On Mon, 6 Mar 2000, David VanHorn wrote:

> Actually, I am looking for a generalized technique that will let me strip
> odd harmonics.
> I have an application that's using the boxcar as I described, both to
> indicate distortion level, and to subtract said distortion from a signal,
> but the odd harmonics have me stumped.
>
> I use one boxcar to take the signal, but of course it also passes the 2H,
> 3H, 4H... right on up, though past the 4th it's pretty well damped since
> it's an eight cap boxcar :)  The second grabs the 2h and 4h components
> perfectly, but I have no simple answer for 3h and 5h. (Maybe I only need
> 3h, but you get the idea.)

If you had a square wave with a 50% duty cycle, there are no even
harmonics. Furthermore, the relative magnitude of the harmonics are
inversely proportional to their harmonic numbers. If you vary the duty
cycle to say 33%, you'll have no 3rd,6th, 9th harmonic, but some of the
evens will pop up. I don't think there's a way to arbitrarily kill the odd
harmonics. But you can do (at least) two things: vary the pulse width of
individual pulses and vary the number of pulses. The plot:

http://www.dattalo.com/ms1.gif

cancels the 2nd and 3rd harmonics. You could say that it consists of three
pulses; one twice as wide as the other. (But the program generating it had
4 bits for those 3 pulses...).

I don't have time right now to explain, but as I mentioned earlier, it's
possible to exactly cancel the first N harmonics. However, the number of
'time slots' or quantized positions at which the pulse edges may occur is
of the order of N! (factorial). There is technique that involves examining
the phases of the harmonics of the individual pulses. I found that pulses
can be collected into groups that totally cancel one another at a given
harmonic number. The smallest group I experimented with is just a pair.
For example, for the second harmonic, the pulses are grouped in pairs. One
pulse is 180 degrees out of phase with the other. The pairs for the second
harmonic are two pulses separated by one pulse. For the third harmonic,
the pulses are separated by two pulses.

2nd harmonic suppressed:
010100000000
000010100000

3rd harmonic suppressed:
010010000000
000100100000

Total pulse stream:
010110100000

So the objective is to discover the pairs that cancel at a given harmonic
and then to find a set of pulses that will have complete coverage for each
harmonic. I've done this for 24 pulses, but beyond that it gets pretty
hairy...

Scott