What is sample rate reduction?

What is sample rate reduction?

Digital audio is a list of numbers. Each one, called a sample, is the height of the waveform at one instant, and the sample rate is how many of those snapshots there are every second. A CD has 44,100 a second, written 44.1 kHz, and video work usually runs at 48 kHz.

A sample rate reduction effect, also called a downsampler or decimator, pretends the sound was captured with far fewer snapshots. It takes a sample, holds it for as long as a slower recording would have, then takes the next one. Your project still plays at its normal rate, but the sound inside it only changes value a few thousand times a second instead of 44,100, so the smooth wave becomes a staircase.

That staircase costs you top end, and it gives you two new sounds in exchange: aliasing, where high frequencies fold back down as tones that don't belong to the music, and a buzz from the sharp corners of the steps. Together they make the grainy, metallic edge people mean by lo-fi sampler grit. The saturation lesson covers the downsampler alongside the other curves; this page stays with the downsampler.

Reading the lab

The lab is the one used on the other saturation pages, set up with the downsampler and the bitcrusher. The Rate knob sets the new sample rate, from Off down to 300 Hz. Drive and Character do nothing on these two cards, so they're greyed out. The Anti-alias switch in the top bar applies to the downsampler only; it starts off, so you hear the plain effect first.

The screen to watch is the close-up labelled One peak, sample by sample. It shows two milliseconds around the loudest moment in the loop, 88 samples at 44.1 kHz, and when you lower the rate you can see the dots line up into flat steps. The harmonics screen runs a 110 Hz sine through the same settings; the grey bar on the right is everything that isn't a harmonic of that note, and on the downsampler it's the buzz of the steps, because a 110 Hz sine never goes over the limit. The spectrum next to it compares the loop before and after.

Auto gain matches the loudness of the processed sound to the original, so when you press A/B you hear the tone change and nothing else. Downsampling barely changes the level anyway, but the extra fizz can make it seem brighter and louder than it is.

Half the sample rate: the Nyquist limit

A sample rate can only describe frequencies up to half its own value. To capture a wave you need more than two samples per cycle, at least one for the push and one for the pull, so 44.1 kHz audio can hold anything up to 22.05 kHz. That ceiling is called the Nyquist frequency, after the Bell Labs engineer Harry Nyquist.

22.05 kHz is above what people can hear, so a CD's limit costs you nothing. Turn a downsampler to 8 kHz and the limit drops to 4 kHz, right in the range where hi-hats, consonants and the bite of a guitar live. Telephone calls have traditionally used an 8 kHz sample rate, which is a big part of why they sound the way they do.

What is aliasing?

When a proper converter records or converts audio, a steep low-pass filter removes everything above the Nyquist frequency first, so it never reaches the samples. A downsampler effect has no such filter. Frequencies above the limit still get sampled, and because there aren't enough samples to describe them, the samples end up tracing a lower frequency instead. That lower frequency is the alias, and it's as real as anything else in the sound.

Between half the rate and the full rate, the maths is simple: the frequency comes back at the rate minus itself. At 8 kHz, a 5 kHz part of a hi-hat comes out at 3 kHz and a 7 kHz part comes out at 1 kHz. Drag the slider in the figure past 4 kHz and watch the same dots start tracing the amber line.

On noisy sounds such as hi-hats, aliasing just sounds like grit, because the folded frequencies land among plenty of others. On a melody it's more obvious. Say you downsample an A at 440 Hz to 6 kHz. Its 7th harmonic is at 3,080 Hz, which is over the 3 kHz limit, so it folds to 6,000 − 3,080 = 2,920 Hz. That's 6.6 times the note, which isn't a harmonic of it, so it clashes with the key. Every harmonic above the limit folds to its own wrong place, and together they give the robotic, ring-modulated colour the lead in the lab picks up in step 5.

Pitch bends give aliasing away. As a note goes up, its harmonics go up too, but the aliases of the ones above the limit go down, because subtracting a bigger number from the rate leaves a smaller one. On a synth glide or a vocal slide you can hear tones moving the opposite way to the note, which real harmonics never do.

The staircase and its buzz

Holding each sample flat adds a second problem. A staircase has a sharp corner on every step, and sharp corners are made of high frequencies, so the steps add copies of the sound centred on the new rate and every multiple of it. Engineers call them images. A real converter removes them with a second low-pass filter on the way out, which turns the steps back into a smooth curve. A downsampler effect leaves them in.

On a 110 Hz sine at a 3 kHz rate, nothing folds, because the sine is nowhere near the 1.5 kHz limit. The step buzz is still there: in the lab it measures about 24 dB below the note, at 2,890 and 3,110 Hz and around every multiple of 3 kHz. It gets roughly 6 dB louder each time you halve the rate, from about −42 dB at 22.05 kHz to −35 dB at 11.025 kHz. That buzz is the part that sounds like a toy keyboard.

The Tone knob in the lab is a low-pass filter after the downsampler, a gentler version of the smoothing filter on a real converter. Set it to half the rate and the buzz above the limit drops sharply: on the same sine at 3 kHz, with Tone at 1.5 kHz, the grey bar drops by about 14 dB. It can't do anything about aliasing, because the folded tones are already below the limit, where the filter lets everything through.

Downsampling a file versus the effect

The word downsample gets used for two different jobs. When you export a 48 kHz project as a 44.1 kHz WAV, or convert a file in an audio editor, your software uses sample rate conversion. It filters out everything above the new Nyquist frequency, then calculates new samples that sit on a smooth curve. Going from 48 kHz to 44.1 kHz that way loses only the content between 22.05 and 24 kHz, which you can't hear, and adds no aliasing and no steps. The sample rate and bit depth lesson covers choosing a rate for a project.

The effect does the crude version on purpose: it skips the first filter so aliasing happens and holds each sample flat so the steps stay. The result is still at your project rate, so you can keep mixing. If a plug-in offers a filter before the downsampler, switching it on gets you closer to clean conversion: much less aliasing, and a sound that's mostly a steep low-pass. Switching it off is what gives you the grit. The Anti-alias switch in the lab is that filter, set at 0.4 of the new rate.

The rate on a downsampler doesn't have to divide neatly into the project rate. At 6 kHz in a 44.1 kHz session, each sample is held for 7.35 project samples on average, so the lab holds some for 7 and some for 8. That unevenness adds a little noise of its own, and some plug-ins have a jitter control that adds more on purpose.

Where the sound comes from

Memory was expensive in the 1980s, and a sampler that stored fewer samples each second could hold more seconds of sound. The E-mu SP-1200 ran at 26.04 kHz with 12-bit samples, so its top end stopped around 13 kHz, and drums sampled into it came out thick and slightly dusty. Hip-hop producers built a lot of records on that sound. Many early samplers also changed the pitch of a sample by reading through it faster or slower, which added more aliasing on top.

Sampled sounds in early games consoles and home computers were often stored at low rates for the same reason, which is part of why they sound buzzy. A downsampler plug-in recreates the side effects of those limits without the memory problem, and you can automate the rate so one section drops into lo-fi and the next comes back out.

Many samplers of that era also had a low bit depth, so the sound on old records usually combines both. The bitcrushing lesson covers the other half, and bitcrushing vs sample rate reduction puts the two side by side.

How to use sample rate reduction

This works on drums, vocals, synths and whole loops. The rate is the main decision, and everything after it is cleanup.

1. Start high and come downBegin at 22 kHz, where the change is small, and lower the rate until the top end starts to go gritty. Somewhere from 8 to 12 kHz most sounds pick up a clear lo-fi edge.
2. Listen for out-of-tune tones on anything melodicOn a lead or vocal, notice whether the new tones sit well with the key. If they clash, try a slightly higher or lower rate; each harmonic folds to a different place, so a small change can move the worst ones.
3. Decide about the stepsIf the buzz above the limit sounds too much like a toy, add a low-pass filter just after, at about half the rate.
4. Blend it back inOn drums or a full loop, a mix of 30 to 50% keeps the clean top end and adds the grit underneath. Use a send if your plug-in has no mix control.
5. Compare at matched loudnessSwitch it off and on with the levels matched. If the effect only sounds better when it's louder, pull it back.

Starting settings for common sounds

These are starting points chosen so the effect is easy to hear. The rate is the new sample rate in hertz; if your plug-in shows a divider instead, divide your project rate by the number.

A phone effect usually needs a high-pass filter too, because a phone line also loses the bass. Something like 300 Hz at the bottom and 3.4 kHz at the top, the band traditional phone lines carry, gets you close. The high-pass and low-pass filters lesson shows how to set both.

Sample rate reduction in your DAW

Most DAWs include a downsampler, usually inside a bitcrusher. Ableton Live has Redux and Logic Pro has Bitcrusher, and both combine sample rate reduction with bit reduction. D16's Decimort 2 is a whole plug-in built around the sound of old samplers. Some plug-ins show the rate in hertz and some as a divider of the project rate, so 4x in a 48 kHz session holds the sound at 12 kHz while the same 4x at 44.1 kHz gives 11.025 kHz.

A rate set in hertz sounds about the same whatever your session runs at, so 8 kHz is 8 kHz at 44.1 or 96 kHz. A divider doesn't behave that way: 4x in a 96 kHz session gives 24 kHz, which barely does anything.

Common sample rate reduction mistakes

Trying to filter the aliasing out afterwards

A low-pass filter after the downsampler removes the step buzz above the limit and nothing else. The folded tones below it stay, because they've become part of the sound. If the aliasing is too much, raise the rate or switch on the plug-in's filter before the downsampler.

Using it on sub bass

A 50 Hz sub is far below any sensible limit, so nothing folds and you only add step buzz high above the note, which tends to sound like a fault. Put the downsampler on the parts with top end, or high-pass the signal going into it and leave the sub clean.

Putting it across the master

On a whole mix, every part folds at once, the vocal included. Lo-fi mixes that work usually have the effect on chosen parts, or on a send blended under the full track, with the kick and bass left alone.

Forgetting the key

Aliasing on drums is free grit. On a melodic part, the folded tones are out of tune, and a rate that sounds fine on one chord can clash on the next. Play the whole section through before you commit.

Confusing it with bitcrushing

If a plug-in labelled bitcrusher isn't giving you the dull, metallic top end you want, the rate control is the one to turn. Bit depth adds hiss and grain in the quiet parts and leaves the frequency limit alone.

Train your ears

The quiz under the lab plays the current sound through either the downsampler at 3 kHz or the bitcrusher at 5 bits, with the screens covered and the loudness matched, and asks which one you heard, eight rounds in all. Listen to the top end. The downsampler takes it away and puts ringing tones in its place, while the bitcrusher keeps the top end and fills the quiet moments with grainy noise.

Questions people ask

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