Sample rate

Digital audio has no stair-steps#

The stair-step waveform is a myth spread by people who don't understand what a low-pass filter is. Every digital system that isn't broken low-pass filters its output, so the voltage coming out of a DAC is perfectly continuous. If you take the most stair-stepped wave in the world, a square wave, and put a low-pass filter on it, it is no longer stair-stepped at all.

The exception is a DAC built without filtering. Then you really are hearing the stair-steps (but even then your ears are their own low pass filters), which is one reason non-oversampling DACs are a bad idea.

Two samples per cycle is enough#

You will hear the claim that digital sounds thin because 44.1 kHz only samples a 15 kHz waveform three times, so it can't capture the whole curve. I have heard it from one of the most famous mastering engineers alive. It is a basic misunderstanding of the Shannon–Nyquist sampling theorem. Thanks to the reconstruction filter, two or more samples per cycle reproduce any frequency up to the limit of hearing faithfully. This isn't a controversial opinion or a philosophical disagreement. It is how sampling works, and Grammys don't make anyone immune to factual errors (see evidence).

The Nyquist theorem as usually taught is wrong#

The version taught at universities and repeated online goes: sample at twice the highest frequency and you are guaranteed perfect fidelity. Even the name is wrong. What people quote comes from Claude Shannon's 1949 formalisation, which is a mathematical proof about ideal reconstruction with sinc pulses. It doesn't necessarily refer to what people have in mind when they think of digital audio. I am not debunking Shannon. I am debunking the layman version.

Here is what happens with the layman version, the outdated method of sampling right at twice the frequency. If you sample a 20 kHz sine wave at exactly 40 kHz and the samples fall on the zero crossings, you record silence. Input: sine wave. Output: nothing. If you lower the tone slightly, the samples drift across the waveform, so you get beating that speeds up as the pitch drops. That is not perfect fidelity, and it is why no good converter has worked that way for decades.

Early digital sounded bad partly because of its analogue filters#

Used as a raw sampling rate, 44.1 kHz gives you the gap between 20 and 22 kHz to get rid of everything that would alias. That needs a filter of something like 600 dB per octave. Really early digital used high-order elliptical analogue filters to do it, and something has to give, so you get huge ripple in the passband. That is partly why some really old digital sounded metallic and unnatural. That part of the fault was in the analogue filter, not in digital itself, and no sensible product has worked that way since the early 80s.

44.1 kHz is a storage rate, not a sampling rate#

Most modern converters are delta-sigma. The modulator runs at millions of samples per second, originally at one bit, and averages them down to the rate on the box. It is like eating the same $27.43 meal every day at a restaurant that only accepts $100 bills: you pay one bill, then nothing for a few days, then another bill, and over time the average converges on the real price. Only on or off, and still a precise value. The same oversampling spreads the quantisation noise thinly over a huge bandwidth, like the same amount of peanut butter on a gigantic slice of toast, and then low pass filters most of it out before storing at 44.1k.

So, as a storage format, 44.1 kHz with an oversampled converter is completely fine. Whether anyone can ever hear a difference is a separate question, and the listening research on it is below. But it's important not to confuse the sound of a DAC which rolls off early at 44.1, and the inherent sound of CD quality itself.

The blind tests find small differences at most#

If I am going to say 44.1 is fine, I should be able to back it up, so I went through the controlled listening research on high resolution against CD quality.

The most practical test is Meyer and Moran's. They inserted a 16-bit/44.1 kHz converter loop into high-resolution playback, level-matched, on several systems, and asked people whether they could hear it switched in. At normal to loud listening levels, nobody could. The number of trials and the amount of training varied, the raw data is thin, nobody knows how much ultrasonic content the source recordings actually had, and the CD stage was a CD recorder of its day, not a modern DAC.

Other tests do find something. In Pras and Guastavino's blind ABX test, sixteen expert listeners could tell certain 44.1 and 88.2 kHz recording and downsampling conditions apart. Reiss pooled 18 experiments, over 400 participants and over 12,500 trials, and found a small but statistically significant ability to discriminate, stronger with training. Averaged across those studies it comes to about 52% correct, where guessing gets you 50%. That's statistically real but practically tiny.

In Waldrep's survey of over 400 people listening at home, most could not tell native high-resolution masters from the same masters converted to 16/44.1, although home listening is less controlled.

A detectable difference doesn't prove 44.1 is too little#

Hearing a difference is not proof that the extra bandwidth or bit depth caused it. 44.1 kHz leaves a narrow gap between 20 and 22 kHz for the filters, and filters differ in ripple, phase, ringing, alias rejection and ultrasonic noise. The same DAC often runs a different filter at 44.1 than at 96, so a "format" comparison can really be a filter comparison. Jackson, Capp and Stuart showed that this kind of mechanism is real: listeners could detect particular digital filters and quantisation changes. That shows particular processing choices can be audible, not that well-implemented CD quality falls short. Going the other way, Nittono played people white noise with and without everything above 22 kHz and found no response to the difference in the auditory cortex, and nobody could tell the two apart by ear either.

One explanation I find plausible is that older converters created artifacts at 44.1 that modern conversion avoids, which would account for some of the positive results. It hasn't been shown. That's just my untested hypothesis.

Properly implemented 16/44.1 playback is highly transparent for ordinary music. Some experiments find small discrimination effects, but none has isolated a benefit that comes from high resolution itself rather than from the filters and converters around it. What I can't say is that nobody could ever hear a difference under any conditions.

To settle this, you would need to take a native 24/96 master and properly convert it to 16/44.1, then back to 24/96 and perform double-blind ABX tests between the original 96k and the down/up sampled version with trained listeners. If it is not just the filters, and quality really is lost, the difference would still be audible.

As far as I know, nobody has done that yet.

Sample-rate conversion is basically a non-issue#

"Leave sample-rate conversion to the mastering engineer."

I flip-flopped a file between 44.1 and 48 kHz 100 times with a generic open-source resampler. The delta was about 40 dB down, and it sounded like crunchy white noise, not metallic chirping. After 1,000 round trips it was about 36 dB down, plus a DC offset.

That is not nothing. At 80 dB down I would have said scam, debunked; at 40 it is on the edge of being low enough down not to really care about but still actually there.

Premium sample-rate converters may well be better on paper but after doing that test, I think I'm going to be less concerned about sample-rate conversion going forward.

A digital copy is a perfect copy#

Claiming to hear a difference between a file and its digital duplicate in a DAW is egregious nonsense, whoever says it. Authority means nothing when it comes to facts.