A Space Orthogonal to Real

[Joe Gwinn]

I found a nice tutorial on complex signals, those having In-Phase and Quadrature components. It goes far beyond what is needed to understand guitar pickups, but I particularly liked the diagrams visualizing the various mathematical concepts.

"Quadrature Signals: Complex, But Not Complicated", by Richard Lyons, January 2008:

http://www.dspguru.com/info/tutor/QuadSignals.pdf


The next website level up is Quadrature Signals: Complex, But Not Complicated.

[salvarsan]

I found a nice tutorial on complex signals,...
"Quadrature Signals: Complex, But Not Complicated", by Richard Lyons, January 2008:...

Excellent find, Joe. In a rare instance, there is enough Lyons to match the christians.

The whole dspGuru site is worth mentioning: dspGuru: DSP Central

Lyons' QuadSignals.pdf fills in some background from his 1997 book, Understanding Digital Signal Processing, ISBN 0-201-63467-8.

Lyons' importance can't be understated. He is to FFT as Heaviside was to Maxwell's equations. Within two years of his book's publication, people began to reference both Lyons and Cooley-Tukey in the same sentence. Then FFT implementations suddenly became a commodity, or so it seemed.

Richard Lyons hasn't rested since publishing and really ought to have his own Wikipedia page.

-drh

[RedHouse]

uh oh, I can smell a Joe-n-Mike duke-out comming.

[salvarsan]

uh oh, I can smell a Joe-n-Mike duke-out comming.

Naah. They quibble over engineering/implementation details.

Argifying over complex numbers is like complaining about the weather.

-drh

[RedHouse]

Naah. They quibble over engineering/implementation details.

Argifying over complex numbers is like complaining about the weather.

-drh

Pheww! I can sleep well tonight.

[Joe Gwinn]

Naah. They quibble over engineering/implementation details.

Argifying over complex numbers is like complaining about the weather.

Naah. In joke. Plot the complex numbers on an Argand diagram Complex plane - Wikipedia, the free encyclopedia.

[Joe Gwinn]

Pheww! I can sleep well tonight.

But won't the unreality of orthogonality to Real intrude? When you will become crosswise.

[salvarsan]

But won't the unreality of orthogonality to Real intrude? When you will become crosswise.

Y'know, I had a perfesser who asserted that one's social acceptance was determined by his quadratic integrability. Once I realized that his Harvardian brutalization in the Electron Spin Resonance field left him with a sesquipedalian idee fixe that manifested as sanctimoniety (which the pre-revolutionary Iranian students summarized as "he thinks he pisses perfume", but we were much more rude), I was much less intimidated by him.

The exegesis of FFT and DSP lies mainly with Lyons, and he
freely acknowledges that he stands on the shoulders of Titans.


End of story.


Another interesting story is:

"Who was Fourier? A Mathematical Adventure"
ISBN-13: 978-0964350403

-drh

[David Schwab]

Once I realized that his Harvardian brutalization in the Electron Spin Resonance field left him with a sesquipedalian idee fixe that manifested as sanctimoniety...

One of these days I'm going to use this for the name of an instrumental piece....


Delayed Choice Quantum Eraser



.

[Possum]

....

How many want to join me in taking the Krell brain boost machine treatment? I can get discount tickets to Altair, they really didn't blow it up as shown the documentary movie Forbidden Planet. Its only 3.9 light years away, but warp drive should get us there and back by noon tomorrow. $39.99, not FDA approved....

[Joe Gwinn]

Excellent find, Joe. In a rare instance, there is enough Lyons to match the christians.

Thanks. Reminds me of a classic Sam Goldwin quote.

Sam had just released the biblical epic movie The Ten Commandments (or the like), where a lion and a lamb are filmed as they lay down together. Sam was asked how this biblical miracle was achieved. Answer: "By frequent replacement of the lamb."

[salvarsan]

Sam had just released the biblical epic movie The Ten Commandments (or the like), where a lion and a lamb are filmed as they lay down together. Sam was asked how this biblical miracle was achieved. Answer: "By frequent replacement of the lamb."

In a similar vein, there was a lawsuit in Westchester, NY titled "Christien v. Lyons".


Sorry about the run-on sentence describing an old prof.
1)It's all true. 2) I shouldn't post while squiffy.



-drh

[Joe Gwinn]

How many want to join me in taking the Krell brain boost machine treatment? I can get discount tickets to Altair, they really didn't blow it up as shown the documentary movie Forbidden Planet. Its only 3.9 light years away, but warp drive should get us there and back by noon tomorrow. $39.99, not FDA approved....

Umm, 3.9 ly only gets one to Alpha Centauri. Altair is 16.8 ly away. And it may be tourist season. So I'd recheck the ticket prices.

[David Schwab]

Umm, 3.9 ly only gets one to Alpha Centauri. Altair is 16.8 ly away.

Actually that wont even get you there... Alpha Centauri (A & B) is 4.37 ly. But Proxima Centauri is only mere 4.22 light-years away, so that might be a good tourist spot. Or at least it will have a truck stop.

[Mike Sulzer]

Times passes, things change.

I found a nice tutorial on complex signals, those having In-Phase and Quadrature components. It goes far beyond what is needed to understand guitar pickups, but I particularly liked the diagrams visualizing the various mathematical concepts.

"Quadrature Signals: Complex, But Not Complicated", by Richard Lyons, January 2008:

http://www.dspguru.com/info/tutor/QuadSignals.pdf


The next website level up is Quadrature Signals: Complex, But Not Complicated.

Of particular interest is his quadrature sampling example. This is exactly how we have sampled our radar data since the 1970s, but...

This is changing. Digital processing is now so fast that the analog base band mixer that he describes (the continuous part of the block diagram in the upper part of figure 14) is going out of use. Samplers are now so fast that one can use a single (real) sampler directly on the rf signal, or if necessary at an intermediate frequency after one stage of mixing, effectively capturing the entire bandpass from dc to beyond the bandpass containing the desired information in one easy step.

But the interesting part is that it is still convenient to move the center frequency to zero; so this is now done in a digital base band mixer. The complex signal is produced digitally from the real digital input stream by multiplying by digital versions of the cosine and sine wave and then filtering the result with digital filters.

The machine for doing this is often called a "digital receiver". It has been around for decades, of course, but in the past only the big boys could afford these toys. Now they can be configured in FPGAs (Field Programmable Gate Arrays), thus avoiding the problem of actually having to make any hardware that can run at hundreds of MHz.