Aliasing, Dither, A/D D/A conversions

[Schwarzenyaeger]

I've got some questions about AD and DA conversions.

I read an explanation on it that showed a primitive quantization based on a 3-bit system to show a close of up the sampled voltages being adjusted the binary values. Is there somewhere where I could hear what this sounds like? Should I imagine the tone noticeably jumping in frequency when it is adjusted to the least and most significant bits?

One of the first steps of conversion is that a low-pass filter is applied to the signal to get rid of distortion caused by aliasing. The aliasing frequency is the sampling freq. minus the violating freq.
So if we sampled at 44.1kHz and our signal had a 26 Hz frequency in it, we'd end up with distortion at about the 18.1 kHz area, yes?

Also, if we assume that 20 kHz is the maximum freq. that we can hear and we're sampling at 44.1 kHz (Does anybody really sample below this?), we'd end up with a distortion at 24.1 kHz, which would (presumptuously) be irrelevant for us anyhow since we can't hear in those frequencies.
Still, might the waveform still be altered so much that it would change noticeably for us?

 

[Mo Facta]

I've got some questions about AD and DA conversions.

I read an explanation on it that showed a primitive quantization based on a 3-bit system to show a close of up the sampled voltages being adjusted the binary values. Is there somewhere where I could hear what this sounds like? Should I imagine the tone noticeably jumping in frequency when it is adjusted to the least and most significant bits?

You can do this by creating an 16-bit sine wave and attenuating it just before the LSB, around 93dB. You need to turn up your speakers all the way to hear it. Then attenuate it towards infinity and you'll hear the chattery effect of the LSB being traversed. You could also try it with an 8-bit sine wave around -43dB. It might be easier to hear. If you apply dither, you can hear well below the LSB.

One of the first steps of conversion is that a low-pass filter is applied to the signal to get rid of distortion caused by aliasing. The aliasing frequency is the sampling freq. minus the violating freq.
So if we sampled at 44.1kHz and our signal had a 26 Hz frequency in it, we'd end up with distortion at about the 18.1 kHz area, yes?

Yes, but the low pass filter eliminates the artifact and it's harmonics, which is the point of anti-aliasing. Remember that the distortion or artifacts introduced by aliasing is not at a single frequency but rather folds back in a sort of harmonic series into the usable band.

Also, if we assume that 20 kHz is the maximum freq. that we can hear and we're sampling at 44.1 kHz (Does anybody really sample below this?), we'd end up with a distortion at 24.1 kHz, which would (presumptuously) be irrelevant for us anyhow since we can't hear in those frequencies.
Still, might the waveform still be altered so much that it would change noticeably for us?

The reason why the sampling rate is 44.1kHz is to accommodate the slope of the low-pass anti-aliasing filter. But like I said, even if an artifact shows up at 24.1kHz it will still fold back in a series into the usable band.

Cheers

 

[Mo Facta]

To illustrate my point, here's a plot of a signal showing quantization noise, harmonic distortion and aliasing effects. As you can see, the aliasing distortion shows up at multiple points in the spectrum despite originating above 20kHz.



Cheers