From: Jens Groh ()
Date: May 10, 2008
Subject:
Re: FAQ is BAQ! - frequency shifting.
I think the principal engineering task is, how good is the alias
suppression. A secondary task is, how good is the amplitude fidelity.
Yeah, and as always, the question is, how much processing effort do I
have to spend.
You can trade amplitude fidelity for alias suppression, if you release
the strict allpass requirement, right?
For the single-filter (Hilbert) phase method and the dual-filter
differential phase method, one could design an approximate allpass,
resp. allpass pair, with a "minimum distance in the complex plane"
design constraint instead of a "minimum distance on the unit circle"
design constraint and probably achieve the same alias suppression with
less filter order. (About half the filter order??) Such a filter
optimization should be possible -- but how??? Probably some
modification of some standard IIR design algorithm would do.
For Weaver's method, the relaxed constraint is inherent. Any normal
lowpass design criteria will do. But Weaver needs two identical
filters, so you have only half as many degrees of freedom for the
filter parameters compared to the differential phase method.
The single Hilbert transformer still has the constraint that the phase
be 90 degrees, not arbitrary, and that costs.
So, I guess the differential phase method with the relaxed constraint
will be the "winner". What do you think?
Would be nice if someone could do a filter pair design after this
approach for assorted filter orders and give us the coefficient sets.
Thank you. ;-)
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