Correct, nothing played back at original sampling rate will alias.
It _won't_ alias; it may already _have_ aliased when sampled in the first place.
Aliasing occurs when sampling.
When you digitalize (ADC), you are sampling. When generating a waveform mathematically, you are sampling the mathematical function at the very moment you compute its value at discrete points.
When you play back a signal at a different speed than the original, you are _resampling_ it, that is, theorically, interpolating it and then sampling it again, and it is the sampling stage, not the interpolating one, that produces the aliasing.
The interpolation, since it cannot be an ideal interpolation, may introduce other noises or artifacts, not aliasing as far as I can see.
Wait, so aliasing occurs when the signal is sampled? So if i have this patch :
[adc~] | | | [dac~]
and if the signal already contains frequencies above the Nyquist, i will get aliasing? I generally use my electric guitar as the main audio source, and i'm assuming that it has lots of harmonics beyond the Nyquist frequency (especially when the strings are new), yet i never noticed any distortion of any sort. I might have a bad ear... Or is it just that the energy of the upper harmonics is too low for me to notice when they cause aliasing?
Pierre
2010/4/1 Matteo Sisti Sette matteosistisette@gmail.com
Correct, nothing played back at original sampling rate will alias.
It _won't_ alias; it may already _have_ aliased when sampled in the first place.
Aliasing occurs when sampling.
When you digitalize (ADC), you are sampling. When generating a waveform mathematically, you are sampling the mathematical function at the very moment you compute its value at discrete points.
When you play back a signal at a different speed than the original, you are _resampling_ it, that is, theorically, interpolating it and then sampling it again, and it is the sampling stage, not the interpolating one, that produces the aliasing.
The interpolation, since it cannot be an ideal interpolation, may introduce other noises or artifacts, not aliasing as far as I can see.
-- Matteo Sisti Sette matteosistisette@gmail.com http://www.matteosistisette.com
Pierre Massat escribió:
Wait, so aliasing occurs when the signal is sampled? So if i have this patch :
[adc~] | | | [dac~]
and if the signal already contains frequencies above the Nyquist, i will get aliasing?
Well obviously (or not) a real-world ADC (e.g. a sound card) always includes an analog lowpass filter that cuts off the frequencies above Nyquit before actually digitalizing!!!!
However, when you sample a mathematically generated signal, such as:
[phasor~ 1000] | [dac~]
then no filtering occurs, and aliasing does occur.
More evident:
[osc~ 40000] | [dac~]
Pierre Massat a écrit :
Wait, so aliasing occurs when the signal is sampled?
yes
So if i have this patch :
[adc~] | | | [dac~]
and if the signal already contains frequencies above the Nyquist, i will get aliasing?
yes, it will. so usually, your sound card have an analog filter prior to digital convertion in order to reduce aliasing.
cyrille
I generally use my electric guitar as the main audio source, and i'm assuming that it has lots of harmonics beyond the Nyquist frequency (especially when the strings are new), yet i never noticed any distortion of any sort. I might have a bad ear... Or is it just that the energy of the upper harmonics is too low for me to notice when they cause aliasing?
Pierre
2010/4/1 Matteo Sisti Sette <matteosistisette@gmail.com mailto:matteosistisette@gmail.com>
> Correct, nothing played back at original sampling rate will alias. It _won't_ alias; it may already _have_ aliased when sampled in the first place. Aliasing occurs when sampling. When you digitalize (ADC), you are sampling. When generating a waveform mathematically, you are sampling the mathematical function at the very moment you compute its value at discrete points. When you play back a signal at a different speed than the original, you are _resampling_ it, that is, theorically, interpolating it and then sampling it again, and it is the sampling stage, not the interpolating one, that produces the aliasing. The interpolation, since it cannot be an ideal interpolation, may introduce other noises or artifacts, not aliasing as far as I can see. -- Matteo Sisti Sette matteosistisette@gmail.com <mailto:matteosistisette@gmail.com> http://www.matteosistisette.com
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Alright, i got it! Thanks everybody!
Pierre
2010/4/1 cyrille henry ch@chnry.net
Pierre Massat a écrit :
Wait, so aliasing occurs when the signal is sampled?
yes
So if i have this patch :
[adc~] | | | [dac~]
and if the signal already contains frequencies above the Nyquist, i will get aliasing?
yes, it will. so usually, your sound card have an analog filter prior to digital convertion in order to reduce aliasing.
cyrille
I generally use my electric guitar as the main audio source, and i'm
assuming that it has lots of harmonics beyond the Nyquist frequency (especially when the strings are new), yet i never noticed any distortion of any sort. I might have a bad ear... Or is it just that the energy of the upper harmonics is too low for me to notice when they cause aliasing?
Pierre
2010/4/1 Matteo Sisti Sette <matteosistisette@gmail.com mailto: matteosistisette@gmail.com>
> Correct, nothing played back at original sampling rate will alias.It _won't_ alias; it may already _have_ aliased when sampled in the first place.
Aliasing occurs when sampling.
When you digitalize (ADC), you are sampling. When generating a waveform mathematically, you are sampling the mathematical function at the very moment you compute its value at discrete points.
When you play back a signal at a different speed than the original, you are _resampling_ it, that is, theorically, interpolating it and then sampling it again, and it is the sampling stage, not the interpolating one, that produces the aliasing.
The interpolation, since it cannot be an ideal interpolation, may introduce other noises or artifacts, not aliasing as far as I can see.
-- Matteo Sisti Sette matteosistisette@gmail.com mailto:matteosistisette@gmail.com http://www.matteosistisette.com
Pd-list@iem.at mailing list UNSUBSCRIBE and account-management -> http://lists.puredata.info/listinfo/pd-list
The interpolation, since it cannot be an ideal interpolation, may introduce other noises or artifacts, not aliasing as far as I can see.
There's two parts to it, aliasing (stopband) and non-flat frequency response (passband). Since interpolation of uniform samples is linear, what we see in interpolation is the introduction of other frequencies.
The intermediate stage between sampling and playback is a dirac-delta comb which takes our original spectrum and copies it centered at n*fs for all n. It's an infinitely long spectrum. The interpolation is a linear convolution operator on the dirac-delta comb. The distortion we observe comes from non-flat frequency response in the passband (0 to Nyquist) and from the copied spectra above the Nyquist frequency.
Now, we hardly realize its there, because we don't represent the intermediate stages. We only need to get the output at a series of discrete points, so we only need to evaluate the convolution at those discrete points.
Chuck
Charles Henry escribió:
The interpolation, since it cannot be an ideal interpolation, may introduce other noises or artifacts, not aliasing as far as I can see.
There's two parts to it, aliasing (stopband) and non-flat frequency response (passband).
Well this seems o be a matter of terminology. I think you call "aliasing" a wider class of artifacts than I was taught to call "aliasing".
Matteo Sisti Sette escribió:
Charles Henry escribió:
The interpolation, since it cannot be an ideal interpolation, may introduce other noises or artifacts, not aliasing as far as I can see.
There's two parts to it, aliasing (stopband) and non-flat frequency response (passband).
Well this seems o be a matter of terminology. I think you call "aliasing" a wider class of artifacts than I was taught to call "aliasing".
Oh no, maybe not. I read your explanation more carefully and of course, the non-perfectness of the interpolation process (i.e. its non-zero frequency response in the stop band) is responsible for the persistence of attenuated copies of the original spectrum at multiples of the original sampling rate, which then appear aliased into the passband when the signal is sampled again at a different rate.
This is what's going on when discontinuities in the interpolated signal cause noise at high frequencies, isn't it?
On Thu, Apr 1, 2010 at 11:11 AM, Matteo Sisti Sette matteosistisette@gmail.com wrote:
Matteo Sisti Sette escribió:
Oh no, maybe not. I read your explanation more carefully and of course, the non-perfectness of the interpolation process (i.e. its non-zero frequency response in the stop band) is responsible for the persistence of attenuated copies of the original spectrum at multiples of the original sampling rate, which then appear aliased into the passband when the signal is sampled again at a different rate.
This is what's going on when discontinuities in the interpolated signal cause noise at high frequencies, isn't it?
Yes, that's my interpretation and explanation of it. It works out nice and linear in the spectral domain *if* we can make that intermediate step with the Dirac-delta comb which copies the spectrum. Then, *all* the deviations in the reconstructed signal come from the places where the spectrum does not match the ideal response.
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Charles Henry -
cyrille henry -
Matteo Sisti Sette -
Pierre Massat