Timeline for Hilbert transformer and minimum-phase
Current License: CC BY-SA 3.0
16 events
| when toggle format | what | by | license | comment | |
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| Feb 18, 2023 at 15:07 | comment | added | Olli Niemitalo | @DanBoschen I seem to have neglected that if the two all-pass filters have conjugate-symmetric frequency responses $H_{\text{ref}}(\omega)$ and $H_{\text{ref}+90^\circ}(\omega)$ then one can simply do $H_{\text{ref}+90^\circ}(\omega)H_{\text{ref}}(-\omega) = H_{\text{ref}+90^\circ}(\omega)H_{-\text{ref}}(\omega) = H_{90^\circ}(\omega)$, where $H(-\omega)$ is the Fourier transform pair of time reversal (the reverse pass) and the subscript denotes the approximate phase shift. | |
| Sep 24, 2022 at 19:15 | comment | added | Dan Boschen | @OlliNiemitalo To clarify your earlier comment about using the reverse complex filter to then recover the Hilbert. As you wrote it, that would result in the square of the Hilbert response? My thinking: x+j hat_x)(x-j hat_x) = x^2 + j x_hat^2. (with delay terms removed). Also - If the linear phase delay is not a concern to us, then the outputs of the pair of IIR filters would indeed be x delayed and the Hilbert of x delayed. | |
| Aug 8, 2017 at 10:15 | vote | accept | greggo | ||
| Aug 7, 2017 at 20:40 | history | tweeted | twitter.com/StackSignals/status/894659615413211138 | ||
| Aug 7, 2017 at 13:54 | comment | added | greggo | Confusion is complete. I mean the Hilbert transform provides the minimum-phase corresponding to a given (log) magnitude. | |
| Aug 7, 2017 at 13:44 | comment | added | greggo | @Olli Niemitalo The Hilbert transform provides the minimum-phase which the question is about. | |
| Aug 7, 2017 at 12:50 | history | edited | greggo | CC BY-SA 3.0 |
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| Aug 7, 2017 at 12:40 | comment | added | greggo | @Olli Niemitalo I do want to use IIR filters. But I don't see how they provide the minimum-phase. I don't think robertbristow-johnson's answer provides it. | |
| Aug 7, 2017 at 10:56 | comment | added | greggo | @OlliNiemitalo I'm sorry, I will try to update the question if I can find a way to make more clear what I'm asking. I think there is some confusion here about the difference between a hilbert transformer and the hilbert transform providing minimum-phase. Maybe, I'm the only one confused here but I don't think they are the same. At some level my question is about the relation between those two instead of how to realize a hilbert transformer (90 degree phase shifter)...which is also interesting and very likely I will ask about that in another question. | |
| Aug 7, 2017 at 8:27 | history | edited | greggo | CC BY-SA 3.0 |
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| Aug 7, 2017 at 7:10 | answer | added | robert bristow-johnson | timeline score: 4 | |
| Aug 6, 2017 at 18:19 | comment | added | greggo | @robertbristow-johnson Exactly. As you probably already are aware of then for a minimum-phase system (LTI) the phase can be fully recovered from the magnitude response. I have been looking for an IIR filter solution and thought that I could use a hilbert transformer because they are built on similar principles such as causality and one-sideness. But after looking for closely I don't immediately see how I can use a Hilbert transformer. | |
| Aug 5, 2017 at 22:42 | comment | added | robert bristow-johnson | before i attempt an answer, i want to understand your question better. by "response", do you mean that you know the magnitude response of an LTI system or "filter" and, from that magnitude response, you want to calculate a phase response that would be the minimum-phase response? | |
| Aug 4, 2017 at 13:24 | history | edited | greggo | CC BY-SA 3.0 |
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| Aug 4, 2017 at 12:57 | review | First posts | |||
| Aug 5, 2017 at 14:55 | |||||
| Aug 4, 2017 at 12:55 | history | asked | greggo | CC BY-SA 3.0 |