On Tue, Feb 7, 2017 at 6:49 AM, Ethan Fenn <et...@polyspectral.com> wrote:
> So I guess the general idea with these frequency shifters is something > like: > > pre-filter -> generate Hilbert pair -> multiply by e^iwt -> take the real > part > > Am I getting that right? > Exactly, this is a single sideband modulation technique, specifically called the Hartley Modulator. I wonder if anyone has compared to the Weaver Modulator approach? That one works like this: input -> quadrature modulate to center image on DC -> (complex) LPF -> quadrature modulate back up to desired frequency -> take the real part Obviously this approach requires two quadrature modulators instead of one, and two (real) LPFs instead of one Hilbert transformer. On the other hand, LPFs are easier to deal with than Hilbert filters - we aren't trying to stick a huge phase transition right at DC, we can use any number of common design techniques/topologies, and we don't have the extra constraint of needing an allpass response. So it's not obvious to me that the two LPFs in Weaver aren't actually cheaper than the one Hilbert filter in Hartley, for equivalent performance. Also the performance is easier to get a handle on, since the unwanted images are controlled directly by the LPFs, rather than relying on phase cancellation of in-band components in the image region. Moreover, the less-ideal parts of the filter response can be pushed up into the transition region (where there is presumably much less signal energy - or even effectively none if there is significant oversampling to allow headroom for frequency shifting), compared to the Hilbert approach which has to try to maintain the correct phase shift all the way across the signal band. Most of the comparisons I've found between Hartley and Weaver are from the analog radio domain, and the concerns mostly don't apply to a DSP context (things about DC coupling in the quadrature oscillators, building matched LPFs with tight tolerance, etc.). Any thoughts? E
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