No you didn't. You have said, but have yet to show how that impulse is band limited as you claimed. Exactly what band limited it? And what is the non-band limited version looks like if that is the case?
This has nothing to do with the discussion at hand. We are talking about the bandwidth of the excitation signal. In this case, the impulse.
Yes I did. And NTK's post, which you presumably read, shows it again. The continuous-time inverse Fourier transform of the rectangular function is a normalized sinc function, and a normalized sinc function aligned to a sampling instant is a Kronecker delta function.
Likewise. This discussion is going nowhere if you refuse to read what I wrote or the references I linked. What you are disputing is proven mathematics that can be found in any digital signals text or in the relevant Wikipedia pages.
JCally JM6 and Samsung dongle can do that, although as per their response (third graph), JCally will heavily attenuate that 20 kHz signal and Samsung dongle will produce some images for signals slightly above 20 kHz. Here's 20 kHz @ 44.1k played through them and captured with RME Adi-2 Pro, 13 dBu @ 96k, cursor at 24 kHz:
Yes, that's nicely explained (imo) in https://www.dspguide.com/ch3/2.htm , starting from paragraph:
Of course it won't hurt to read that chapter from the beginning
There is nothing whatsoever about the topic under discussion in that chapter or what you quoted from it. Nothing has been "sampled." Nothing started in analog/continuous domain. A file was created digitally and hence, bypassed both of those stages and with it, violates sampling theorem. To understand that, you need to have an understanding of impulse function by itself and what it represents. If you are confused about that and think it is band limited, there is no hope of you ever figuring out anything about signal processing.Yes, that's nicely explained (imo) in https://www.dspguide.com/ch3/2.htm , starting from paragraph:
Of course it won't hurt to read that chapter from the beginning
(one slightly annoying thing is that the description references figure 3-5 which is in the next chapter)
The answer to that question is "it's indeterminant" at pi. Consider what the phase of the spectrum does at -1,0 . For testing a DAC filter it's ok, but it presents a problem in the same way that half-band filters in a DAC upsampling/ADC downsampling chain create a problem with aliasing/imaging reduction. Don't ask me to explain that, Ingrid Debauchies and Rob Calderbank are required to explain that. It's tied into the regularity theorem for wavelets and biorthogonal wavelets. I simply remember that it's resolved by having at least 1 zero at pi, which means you can never MAKE that signal from a continuous system that's being sampled, and that you'd better have at least one zero or zero pair at pi of the final (smallest) sampling rate of the actual system. Generation in the sampled domain of course allows you to make this signal, but it's an oddity at the very least.
err, yeah. d'oh.
Thank you! Your post can't make it any clearer the point that this signal with only a single non-zero pulse (the Kronecker delta function) is entirely "artificial" in nature.
If even an idealized ADC cannot create that signal, then you have your answer.
That's like saying a car should go just as fast backward as forward.... Just because test signals can all be created by a computer doesn't mean they are all just as applicable to the system under test. Signals that fundamentally violate sampling theorem must be used with caution and full knowledge of what you are doing.
