ODP: Bill's Bits

[Harvey Devoe Thornburg]

> 
> I was thinking about simple waveforms like sine, sqr and triangle
> which wouldn't suffer from aliassing.
> I don't want to put heavy 2meg sample in it!
> And if I wanted, I'd filter the sample
> at higher DCO frequencies since DSP is involved anyhow
> But then, it suddenly it becomes a d*g*t*l synth!
>

Both square and triangle *will* suffer from aliasing because they
are not bandlimited.  The problems are easily seen in the time domain,
without resort to Fourier theory. Suppose your sampling rate is 25 Khz and
the square wave is 10 Khz. Then the period of the square wave will 
alternate between 2 and 3 samples.  This will produce a periodic waveform
of period 5 samples, with fundamental frequency 5Khz. The
5 Khz frequency is obviously an alias, since it is not present in 
the original (analog) wave.

Generally, you will have alias components down to DC, so postfiltering
(eg. "filtering the sample") in digital domain will not get rid of
them. 

When the frequency of the square wave is integer division of the sampling
rate (there are exactly integer number of samples/period), then 
aliasing is tolerable, because the alias frequencies coincide with harmonics.
In particular when there are an even number of samples/period, then 
the aliases fall only on odd harmonics; in this case they cancel!

This may be the situation you were thinking of, where you store a waveform
and vary the frequency by varying the clock speed.   But running a DSP
with fixed sampling rate, and trying to output waveforms that can be
frequency-swept leads to aliasing problems.

--Harvey