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Representing frequency of n Hz needs sampling rate >2n Hz, not =2n, From: Badly drawn waveforms vs. the audio that’s actually output/93496
icstm
post Feb 16 2012, 11:56
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QUOTE (Wombat @ Feb 14 2012, 16:47) *
Hehe, shortly after posting here there was a nice picture posted that tells the whole story smile.gif
where is the nice picture? That is really important to share!
The whole point of FFTs is that using if I am drawing what the FFT has stored in the time domain (ie if I am drawing sine waves) then I only need a couple of points to draw a PERFECT reproduction!
That is one of the biggest issues that people need to first get their head around when understanding digital audio.

when you see an irregular wave, what you need to ask your self is "what regular wave would I have to add together (ie what frequencies would have to be simultaneously present) to create the irregular wave I see”

so an irregular sine wave is in effect a regular one augmented with higher or lower frequency wave to varying amplitude.

Each of the additional waves only needs a couple of points to represent their frequency. As per usual it appears that CA article really doesn’t get what the Nyquist theorem is saying…

However it is right when it says that it is possible for a perfect 8kHz signal sampled at 96kHz to sound better than sampled at 192kHz if the DAC has trouble with 192kHz (ie is a cheaper DAC). The whole point is that a perfect DAC will produce a perfect 8kHz signal when sampled at 16kHz. But the quality of the output has little to do with the conversion and more to do with the analogue output. One of my earliest posts on HA was asking about DACs in AVRs as I am keen to understand the practicalities on consumer grade stuff.

QUOTE (my earlier post)
What determines a good DAC?
I assume the main issues are post the conversion to analogue and that these issues are the usual ones that impact an amp (pre or power), such as clean power supply, suitable analogue filters, etc.
However are there any differences in the digital part of the amp (such as up/over sampling circuits, or the conversion itself)?
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DonP
post Feb 16 2012, 17:13
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QUOTE (icstm @ Feb 16 2012, 06:56) *
Each of the additional waves only needs a couple of points to represent their frequency. As per usual it appears that CA article really doesn’t get what the Nyquist theorem is saying…
....
The whole point is that a perfect DAC will produce a perfect 8kHz signal when sampled at 16kHz.


This key mistake in citing the Nyquist theorem leads to no end of potential trouble. The sampling frequency has to be greater than 2x the maximum signal frequency you want to reproduce.
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pdq
post Feb 19 2012, 05:16
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If you know that the waveform consists of a single unvarying sine wave whose frequency is less than half the sampling rate then a fairly small number of data points are required to determine the waveform's frequency and amplitude.

On the other hand, if there are multiple frequencies or the amplitude is not constant then you will need a longer observation period.
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2Bdecided
post Feb 20 2012, 12:32
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QUOTE (pdq @ Feb 19 2012, 04:16) *
If you know that the waveform consists of a single unvarying sine wave whose frequency is less than half the sampling rate then a fairly small number of data points are required to determine the waveform's frequency and amplitude.

On the other hand, if there are multiple frequencies or the amplitude is not constant then you will need a longer observation period.
For any arbitrary waveform, correctly sampled, you can reconstruct all frequency components under fs/2 perfectly - but you need an infinite number of sample points.

If we consider quantisation it's far worse.

If however we consider that we don't care about anything beyond ~120dB down, it becomes easily realisable in 1990s-style DSP.

I know everyone here knows this. That computeraudiophile thread is just a parallel universe which I don't want to enter wink.gif

Cheers,
David.
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