The initial discussion was if cd rate was sufficient. Cymbals were introduced as an offending signal.
My statement is in essence...
1. When a sine is envelope modulated, there will be sidebands generated. This was my example of 20k modulated by 2.5k.
2. One sideband will be below, the second above the primary signal. And they will show the same spectral shape as the modulating signal.
3. If the primary signal is high enough in frequency, a modulating envelope may produce sidebands where the upper sideband will exceed the filter cutoff. If that occurs, the consequence will be that the envelope of the filter output will be changed from that of the original.
4. A high bandwidth signal such as a cymbal will have envelope modulated components we can hear, producing sidebands above and below primary, as well as ultrasonic components with both upper and lower content. Filtering the upper part out above Fs will still alter the final reproduced envelope.
Using a cymbal recording to evaluate is a mixed bag.. Yes, something is being filtered out, hence the Gibbs differences. But it is impossible to know what is exactly being lost, as it is impossible to understand the instantaneous frequency content of a cymbal.
Examination of how a cymbal actually develops it's sound is, um, impossible. It is a combination of three wave types propagating the disc, three sound velocities, and non linearities out the wazoo. And, edge boundary reflections that are timed based on location of impact, cymbal shape...hopeless..The best we can hope for is to test our filter system using well known and characterized functions.
My example of the sine modulated by a sine, or by an exponential, are the easy types. Unfortunately, an exponential does not have one frequency, nor is it time invariant. FFT analysis does not easily provide an instant by instant spectra, so cannot tell us what part of the waveform will be filtered, just what frequencies.
The Gibbs envelope does. It can show us when the product goes above Fs.
That is why I earlier stated that using the Gibbs envelope is the best way to spot when content is pulled.
And, looking at the Gibbs envelope with cymbals, it is clear the decision to stop at 44k was not perfect... Now, higher rates are not so much a technical challenge..
Jn
Ps.. And no, scottjoplin, it wasn't about ITD...
