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Old 30th August 2009, 12:43 PM   #1
oshifis is offline oshifis  Hungary
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Default NOS and sampling theory

Hi all,

I am thinking about how perfect can be the DAC playback in NOS mode. The problem is that the analog sample is taken periodically at a given time, and the sampling reads the instantenous signal value. So we know the analog value in 1/44100 seconds intervals, but we know nothing about it in between.
At playback and digital-to-analog conversion, we restore the sampled analog value, the next analog value, and so on. If the restored analog values were infinitely short pulses (giving back the analog value at A/D conversion, but nothing between the sampling points), we would get very low level analog signal. So we keep either the analog signal level unchanged until the next sample (0-order sample-and-hold at NOS), or we use some kind of interpolation between the samples. Neither gives back the original analog waveform. I think the best would be to get infinitely short analog pulses at playback, but how can this be realized?
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Old 30th August 2009, 12:47 PM   #2
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toggle the reference voltage of an r2r on&off,but (as always) 44.1 isnt much to begin with.
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Old 30th August 2009, 01:05 PM   #3
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You'll need an infinetly high sampling rate to produce an analog signal completely. There's no way to do that. Nyquist's theoreme says you'll need at least twice the sampling frequency of the highest freqency you'll want to digitalize. This also means that you'll need a low pass of some sort between the analog source and the ADC to prevent artifacts. Humans can only hear up to 20 kHz so a sampling rate of 44100 Hz would in theory suffice for 22.5 kHz, more than most humas can ever hear.

You'll need some sort of interpolation (i.e. a low pass) at the DAC's output because short pulses "contain" almost "all" frequencies as can be proven by a Fourier transformation.
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Old 31st August 2009, 07:48 AM   #4
berni8k is offline berni8k  Slovenia
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Yes this is why audio ADCs have low pass filters even built in the chip it self also most audio ADCs will oversample the signal and then join the samples together in to the actual sample that is sent out the I2S or whatever you use.

DACs also use various methods like filters and oversampling to reproduce a more accurate signal
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Old 2nd September 2009, 07:54 PM   #5
4real is offline 4real  Netherlands
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Look at it like this: take sheet of metal with small holes in it. From near by, you can see the holes just fine, but from far away, you just see a sheet of metal a little of colour, but no holes.

So can you see the difference between the sheet with the holes, or a sheet without holes when they look the same from a distance? Probably not...

The same with the samples: what is inbetween the samples is irrelevant, since it is of a higher frequency that humans can hear.

The only thing that does matter is the reconstruction of the analog signal. That needs to be done correctly, either NOS of OS....
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