaScript: a 4-minute stereo song is about 42.3 MB as CD audio (1,411.2 kbit/s), 3.8 MB as 128 kbit/s MP3 and 2.9 MB as 96 kbit/s Opus.

The DAW: tracks, buses, sends and summing

A digital audio workstation is a recorder, a mixing desk and a patch bay in one program, and all three run on the numbers above. The vocabulary is borrowed from analog consoles, and it is worth knowing exactly.

Term	What it is
Track	A channel that holds audio clips (or MIDI that drives an instrument), with its own fader, pan and mute.
Insert	A plug-in placed in the track's own chain. All of the signal goes through it: an equaliser, a compressor.
Send	A knob that copies part of the track to another place, usually an effect such as reverb. Pre-fader sends ignore the fader; post-fader sends follow it.
Bus	A shared channel that many tracks feed: all the drums to a drum bus, all the effects to a reverb return. Its fader moves the whole group.
Master	The final bus, where everything is summed and sent to the converter or to a file.
Automation	Recorded movement of a knob over time: a fader ride, a filter opening through a chorus.

The step that surprises beginners is summing. Mixing is addition of samples. If two tracks are uncorrelated, such as two different instruments, their powers add, and two equal tracks together are 3 dB louder than one. If they are identical, as with a doubled recording or a mono signal sent to two places, their amplitudes add, and the result is 6 dB louder. Eight uncorrelated tracks make a signal about 9 dB louder than one of them; eight identical ones, 18 dB. Real tracks fall in between, so a master meter climbs as a session fills up even if no fader moves.

Without JavaScript: eight tracks at −18 dBFS sum to about −9.0 dBFS if they are different parts and 0.1 dBFS, just over full scale, if they are identical. Thirty-two different parts at −18 dBFS sum to about −2.9 dBFS.

What a graduate just sees

• Sampling loses nothing below half the sample rate and invents false tones above it; the anti-alias filter exists because of that.
• A bit is worth 6 dB. 16 bits is fine for a finished track; 24 bits is for working, where nobody has to scrimp on headroom.
• Dither trades a little steady hiss for an end to distortion in quiet passages, and goes on once, at the last bit-depth reduction.
• Sample rate sets the highest frequency; bit depth sets the noise floor. They are independent.
• Latency is buffer ÷ rate, paid twice on a round trip; choose a small buffer to record and a large one to mix.
• Lossy is one way: make the master lossless and encode last.
• Tracks add. A mix that sounded fine at 4 tracks may clip the master at 24, even when no single track is loud.
• Floating point inside the DAW will not clip, but the converter and the exported file will.

Where it shows up next

• Mixing & Signal Processing (36/63): the equaliser and compressor you will meet are filters and gain curves running on these samples, and summing headroom decides how hot a bus can be.
• Mastering & Loudness (36/64): dither, the final bit depth, and which codec the streaming service will apply on the way out.
• Synthesis & Sound Design (36/68): naive sawtooth and square waves alias, and anti-aliased oscillators are the cure.
• Beatmaking, Sampling & Arrangement (36/69): early samplers sounded the way they do partly because of their low sample rates and bit depths, and producers still imitate that on purpose.
• In the world: phone calls, streaming radio, video-game audio engines, podcasts, hearing aids and every smart speaker.

If you want to go deeper

• 📘 Textbook. Ken C. Pohlmann, Principles of Digital Audio (6th edition, McGraw-Hill, 2010), the standard reference from the University of Miami's Music Engineering programme; and David Miles Huber, Emiliano Caballero and Robert Runstein, Modern Recording Techniques (10th edition, 2023), for the studio side.
• ▶️ Gentler. Xiph.Org's Digital Show & Tell, a video that demonstrates sampling, quantisation and dither on real equipment; and Monty Montgomery's article 24/192 Music Downloads Are Very Silly Indeed, for one side of the high-resolution argument.
• 🌐 Free course. MIT OpenCourseWare 21M.380 Music and Technology: Recording Techniques and Audio Production, which covers digital audio workstations and processing.