KVR Audio

Dúnedain · Post by **Dúnedain** » Mon Dec 05, 2016 2:03 pm

When you convert an analog signal to a digital signal at a sample rate of say 44100 Hz you need to filter all frequencies above 22050 Hz before sampling, otherwise you will get aliasing. However filters are not perfectly steep but have a range were they work. The smaller the range the harder it gets to produce them. So if you would sample at 44100 Hz with a filter with a slope which starts at say 18000 Hz and ends at 22050 Hz you will remove all frequencies above 22050 Hz, but also reduce frequencies above 18000 Hz as well. You don't want that, you only want remove frequencies above say 22000 Hz.

So what does a manufacturer like RME, they use a very cheap filter to sample at a very high rate, talking about MHz here, to avoid aliasing. Then after that they use a digital filter (which is very cheap to implement), which can have much steeper slopes than cheap analog filters, to prevent aliasing when downsampling to say 44100 Hz or 96000 Hz.

That is the aliasing for A -> D -> D. But what about the aliasing of the oscillators in subtractive soft synths everybody is talking about?

If I have a saw (in discrete time of course) which has linear increments and at the highest point drops immediately to the lowest point (where it starts all over agian), then how do I have aliasing?

.jon · Post by **.jon** » Mon Dec 05, 2016 2:23 pm

You're confusing the waveform, a graph used to represent the periodic oscillation, with the frequencies the signal contains.

Dúnedain · Post by **Dúnedain** » Mon Dec 05, 2016 2:25 pm

.jon wrote:You're confusing the waveform, a graph used to represent the periodic oscillation, with the frequencies the signal contains.

How do I confuse them?

.jon · Post by **.jon** » Mon Dec 05, 2016 2:28 pm

The waveform graph, where the sawtooth assosiation comes from, displays amplitude against time. Not frequencies.

Dúnedain · Post by **Dúnedain** » Mon Dec 05, 2016 2:28 pm

.jon wrote:The waveform graph, where the sawtooth assosiation comes from, displays amplitude against time. Not frequencies.

I know.

exmatproton · Post by **exmatproton** » Mon Dec 05, 2016 2:31 pm

Dúnedain wrote:That is the aliasing for A -> D -> D. But what about the aliasing of the oscillators in subtractive soft synths everybody is talking about? If I have a saw (in discrete time of course) which has linear increments and at the highest point drops immediately to the lowest point (where it starts all over agian), then how do I have aliasing?

Because some of the content in a saw will get filtered by the high low-pass filter (22050Hz). If you filter the saw around 19500 with a 24dB slope for instance, you delete the content which is generating the aliasing artifact. If you don't filter the saw (or pulse, or square, or whatever...) then all the content is being stopped by the "end filter". Your saw simply contains content that is higher "pitched" then nyquist

Dúnedain · Post by **Dúnedain** » Mon Dec 05, 2016 2:34 pm

exmatproton wrote:
Dúnedain wrote:That is the aliasing for A -> D -> D. But what about the aliasing of the oscillators in subtractive soft synths everybody is talking about? If I have a saw (in discrete time of course) which has linear increments and at the highest point drops immediately to the lowest point (where it starts all over agian), then how do I have aliasing?
Because some of the content in a saw will get filtered by the high low-pass filter (22050Hz). If you filter the saw around 19500 with a 24dB slope for instance, you delete the content which is generating the aliasing artifact. If you don't filter the saw (or pulse, or square, or whatever...) then all the content is being stopped by the "end filter". Your saw simply contains content that is higher "pitched" then nyquist

But if the saw is at 44100 Hz, then hoe can it carry content above 22050 Hz?

.jon · Post by **.jon** » Mon Dec 05, 2016 2:34 pm

Dúnedain wrote: I know.

Sure

exmatproton · Post by **exmatproton** » Mon Dec 05, 2016 2:38 pm

Dúnedain wrote:
exmatproton wrote:
Dúnedain wrote:That is the aliasing for A -> D -> D. But what about the aliasing of the oscillators in subtractive soft synths everybody is talking about? If I have a saw (in discrete time of course) which has linear increments and at the highest point drops immediately to the lowest point (where it starts all over agian), then how do I have aliasing?
Because some of the content in a saw will get filtered by the high low-pass filter (22050Hz). If you filter the saw around 19500 with a 24dB slope for instance, you delete the content which is generating the aliasing artifact. If you don't filter the saw (or pulse, or square, or whatever...) then all the content is being stopped by the "end filter". Your saw simply contains content that is higher "pitched" then nyquist
But if the saw is at 44100 Hz, then hoe can it carry content above 22050 Hz?

LOL...it won't?? Where did you state that this question was about a saw @ 44100Hz?
Again, the "end filter" stops all sound above nyquist.

All material/content below that point will be able to be "heard" or measured

Dúnedain · Post by **Dúnedain** » Mon Dec 05, 2016 2:41 pm

exmatproton wrote:
Dúnedain wrote:
exmatproton wrote:
Dúnedain wrote:That is the aliasing for A -> D -> D. But what about the aliasing of the oscillators in subtractive soft synths everybody is talking about? If I have a saw (in discrete time of course) which has linear increments and at the highest point drops immediately to the lowest point (where it starts all over agian), then how do I have aliasing?
Because some of the content in a saw will get filtered by the high low-pass filter (22050Hz). If you filter the saw around 19500 with a 24dB slope for instance, you delete the content which is generating the aliasing artifact. If you don't filter the saw (or pulse, or square, or whatever...) then all the content is being stopped by the "end filter". Your saw simply contains content that is higher "pitched" then nyquist
But if the saw is at 44100 Hz, then hoe can it carry content above 22050 Hz?
LOL...it won't?? Where did you state that this question was about a saw @ 44100Hz?
Again, the "end filter" stops all sound above nyquist.

All material/content below that point will be able to be "heard" or measured

But without filters: how does a "perfect" saw (with a fundamental of say 1700 - 2000 Hz) at a sample rate of 44100 Hz alias?

exmatproton · Post by **exmatproton** » Mon Dec 05, 2016 2:44 pm

Dúnedain wrote:
exmatproton wrote:
Dúnedain wrote:
exmatproton wrote:
Dúnedain wrote:That is the aliasing for A -> D -> D. But what about the aliasing of the oscillators in subtractive soft synths everybody is talking about? If I have a saw (in discrete time of course) which has linear increments and at the highest point drops immediately to the lowest point (where it starts all over agian), then how do I have aliasing?
Because some of the content in a saw will get filtered by the high low-pass filter (22050Hz). If you filter the saw around 19500 with a 24dB slope for instance, you delete the content which is generating the aliasing artifact. If you don't filter the saw (or pulse, or square, or whatever...) then all the content is being stopped by the "end filter". Your saw simply contains content that is higher "pitched" then nyquist
But if the saw is at 44100 Hz, then hoe can it carry content above 22050 Hz?
LOL...it won't?? Where did you state that this question was about a saw @ 44100Hz?
Again, the "end filter" stops all sound above nyquist.

All material/content below that point will be able to be "heard" or measured
But without filters: how does a "perfect" saw (with a fundamental of say 1700 - 2000 Hz) at a sample rate of 44100 Hz alias?

There isn't "without filters". You can highten the filters cutoff by increasing the sample rate. That's why at 96KHz, or 192KHz there is almost no aliasing. This is what oversampling is doing as well btw (although a bit less).

I think you don't understand why sound is aliasing in the first place. A saw (because of the sudden jump from +1 to -1) gives content in regions beyond 44.1, 88.2 or even 192KHz. This jump from +1 to -1 (or inverted ofcourse) makes a speaker go from out to in in 0 seconds (theoretically, this isn't possible ofcourse). In other words, there is a maximum amount of energy getting released in 0 seconds. This means, at that point from the fundamental, to infinity Hz (again, in theory) there will be sound.

Dúnedain · Post by **Dúnedain** » Mon Dec 05, 2016 2:46 pm

I do not understand why there is no "without filters"?

exmatproton · Post by **exmatproton** » Mon Dec 05, 2016 2:51 pm

Dúnedain wrote:I do not understand why there is no "without filters"?

Because in the digital realm a filter is there for the processor to be able to process the signal. Otherwise you'll need a supercomputer to be able to calculate all those high frequenties.

(i've edited my earlier post btw)

Dúnedain · Post by **Dúnedain** » Mon Dec 05, 2016 2:58 pm

exmatproton wrote:
Dúnedain wrote:I do not understand why there is no "without filters"?
Because in the digital realm a filter is there for the processor to be able to process the signal. Otherwise you'll need a supercomputer to be able to calculate all those high frequenties.

(i've edited my earlier post btw)

Thank you, reread it, but you new added content is incorrect. There is no jump from +1 to -1 (I think). It is there in the discrete domain, but not in the real time domain. Only sines in the real domain (can not remember from math classes if that rules out discontinuity).

DJ Warmonger · Post by **DJ Warmonger** » Mon Dec 05, 2016 3:06 pm

Just to cut all this nonsense:

Sampling Theorem says that all frequencies above Nyquist frequency cannot be represented correctly. It doesn't say they magically dissapear. They don't dissapear, they cause aliasing.

Since perfect sawtooth has infinite bandwidth, all coimponents over 22500 Hz will cause aliasing and will be reflected in audible spectrum, as in the picture:

What aliasing in the digital domain