The model cycles aliases nicely.

I’m a Discordian Pope and hereby ordain you a Certified Synthologist!

Death Note in Japanese, probably.

Technically everything digital is also analog. I don’t even like music or synths, I’m only here for the amazing pedantry opportunities.

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The best thing about directness is that it doesn’t bait people into angry concern :stuck_out_tongue:

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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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giphy (4)

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That explaination is like a Dan Worrall video. I know I’ve learned something, I just couldn’t tell you exactly what it is I’ve learned.

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I suspect you’re joking, but in case you’re not, here’s a restatement.

There’s a theorem (Nyquist, Shannon, Whittaker) that says that if you have a signal (say, graphed with time on the x-axis and amplitude on the y-axis) that has no frequency components higher than some bound B (say 20kHz), then the signal can be reconstructed by samples at a rate 2B or higher.

But the theorem assumes that the samples are exact and not approximations, as is the case in practice with digital sampling (because the y-value is from some finite set, like 0 to 65535). This difference is quantization. There are also effects due to the imperfections of physical A/D and D/A converters.

If the samples are taken at a rate less than 2B, the reconstruction can have spurious frequencies that were not present in the original signal, because there isn’t a unique solution to the problem of reconstructing the original signal from the inadequate samples. This is aliasing.

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sorry , i still don’t understand what is this topic about :smile: but it doesn’t metter

Here’s a short and sweet mini lecture on the Shannon/Nyquist theorem:

I like this professor’s channel. Great stuff in there

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Great video, thanks for sharing.

The Nyquest Theorem essentially states that CD quality (16bit 44,100hz) should be enough to clearly represent any audio recording / processing up to 22,050hz, however things like bit depth also have an influence, plus through personal experience higher sampling rates can make a difference to digital audio quality output.

Thank you everyone for the interesting responses to my original post.

Maybe a clearer title to the post might have been more helpful, as in posed as more of a question instead of appearing like a statement, nevertheless thanks again for all the input.