Re: Anti Aliasing of Arbitrary Waveforms



Jerry Avins wrote:

jim wrote:

Jerry Avins wrote:
On Sep 29, 2:11 pm, jim <"sjedgingN0sp"@m...@xxxxxxx> wrote:
Jerry Avins wrote:

You claimed that the cos(2pi) terms added nothing to the summation. Is
that still your belief?
I'm tired of editing your fable.
I'm stuck posting from Google, where it's hard following a thread. I'm
happy to end with this post.

My belief is that with a little intelligence he can get a clean signal with
precisely the specific harmonics he wants. It won't fit your story of what it is
you think his process represents. But why should anyone care if it fits that
story?
Suppose that Scott ultimately wants to emulate a tube amplifier's soft
nonliner transfer function. He would want all the audible harmonics
but none too high for the sample rate. What would you suggest to him?

I don't understand how what you just proposed has anything to do with the
current thing he is doing? What I mean is will he start that project from the
beginning or will he somehow turn this into that. This whole business of once he
has it solved for this one waveform he will be able to do any other looks like a
bunch of handwaving to me.

Scott asks for (a) general method(s) to avoid "aliasing" of
computer-generated signals: "What are the common method(s) for
preventing aliasing of arbitrary waveforms generated within a DSP
application?"

So when did he become an authority on the subject. Just because he asked for
general solution doesn't mean you have to pretend there is one.


His sawtooth generated by incrementing a register with
overflow or other reset is a stalking horse, a cheap convenient test
signal to illustrate the properties of of the (apparently uncommon) method.

But he can't solve the problem of aliasing after the aliasing is done. So there
is no general solution because he hasn't come up with a good way to make a
signal that avoids unwanted low frequencies.



As far as I can tell he hasn't accomplished anything yet. The more I think
about it this business of generating at higher sample rate isn't going to solve
his problem of unwanted frequencies. He still will have artifacts in the higher
frequencies. It's a very bad solution to his problem.

An impulse train is sufficient counterexample to demonstrate that there
is no overall solution. Nevertheless, most periodic waveforms' spectra
eventually roll off in amplitude as the frequency increases. For all of
those, generating the waveforms at sufficiently high sample rate solves
Scott's problem. Lowpass filtering the result to remove irrelevantly
high harmonics and most of the folded ones leaves a signal that can be
downsampled to the desired range without aliasing. (For efficiency, the
filtering and downsampling can be combined. There is no reason to
compute samples destined to be discarded.)

So you agree the current problem he is working has pretty much nothing to do
with the methods he will later use. I agree if he had chosen a different method
to start with it might work.



For most signals, including his arbitrarily chosen test signal, ir is a
very good solution.

No it won't work for this method of generating a signal at least not unless he
is very careful about what increments he chooses to use. In general for any
random increment that produces a high frequency (i.e. very large increments) he
will still get unwanted frequencies. And any filtering he does when down
sampling won't remove them because they are not high enough to be removed. The
low frequency noise generated is going to be directly proportional to the size
of his increment.

-jim


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