OT: How can 44.1KHz possibly capture anything near the top of the spectrum?

[Dave Labrecque]

This is just dawning on me. And I don't have time to start Googling my way to an understanding. Experts, please chime in if you have the time.

If frequencies toward the top end are getting so few samples per wave (less than three samples we wavelength at 20KHz!), how can we get the accuracy we get? Filtering a 20KHz square wave can't be the answer. Can it?

[cgrafx]

https://www.youtube.com/watch?v=vrXGaFV1AmE

[jmh]

If frequencies toward the top end are getting so few samples per wave (less than three samples we wavelength at 20KHz!), how can we get the accuracy we get? Filtering a 20KHz square wave can't be the answer. Can it?

I don't qualify as an expert - as there may be things I'm overlooking. It's been a while since I looked into this.

We actually don't get accuracy. There is a great deal of noise in your 44.1k representation of 20k - but the noise portion consists of harmonic frequencies (of the simple 20k sin wave - which are) higher than 22.05k. The magnitude of the noise relative to signal level increases as you approach that frequency and becomes very significant. If playing back that irregular signal you (if you can) hear only the 20k signal as the harmonics would be inaudible. However that is not the end of the story. Sound doesn't usually consist of single sin waves, all of this high frequency energy can become audible under certain conditions like the low beat frequency that becomes audible when two guitar strings are tuned nearly - but not in tune. In a musical signal, these interactions could occur in the audible realm in bewildering ways - noise. The filtration at this step is essential to prevent the high frequency energy getting reproduced in physical space.

Building an analog filter with a steep enough curve to have 96db attenuation in the few semi-tones between 20k & 22.05k is difficult (if not impossible) without introducing phase-shifts and other distortion on your signal. DAC engineers have developed various tricks to get around this challenge such as oversampling where you digitally filter above 20k then if the DAC is, say 176.4k (4x - or much higher) rate, the harmonics are higher above the hearing spectrum, so your analog filter can be designed to less stringent requirements to achieve similar results with less artifacts.

[jmh]

cgrafx,

Just watched that video which was rather excellent. There was one part that got me thinking was when he generated the 3999 hz frequency. I think he generated the oscillating waveform by recording the output at a higher sampling rate. Why this occurred was that the anti-aliasing filter was not adequately steep enough to attenuate the high frequency component after un-digitizing the signal (and before filtration).

I think had he been playing back through a converter that utilized oversampling, the 3999hz signal would have also played back fine.

What he identified as aliasing was actually aliasing - but in most cases, the goal is to filter frequencies above the nyquist frequency (half the sample rate). DAC engineers figured out this shortcoming from the start. Rather than sample at 40k (for human range), an fudge factor is built in to provide sufficient bandwidth for the brickwall filtration to be sufficiently effective.

He actually made a caveat when generating the signal in the digital realm. Anyway, a trivial point to an informative video...

[jmh]

I was missing a point in the last comment - and that is in a 'real world' wav file - by that I mean one that was encoded by a quality ADC, you would not have a large amplitude 3999hz signal in an 8k wav. High cut filtration with the inclusion of that fudge factor is also a required portion of the encoding process. If any high frequency information over the nyquist frequency arrives at the sampling portion of the ADC (of which the preceding analog filter is a necessary portion), it will also (and undesirably) be encoded as part of the digital signal.

The DAC works with the definite expectation that there is absolutely no high frequency information contributing to the digital representation of the waveform (being incapable of reproducing anything over the nyquist frequency). Any distortion in the encoding step would now become noise.

An ADC can also incorporate methods like oversampling to allow the encoded signal to get quite close to the nyquist frequency, however it has no way to know the specifications of the DAC that will be re-constructing the signal at playback - thus any quality ADC would still have the same 20k cutoff frequency for a 44.1k wav. Also the typical goal of oversampling is not to slightly extend the bandwidth, but to enable the use of analog filters that are easier to construct and cause less distortion to the signal - because circuits do not necessarily work the way we would like them to - but the way the laws of physics requires them to.