Two numbers doing two different jobs

Two numbers that do different jobs

A digital audio file is described by a sample rate and a bit depth, and they control entirely separate things. Sample rate sets the highest frequency that can be represented. Bit depth sets the dynamic range between the loudest and quietest representable signal. Neither improves the other.

Sample rate and the folding problem

The sampling theorem says a sample rate of f can represent frequencies up to f/2, the Nyquist frequency. 44.1kHz gives a ceiling of 22.05kHz; 48kHz gives 24kHz. Both are comfortably above the usual upper limit of adult hearing, which is why 44.1 was chosen for the compact disc in the first place.

What happens to frequencies above the ceiling is the part worth understanding. They do not disappear. They fold back into the audible range, mirrored around the Nyquist frequency. A 25kHz tone sampled at 44.1kHz appears in the file as 44.1 − 25 = 19.1kHz: an audible tone that was never in the room, unrelated harmonically to anything else. This is aliasing, and because the folded frequencies bear no musical relationship to the source, it sounds harsh and metallic rather than merely bright.

Converters prevent it with a steep anti-aliasing filter before the sampler. That filter is the real reason people argue about sample rates: a brick-wall filter at 22kHz has consequences in the top octave, and running at 96kHz lets the filter be gentler and moves its effects well out of hearing.

48kHz, and why video uses it

48kHz is the standard for video and film. It is not audibly better than 44.1; it was chosen for professional video systems because it gives a whole number of samples per frame at the common broadcast rates, which makes editing and synchronisation arithmetic exact.

Use 48kHz for anything that will meet a picture. Converting 44.1 to 48 is a resampling operation. It is fine, but it is an extra process and a chance for a small error, and there is no benefit to starting at 44.1 for video work.

When higher rates help

Not for fidelity of the recording, for most purposes. There are three real cases:

• Extreme pitch-shifting or time-stretching. Slowing a 96kHz recording to a quarter speed brings content that was at 40kHz down to 10kHz, where you can hear it. Sound designers record at 96 or 192kHz for exactly this.
• Non-linear processing. Distortion, saturation and some compressors generate harmonics above Nyquist which alias back down. Good plugins oversample internally to avoid it; running the whole session higher is a blunter version of the same fix.
• Very low latency monitoring, because a buffer of a fixed number of samples is shorter in time at a higher rate.

Against those: double the storage, double the processing, and for a spoken-word recording, no audible gain. 48kHz is the correct default.

Bit depth is dynamic range

Each bit adds about 6.02dB of range. 16-bit gives roughly 96dB; 24-bit gives roughly 144dB.

144dB is larger than any analogue front end can deliver. The best preamps and converters have a noise floor around 120dB below full scale; most interfaces are nearer 100 to 110. So in a 24-bit recording, the bottom two to four bits are recording the analogue circuitry’s noise, not silence.

This is exactly why the headroom advice in the previous lesson is cheap. Recording at −18 dBFS average rather than −6 costs you 12dB of the available range. In 16-bit that would be a real sacrifice; in 24-bit, you still have more range than your preamp can use. Record in 24-bit and leave headroom is the whole practical conclusion.

Dither, and why it matters going down

When you reduce bit depth (a 24-bit master to a 16-bit file) the extra bits have to be discarded. Rounding produces quantisation distortion, and unlike noise it is correlated with the signal, so it appears as a granular, crunchy texture on quiet fades rather than as steady hiss.

Dither is a tiny amount of random noise added before the truncation. It decorrelates the error: instead of a fade stepping down through discrete levels, it dissolves into noise. You have traded a signal-dependent distortion for a constant, benign noise around −90 dBFS, which is inaudible in almost any real listening situation.

The same mechanism as the video banding lesson, for the same reason.

Apply dither once, at the final reduction to 16-bit, and never twice. Staying in 24-bit or 32-bit float throughout means it never arises until the final export.

What to use, in practice

• Recording: 48kHz, 24-bit. Always, for anything meeting picture.
• Working: keep 24-bit files; work in 32-bit float internally, which every editor does by default.
• Delivery to video: 48kHz, and let the encoder handle the rest. AAC at 192 to 256 kbit/s stereo is transparent for speech and generous for music.
• Delivery as WAV: 48kHz 24-bit for masters, 16-bit with dither if something demands it.
• Sound design source material: 96kHz if you intend to stretch it.

The free path

Audacity records at any rate and depth, works internally in 32-bit float, and includes dither options in its export settings. Ardour is a full open-source recording environment. ffmpeg resamples with the high-quality soxr resampler:

ffmpeg -i in.wav -af aresample=resampler=soxr:precision=28 -ar 48000 out.wav
ffmpeg -i in.wav -af aresample=osf=s16:dither_method=triangular -ar 44100 out16.wav

The limitation

Very little of this is audible on a spoken-word recording made in a normal room. The room, the distance and the microphone’s placement account for nearly all of the perceived quality; the difference between 48 and 96kHz accounts for approximately none of it.

Claims about high sample rates sounding better are also contested. Controlled listening tests have repeatedly failed to show a reliable difference on playback of material within the audible range, while the practical benefits for processing are real and measurable. The two claims get conflated in marketing, and the honest position is to use higher rates where there is a process that benefits and not to expect a difference otherwise.