Re: Complex in/Complex out Hilbert?

[David Hagood]

When demodulating a real-world signal, you have the problem that there's 
other signals too - there's the other station 4kHz down that you want to 
remove. So yes, you can say the signal of interest is an analytic 
signal, but then there's everybody else too. True, you can demodulate 
the signal by shifting it one half bandwidth, low passing it, shifting 
it back, re-injecting the carrier, and then demodulating it. Just 
throwing away the imaginary part causes issues if you don't have 
precisely the correct frequency. That's the difference between 
theoretical DSP and real-world work - you are never on frequency, there 
are always other signals, etc.

Mostly, this is because I do SDR for a living, so I am "pushing the 
envelope" to see what GnuRadio can do - and IMHO, while there's a lot of 
good work, there's also room for improvement. The demodulators that ship 
with it could stand some improvement - look at the LiquidDSP AM 
demodulator, which DOES do USB, LSB, and DSB correctly, vs. what is in 
GnuRadio.

Yes, I know - "If you want it, write it yourself, then". And I may just 
do that, but since I hate duplicating effort, I'd like to know if 
anybody else has done that, or is doing that.

The Hilbert transform is supposed to shift the positive frequency 
components -90 degrees, and the negative frequency components 90 
degrees. That's why a Hilbert that only accepts real values is 
problematic - you cannot truly represent a negative frequency with only 
real values. A complex-in/complex-out Hilbert would be able to do just that.