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- 44kHz sampling freq. gives 1 sample per halfwave for 20kHz sine ?

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- Thread starter Bernhard
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Even though it looks hideous, theoretically* your 20KHz sine wave is perfectly represented at a 44.1KHz sampling rate.

*neglecting 16-bit quantization noise, zero-order-hold attenuation, system noise/distortion, assuming a perfect reconstruction filter to eliminate images, etc.

Bernhard said:So resolution at 20kHz is only one bit out of 16bits for each halfwave ?

You still have 16 bit resolution, but only 1 sample (with 16 bit resolution) for every half wave.

\Jens

JensRasmussen said:

You still have 16 bit resolution, but only 1 sample (with 16 bit resolution) for every half wave.

\Jens

Indeed, in fact you should look at it as 2 samples each 16 bit for a 20kHz wave. The reconstruction filter, which is an integral part of the D-A conversion process, will make sure you get a nice sine wave. That is the background behind the Nuiquist criterium: to reconstruct a given freq you need at least 2 samples to nail down the level and phase, so you can convert frequencies up to half the sample rate.

Jan Didden

soongsc said:

Well, 44.1 or 192kHz gives the same reconstitued sine at 20kHz from 2 samples or 6 samples or what have you. The difference lies in the noise spectrum. The higher you sample, the higher the noise turns up in freq, so the easier it is to filter out. At 44.1 kHz you would need a brick wall filter at 22kHz to get rid of all the noise, and brick wall filters don't exist in analog. They do now, of course, in DSP implementations. So, there are different issues, that are related, but not interchangeable.

But, how counterintuitive it feels, 2 samples will nail ANY wave, provided you take care of the postfiltering.

Jan Didden

By the way, I am referring to sampling the analog real world signal, not just oversampling existing digital data.

Originally posted by Francis_Vaughan

Let me try and understand this. You have an analog signal at 20K that you sample at 44.1 Hz 16 bits. You can only use one cycle to determine the exact shape of the original wave because the next cycle is a different part of music. Since there is no way to determine whether you sampled the peaks or other locations.. Oh! I see! the difference amplitude in the two samples help you determine the lowest frequency possible, so the theory works.

Now since you only have 16 bits, you really need higer bit resolution or some sort of analog filter to smooth the discrete data into continuous wave. I wonder if sound cards do this kind of processing or not, or whether it's done in the software.

Originally posted by soongsc[snip]Now since you only have 16 bits, you really need higer bit resolution or some sort of analog filter to smooth the discrete data into continuous wave. I wonder if sound cards do this kind of processing or not, or whether it's done in the software. [/B]

That is why the post-DAC filtering is AN INTEGRAL PART of the conversion process. It only works as advertised if you include the filtering.

Jan Didden

Bernhard said:So how good work the mostly unfiltered TDA1543 non-os dac ?

I don't know exactly what the 'mostly unfiltered' DAC is, but if you skimp on the filter, you get the noise in the upper spectrum in your signal, the familiar staircase components.

Perceptually, if you are not experienced in recognising it, you will get the impression that your system is bright, clear and analytical. But, that's the perceptional side of it.

Jan Didden

Bernhard said:If you have 2 samples @ 20kHz you have 20 samples @ 2 kHz and you already can see the stairs on a scope.

Oh yes, that is also the reason why it is so difficult to find a good opamp for an I/V converter. That opamp has, in theory, to respond to those staircase steps with the risetime of that signal. Not easy.

Jan didden

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