I have found a technique detailed on page 34 & 35 of this thesis.

In this, the author states a complex bandpass filter can be derived by first making a prototype real valued IIR filter, then setting the complex conjugate poles equal to each other. He then states the resulting complex filter will have a quality factor half that of the real valued one but the same centre frequency. The resulting filter is then more efficient than a combination of bandpass filter + Hilbert transform.

I can find no reference to this technique anywhere! Can anyone point me towards a reference explaining the mathematical concepts of this or an example of it's implementation so I can understand it better? How would you rate this technique compared to a bandpass+hilbert transform, or is there an even better way? I am only looking to achieve a quadrature signal for further processing, in this case frequency shifting.

  • $\begingroup$ This is not a direct answer, but you might be interested in this list of methods to generate an analytic signal: dsprelated.com/showarticle/153.php $\endgroup$ – MBaz Jul 19 '17 at 19:31
  • $\begingroup$ Thanks I have seen that list and it seems an excellent summary, it doesn't cover this specific method though. $\endgroup$ – josh Jul 19 '17 at 20:28
  • $\begingroup$ You do know the unit circle represents the digital frequency axis? If not, understanding that does make it very clear with observation of the pole placement how this approach creates a "single-side-band" filter similar to using real band pass filters and Hilbert transforms. $\endgroup$ – Dan Boschen Jul 20 '17 at 0:45
  • $\begingroup$ Yes I can visualize 'how' it was working (no negative frequency content as you said) but was curious as to why I could find no mention of it anywhere, it seems a much quicker method than most. $\endgroup$ – josh Jul 20 '17 at 8:55

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