Hilbert Transform in verilog or VHDL -- it has got to be out there somewhere

This paper has something on page 11:

Cheers,

Guenter

Guenter,

Boy, is that embarrassing: it is right where it is supposed to be, on the free logic cores stuff.

But, in my defense, it was 'hidden' in with the FIR filter wizard, as that is how they chose to implement it.

Now if only the search engine would have found it?

Maybe if I didn't look for "Hilbert", but instead looked for "FIR filters"?

Who would have guessed?

It is not only there where you pointed me, but also:

Veil dank Guenther,

Aust> Aust>> OK,

An opamp-based allpass 90 degree phase shifter is pretty simple; 8 opamp sections, 8 caps, 24 resistors gives nice quadrature signals over the voice range. And simulating a R-C section in an FPGA is trivial. So it seems to me that one could do a nice Hilbert with a fairly small amount of FPGA resources by just mimicing the opamp circuit in discrete time. That would be a lot smaller than a FIR implementation.

Anybody done it this way?

John

That's an IIR implementation. Generally speaking, IIR filters do not have the phase linearity required by many of the modern modulation schemes. They are fine for AM/FM, but when you start dealing with phase modulation, the non-linearity can make it extremely difficult to demodulate the signal.

Maybe so, but my trusty old Williams filter book has, for a 10-element opamp-based allpass network,

57:1, 0.026

1146:1, 0.66

which look pretty good. And a digital implementation should nail the pole/zero locations exactly. I do lowpass filters this way some times... just design an active analog filter, and simulate it digitally.

John

Those don't have linear phase. There are also the issues with finite precision in IIR filters which lead to limit cycles and misplaced poles/zeros. For digital comms applications, we generally use FIR filters because they eliminate those issues, albiet with some added computational complexity.

For downconversion, the Hilbert transform can generally be done with a complex mixer and the low pass filters you'd need anyway.

Given a signal frequency range F1 to F2, and, say 0.5 degree or less error, do you have any wild/rough guess as to the minimum clock frequency and number of taps for an FIR Hilbert phase shifter? I assume that, as absolute minimum conditions, the delay line must be at least long enough to store 180 degrees of the waveform at F1, and that the clock has to be at least 2 times F2. What sort of real-life numbers do people use?

I'm thinking here about digitizing AC voltage and current waveforms in stationary and aircraft power systems and extracting the real and imaginary power components, so I'd need a wideband (say, 40 to 800 Hz)

John