more lunacy from the BBC

Given signal S and bad comm channel C, the product is ugly signal

S * C.

If you work in frequency domain, S has a complex spectrum and C has a complex transform and the * above is a complex multiply of the spectra.

If you work in time domain (as I do) S is a waveform and C is the impulse response of the channel, and the * operator is convolution.

In either case, we want an equilizer E such that

S * C * E = S

namely C * E = 1

In frequency domain, you do a complex divide to calculate E, which genereally explodes.

In time domain I have an iterative algorithm to get E. Iterate too many times and it explodes too.

The problem is ill-posed and non-causal, which is what makes it interesting.

Adaptive equalizer chips can input an unrecognizable hairball and output a beautiful data stream. Things like fast PCIe wouldn't work without adaptive equalizers.

John Larkin Highland Tech Glen Canyon Design Center Lunatic Fringe Electronics

It doesn't "explode". Rounding error and random noise wreck the result, which is close enough to "explode" for all practical purposes.

Same problem.

If you don't understand what you are doing, it may look "interesting"

Up to a point. It's a "beautiful data stream" because what you want a are ones and zeros at specific data rate - if the transitions between bits move around a bit you don't care as long as doesn't move around enough to turn a one into a zero

If you want a clean result, it makes sense to make your transmission lines clean and simple - nice homogeneous dielectrics, rather than FR4. They won't be as mechanically strong or as cheap, but if you confine them to fast buried non-dispersive signalling layers, it can be a practical - if not a dirt cheap - solution.

If you want precision timing, you need to spend the money.

You are universally wonderful.

The frequency-domain way to calculate the equalizer is to do a complex divide of the equivalent FFTs. That tends to blow up with divides by small numbers or zeroes.

There is a world of academic papers on how to work around the FFT division crisis, and they turn out to be messy and iterative and ill-posed too.

As the book says, frequency domain and time domain are just ways to look at the same things.

John Larkin Highland Tech Glen Canyon Design Center Lunatic Fringe Electronics

Yes, later I had a ZX81 too.

Not sure what you mean by that? I used a 5/1/4 inch floppy drive on the ZX80 :-) (Kaypro 2 format)

But to speed up things I made a 250 MB RAMDISC, so at power up loaded everything into that (dynamic) RAM DISC, and worked from there,. My Z80 system was faster than the first IBM PCs that way, no seek times!!

I moved to Linux around 1993 or so and still use it.

At work I had to work with MS windows at times.

I do have a 3.5 inch USB floppy drive for old floppies, not used for years? Computers here are now Raspberry Pis mostly ...

There a long gap between "not being a dummy in a specific area" and being universally wonderful (which is not a state mere humans can attain). These discussions are more like Dr. Johnson's "Sir, there is no settling the point of precedency between a louse and a flea". Since you do make more money out of selling your electronic expertise than I do, you must be the more effective blood sucker.

Effectively you have to invert a matrix, and if your matrix is ill-conditioned, most of the entries in your inverted matrix are excessively sensitive to noise in your original observations (which can be rounding errors in your numerical representations of those observations)

That's one way of putting it.

Not the same things, but the same thing. And the book is just reiterating the obvious, which you do have to do when instructing dummies.