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