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Can a standard CD reproduce a 12kHz square wave?

Q: “I recently read an article that said a standard CD couldn’t reproduce a 12 kHz square wave – it turns it into a sine wave, but a DSD recording could. I thought CD’s could reproduce up to 20 kHz. Does this have something to do with it being 16-bit?”

A: This really has more to do with the sample rate than the bit depth per se. When storing audio at, say 44.1 kHz, it is not really possible for the electronics to differentiate between a sine or square wave at above 10 kHz. For reasons that are too involved to get in to here, the electronics in the D/A Converter will assume it’s a sine wave even if the data is somehow captured as a square wave. This has to do with the properties of the reconstruction filters and is part of what makes a 44.1kHz sample rate work on audio of higher frequencies – all the way up to 20 kHz – just as well as it does on audio down at 20 Hz (grossly oversimplified explanation, but…). The difference between a sine and square wave is harmonics. The first harmonic of a 12 kHz square wave is at 24 kHz, and all the subsequent harmonics are above that. Consequently a recording that can’t capture audio up to 24 kHz, such as with a sample rate of 44.1 kHz, will not capture any of the harmonics that make a square wave square. The result of stripping a square wave (or any complex waveform) of all of its harmonic information is a sine wave at the fundamental frequency.

Because DSD captures, stores, and reproduces the audio data at a very high sample rate (in the megahertz range) it can differentiate between the two waveforms at that frequency (and higher). It is worth noting that most of the A/D converters in use today for PCM based systems initially capture at equally high sample rates (oversampling), but much of that extra information is thrown away (decimation) prior to storage, which leaves us with our 16 to 24 bit words at a sample rate of choice (44.1 kHz, 48 kHz, 96 kHz, etc.) stored as PCM data.

Now, before you go telling all your friends why standard CD is deficient and DSD/SACD is clearly superior keep in mind that this matters primarily if you believe humans can hear above 20 kHz (and that you have audio equipment capable of accurately reproducing these higher frequencies)! Think about it. The difference between a 12 kHz sine wave and a 12 kHz square wave is harmonics – the sine wave has none, only the fundamental. Most people believe our ears filter out information above 20 kHz (hence the well established range of hearing (20 Hz – 20 kHz)). In that case the 12 kHz sine and square waves – if they could really be reproduced and amplified properly (which is no easy task) – would sound the same to us anyway.

Obviously there’s a strong movement in audio these days to try to capture and accurately reproduce sound above 20 kHz. How much weight you give to the hearing beyond 20 kHz concept is up to you. If, for some reason, you decide you want to be able to reproduce square waves at 12 kHz and above then you need to record at a sample rate higher than 44.1 kHz. Even at a sample rate of 48 kHz you’d barely be able to get the first harmonic, which wouldn’t be nearly enough to capture it as a square wave. A sample rate of 192 kHz gets you closer… Of course, to get a 100% “true” square wave an infinite sample rate would be required, but that’s going even further off in the weeds than we already are here.

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