AM Modulation

Yeah, well, what can I tell you...I took Fourier from Bracewell himself, and he made it such fun that I can't resist playing with it sometimes. My bad.

Cheers,

Phil Hobbs

Neat! Bracewell is a very cool dude; I wish I'd met him.

The HP/Agilent sampling scopes used (maybe still use) the Bracewell Transform for TDR deconvolution, and he has interesting ideas on extraterrestial life and stuff.

John

ps - ever get involved in deconvolution? I accidentally invented a very simple and fast deconvolution algorithm for TDR equalization, and I wish somebody would explain to me how it works.

Well, my problem is, I got stuck in mathematics at that level. I've been programming FFTs on DPSs and I can perfectly see what the transform does, algorithm-wise, but these mathematical representations are just plain chinese to me ;-)

My bad too...... (heading for the pubs instead of going to math classes, but that was 20 odd years ago. I'm wiser now, I now drink at home ;-))

Meindert

Have you tried reading E. Oran Brigham's edition(s)?

I instantly saw sin() component effect the moment I'd read John's question. The (1/2j) * (e^jwt - e^-jwt) popped immediately to mind as equivalent and the last part of that multiplied by the e^2j pi ft immediately yields the f-f0 f+f0 splitting.) But I didn't bother with the 't' spectrum to see what shape would be split, at the time. I followed Phil's response quickly, though.

Anyway, that's where I learned to vaguely read such things, despite the fact that it was just a passing curiosity and I don't normally need to apply FTs. His writing worked for me better than other places I'd looked. Might help you, if you haven't already tried him.

Jon

I did some of that for my thesis research, but the most interesting was for my $10 thermal IR cameras--I needed to take the response of each pixel and deconvolve it with a filter about 25 or 30 samples long, on a micro with a capacious 902 bytes of RAM--there was no way I could use that many frame buffers.

It turned out that the deconvolver could be factored pretty accurately into a 3-sample FIR filter followed by a 1-sample IIR integrator, which made it much more feasible. It still wound up in the PC code and not in the micro, but oh, well.

Cheers,

Phil Hobbs