This is where the distinction between aliasing and quantization errors that I mentioned earlier was first pointed out to me. It took me years to ultimately understand it, but that understanding started here. It also helps you realize that analog and digital audio really are two sides of the same coin with different tradeoffs. The explanation of the Nyquist theorem is a little light here, but it’s more than enough for what you need to know if your focus is synthesis and not DSP.

But if you must know more about Nyquist...

If you want to save about 4 years of me ramming my head against a wall before seeing an interview with a DAC designer helped me understand what the difference is between aliasing and what quantization error is, then read on.

As the article says, Nyquist states that any signal can be accurately sampled and reconstructed as long as you sample the signal at least twice as fast as the highest frequency in the signal. HOWEVER, the article here kind of glosses over the fact that this is true if and only if you assume that two things are true:

  1. You have a perfect brickwall filter on the input and output A/D and D/A converters - which don’t exist in the analog domain so that one’s an impossible condition to fulfill, and even digital filters are still a work in progress to some extent - AND

  2. You have an infinite bit depth for each sample - which is also impossible to do because then a single sample would take up an infinite amount of storage space (plus there’s a whole equivalency of digital bits to analog noisefloor and the truth is that the best low noise systems in the world today can function at less than 24 bits of resolution in terms of noise, and those aren’t being used in audio I promise you)

So just saying that the sample rate of all digital audio today is greater than 40khz so therefore all digital audio is perfectly lossless is definitely oversimplifying the challenges that were and are still present in creating an accurate and artifact-free piece of digital audio. It’s totally a solvable problem with today’s technology, but it doesn’t happen with every DAC and ADC out there (like the 10 cent ones in most phones) and there is more than one way to skin this proverbial cat. I don’t have fancy $10,000 A/D and D/A in my studio, but I ask my clients for 32-bit files and use the best dither I can to give them the best 24-bit masters possible, with oversampling in all the key calculations (which is a brute force method of anti-aliasing, but it’s all we have in audio that I’m aware of). With that, I can be reasonably certain that I’m not going to add any aliasing and any quantization error will be drowned out by the noisefloor of any potential playback system - Nyquist rides again.

Boy do I have good news for you, click the spoiler tag :wink:

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