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9th May 2005, 12:23 PM  #1 
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44kHz samling freq. gives 1 sample per halfwave for 20kHz sine ?

9th May 2005, 12:59 PM  #2 
diyAudio Member

That's correct.
Even though it looks hideous, theoretically* your 20KHz sine wave is perfectly represented at a 44.1KHz sampling rate. *neglecting 16bit quantization noise, zeroorderhold attenuation, system noise/distortion, assuming a perfect reconstruction filter to eliminate images, etc. 
9th May 2005, 01:10 PM  #3  
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Re: 44kHz samling freq. gives 1 sample per halfwave for 20kHz sine ?
Quote:
\Jens 

9th May 2005, 02:14 PM  #4  
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Re: Re: 44kHz samling freq. gives 1 sample per halfwave for 20kHz sine ?
Quote:
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 DA 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
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9th May 2005, 03:23 PM  #5 
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I don't like it either, You can analyze frequency content from real data, but the reverse is not totally possible. DVD audio and some newer stuff are going to higher sample rates. I spersonnaly like 10 samples per sine wave, but there might be some other theory indicating that possible increasing the number of bits provide more significant improvements.
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9th May 2005, 06:18 PM  #6  
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Quote:
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
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10th May 2005, 08:12 AM  #7 
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If you are trying to reconstruct a simple sine wave, I suppose 2 samples will do as long as you don't care about any phase shift, because there is no way to determine where in the sine wave the sample took place. Thus you might come up with a smaller amplitude sine wave with a phase shift.
By the way, I am referring to sampling the analog real world signal, not just oversampling existing digital data.
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10th May 2005, 01:08 PM  #8 
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Um, no. You have very good phase resolution. In fact if you have a full height (i.e. +32,767 to 32,768) sine wave at 20kHz you have a phase resolution of well under 1/100th of a degree. At lower amplitudes it drops proportionally. Only at an amplitude of the LSB do you lose most of your phase resolution. Think about the amount of information in the stream.

10th May 2005, 04:10 PM  #9  
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Quote:
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.
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10th May 2005, 04:43 PM  #10  
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That is why the postDAC filtering is AN INTEGRAL PART of the conversion process. It only works as advertised if you include the filtering. Jan Didden
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