Timeline for What is the algorithm to do a Discrete Hilbert Transform?
Current License: CC BY-SA 4.0
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| Nov 11 at 3:18 | history | edited | robert bristow-johnson | CC BY-SA 4.0 |
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| Dec 20, 2023 at 6:28 | history | edited | robert bristow-johnson | CC BY-SA 4.0 |
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| Dec 20, 2023 at 6:07 | history | edited | robert bristow-johnson | CC BY-SA 4.0 |
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| Dec 19, 2023 at 3:14 | history | edited | robert bristow-johnson | CC BY-SA 4.0 |
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| Dec 19, 2023 at 3:07 | history | edited | robert bristow-johnson | CC BY-SA 4.0 |
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| May 2, 2019 at 3:38 | comment | added | robert bristow-johnson | Dog, i had to make a small correction. suppose you were to use the Hamming window (which is easier to understand than the Kaiser), can you translate this math into code and get what you're looking for? remember your result is necessarily delayed by $\frac{L}2$ samples and $L$ needs to be reasonably large, like $L$=50 or something. | |
| May 2, 2019 at 3:36 | history | edited | robert bristow-johnson | CC BY-SA 4.0 |
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| May 2, 2019 at 3:32 | vote | accept | Duck | ||
| May 1, 2019 at 22:25 | comment | added | robert bristow-johnson | So Dog, if you have a narrow-band discrete-time signal $x[n]$ and its Discrete Hilbert transform is $\hat{x}[n]$, defined as above, the instantaneous frequency in radians/sample (which is dimensionless) is $$ \omega[n] = \operatorname{arctan}\left(\frac{x[n-1]\hat{x}[n] - x[n]\hat{x}[n-1]}{x[n]x[n-1]+\hat{x}[n]\hat{x}[n-1]} \right) $$ The instantaneous phase will advance by $\omega[n]$ for each sample $$ \phi[n] = \phi[n-1] + \omega[n] $$ | |
| May 1, 2019 at 19:49 | history | edited | robert bristow-johnson | CC BY-SA 4.0 |
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| May 1, 2019 at 19:17 | history | edited | robert bristow-johnson | CC BY-SA 4.0 |
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| May 1, 2019 at 19:13 | comment | added | robert bristow-johnson | well, Dog, i haven't really figgered out what the IMFs (i guess they're "Intrinsic Mode Functions") are either. there is a semantic usage issue, but the Discrete Hilbert Transform is well defined in the textbooks and the lit. And the definition is what I said at the top. The windowing and delaying is necessary to make your filter FIR and causal. If you're trying to use a Hilbert Transformer to estimate an instantaneous amplitude envelope or instantaneous frequency, that's good for a whole 'nother question. | |
| May 1, 2019 at 19:11 | history | edited | robert bristow-johnson | CC BY-SA 4.0 |
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| May 1, 2019 at 19:04 | history | edited | robert bristow-johnson | CC BY-SA 4.0 |
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| May 1, 2019 at 10:00 | comment | added | Duck | thanks. I guess I must be dumb because I was unable to understand a single line of your answer. Sorry. Suppose for example I already have decomposed the signal using Empirical Mode Decomposition and obtained several IMFs. How can I do a HT on those IMF and get the frequency of each one, for example. Again, sorry for my ignorance. | |
| May 1, 2019 at 9:28 | history | answered | robert bristow-johnson | CC BY-SA 4.0 |