Re: Anti Aliasing of Arbitrary Waveforms

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?" 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.

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.)

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

...

Jerry
--
Engineering is the art of making what you want from things you can get.
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