Theory is that, so long as the sampling frequency f(sa) is operating
within the Nyquist Criteria (name after John Nyquist, I think) that 
is, twice the highest frequency of content that is to be sampled, 
then aliasing would not be there in the content. 

f(sa) > 2f(content)

To be sure this is the case, filters are used to band limit the content
and keep it below that point. For 20kHz frequency and 2 x 20kHz = 40kHz, 
you need a sampling frequency of 44.1kHz to do the job.

Take the Sawtooth wave and filter it so there is a Nyquist band limit
to limit aliasing and a few upper harmonics will drop out, but that
may be okay.

If you sampled audio, with the highest frequency being 20kHz, and you 
have a sampling frequency of 192kHz (or 2.8442MHz sometimes used in
Broad Band Streaming [BBS]), then the aliasing components are so far
out of the audio band that you even need front-end filtering. But 
some people use front-end anti-aliasing filters anyway, it's like
Linus and his security blanket. It's a just-in-case rationale to use
anti-aliasing filters at those higher sampling frequencies.

96kHz, 192kHz and 2.8442MHz are typically used for 24-bit sampling
in digital multitrack, High Resolution (HiRes) for the 96kHz and 
192kHz, and 24-bit Broad Band Streaming (a version HiRes across 
the internet for the 2.8442MHz rate).


So depending on what your bit depth and sampling rate are using, will
result in how good any Sawtooth wave will be. You can find the best
Sawtooth opcode in all of Csound, but if you send it thru 8-bit digital
at a 11kHz or 32kHz sampling rates, it's going to sound crummy. 

The overall quality will only be as good as the weakest link in 
the audio chain.


Well, lunch break is over,
back to fixing amps and such.
-Partev



==================================================================== 



--- mpm@alumni.caltech.edu wrote:

From: Michael Mossey 
To: csound@lists.bath.ac.uk
Subject: [Csnd] Re: Re: Re: What's the highest quality sawtooth in Csound?
Date: Sun, 03 Oct 2010 20:06:17 -0700



On 10/3/2010 3:46 PM, Partev Barr Sarkissian wrote:
> Hasn't been a problem yet. If it does become a problem, then I'll
> just run it thru some filters til I get it to how I like it, and
> may be even band limit it to prevent aliasing. It's just not a
> big concern yet.  If aliasing becomes a problem I'll use the
> subtractive process via however many filters I need and want.
>
> Like Alan Parsons once told me,"Don't be afraid of noise,...
> if all else fails, filter the hell out of it".
>
>
> -Partev
>

You're talking practice and I'm talking theory. The OP requested an 
analysis of the quality of sawtooth waves and pointed out that a 
theoretically correct implementation is necessary in his application.

Mainly, what I would like to understand is the theory, so it would be 
helpful if someone here could explain it from that point of view.

I don't think you can band-limit it to prevent aliasing---the aliased 
harmonics are interspersed between the correct harmonics at the point of 
origin (in the oscillator itself). Is this correct?

It has also been made clear by several posters that vco2 is a theoretically 
correct implementation.

Switching briefly to the issue of practice... I've noticed that I like 
synthesized sounds which have a wide bandwidth (in particular a top end 
that goes all the way up).. so I try to look for ways not to filter out all 
the highs. Yes, you want varied tonal balance, some things brighter than 
others. But a completely dull sound is, well, dull. (Unless maybe it's 
there purely for contrast.)

Mike


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_____________________________________________________________
Netscape.  Just the Net You Need.


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on 2010-10-04 at 14:05 Partev Barr Sarkissian wrote:

> the Nyquist Criteria (name after John Nyquist, I think) 

harry?


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