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Signal Processing

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    $\begingroup$ Thank you Matt! These are great thoughts, and it makes sense to me. Still not as convincing without an example and would be so thankful to see one-- I think you are getting to the core of my question: does the optimality as defined by the placement of the poles and zeros in the s-plane as given by the classic analog filters and then mapped to the z-plane using our various mapping techniques, bilinear etc (in sharp contrast to determining the same optimality constraints in z directly) really result in a higher performance filter? If delay is an issue and I am not concerned about phase.... $\endgroup$ Commented Dec 2, 2021 at 13:32
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    $\begingroup$ can't we decompose the linear phase filter into its minimum phase and all-pass components? I plan to bounty this as soon as I am able, but having a real example where we see this is the case would be so sweet. I tried a simple test case and found it to not be the case. And great comment and Thiran reference on Bessel filters. $\endgroup$ Commented Dec 2, 2021 at 13:33
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    $\begingroup$ @DanBoschen: Yes, we can decompose a linear-phase filter into a minimum-phase and an all-pass component. But that means to compute zeros and factor the transfer function. That's a potentially ill-conditioned problem for high filter orders (think of FIR filters with many hundreds or thousands of coefficients). $\endgroup$ Commented Dec 2, 2021 at 14:00
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    $\begingroup$ @MattL. It's been awhile since I've looked at this, but the Lindsay-Fox algorithm as per these papers: ieeexplore.ieee.org/document/1437932, and ieeexplore.ieee.org/document/1253552 has been used to factor 1 million degree polynomial (as per the paper). These papers are approx. 15 years old, so I'm not sure of more current state of the art. $\endgroup$ Commented Dec 2, 2021 at 16:43
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    $\begingroup$ @DanBoschen: For the sake of completeness I've changed to group delay figure to include the group delay of the FIR minimum-phase component, which shows that if phase linearity is not important, an FIR filter can have group delay characteristics that are very similar to the corresponding IIR filter. This is of course no surprise, given that the magnitude responses are very similar and that the phase of the minimum-phase system is determined by the magnitude. $\endgroup$ Commented Dec 8, 2021 at 15:26