SouthSIDE Glen
independentrecording.net
Respectfully, Tim, this is just the kind of misunderstanding/mis-explanation that makes this subject so dicey. What you're saying is kind of right, but it's equally kinda wrong in a couple of important ways.
Any single frequency tone can *only* be a sine wave. There is no such thing as a complex wave at 20kHz (or any other frequency, FTM.) If you're looking at a 20kHz wave that's complex or irregular in that it has bumps in it, those bumps, by definition, are at higher frequencies, and the mix of frequencies is what creates the complex waveform. But it's NOT a "complex 20kHz waveform"; it's not a distortion at/of 20KkHz. So, yes, if you're looking at the wave the distortions on it may not be reproduced, but all that means is that frequencies above 20k will not be reproduced, which we already know. But the actual 20k content will remain untouched.
Other "simple" geometric waveforms such as sawtooth waves, square waves, etc. are not pure frequencies, they are compound signals built from sine waves of greater frequencies, and simply repeat their pattern of higher frequency wave combinations at the observed frequency. This is why George's sawtooths (and almost all real sawtooths) look awful and why aliasing is so difficult to avoid in soft synths at lower sample rates, because they require higher frequencies to generate. By definition, a "20k sawtooth" is not a bandwidth-limited signal limited at 20k.
But, except in George's lab, in music and real life one is virtually never going to find 20kHz sawtooths or square waves (sawtooths and squares are hard enough to find at *any* frequency, except in synths), simply because they would require so much in the way of constituent ultrasonic and hypersonic wavelets to create, and Mom Nature just is not into that bag. And as George said, if you have sounds with fundamentals above 10k or certainly 15k, such as a 10 or 15k sawtooth, you've got more problems than Nyquist to worry about
.And yes, the Nyquist theory *does* state that it will reproduce 20k *exactly* as long as the entirety of the signal is of limited bandwidth. Excluding physical limitations in actually implementing the theory in physical components, the theory proves that doubling the sample rate of the highest frequency in a limited bandwidth signal will reproduce that signal with no information loss. "With no information loss" is IT-speak for what we in the audio world call lossless, it means 100% accuracy.
Where we have the biggest problems in physically implementing the theory is in actually limiting the signal bandwidth and in the accuracy of the sample timing. In today's technology and business market, quality bandwidth limiting and sample clocking are not ubiquitous. This is what introduces the HF errors (some more audible, some less so) we actually get from our converters, not any inaccuracies in Nyquist itself.
G.
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…you can pull up ANY audio magazine (Mix, EQ, Tape Op, EM, etc)...and I guarantee you will find most articles/interviews where the interviewees (I'm going to assume they are "pros" since the magazine decided to interview them) are almost always talking about using the higher sampling rates and deeper bits. I have yet to see one point-blank say they are not….though they may be saying one thing for the interview and doing something different in the studio???
