Timeline for Symmetries of analyticity / zero self-correlation
Current License: CC BY-SA 4.0
21 events
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| May 1, 2022 at 13:01 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Jan 1, 2022 at 12:06 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Sep 3, 2021 at 12:03 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Aug 4, 2021 at 11:08 | answer | added | Hilmar | timeline score: -1 | |
| Aug 4, 2021 at 9:16 | history | edited | OverLordGoldDragon | CC BY-SA 4.0 |
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| Aug 4, 2021 at 9:16 | comment | added | OverLordGoldDragon | @Hilmar Right, I missed conjugation, which does return energy at origin. | |
| Aug 3, 2021 at 14:30 | comment | added | Hilmar | But than it's not an autocorrelation. It's something else. | |
| Aug 3, 2021 at 3:18 | comment | added | OverLordGoldDragon | @Hilmar $r_{xx}(T) = \sum x[n]x[n+T]$ is the definition I use (and is the standard w/ normalization) which differs from $|x...|$ for complex $x$. | |
| Aug 3, 2021 at 3:08 | history | edited | OverLordGoldDragon | CC BY-SA 4.0 |
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| Aug 2, 2021 at 22:23 | comment | added | Hilmar | Sorry, I'm not getting this. The autocorrelation can't be 0. $r_{xx}(0) = \sum |x[n]|^2$ so it's the power of the signal. | |
| Aug 1, 2021 at 23:05 | comment | added | OverLordGoldDragon | Correction: zero autocorrelation (asm. zero-mean), or conv with own conjugate. | |
| Aug 1, 2021 at 22:19 | comment | added | OverLordGoldDragon | @Hilmar Interesting article. I intend "analytic" in discrete/finite sense: negative DFT bins = zero. This guarantees zero in self-convolution. | |
| Aug 1, 2021 at 21:51 | comment | added | Hilmar | @OverLordGoldDragon: can you give a crisp definition of what exactly you mean by "analytic sequence". The standard definition of a continuous analytic signal is "has no negative frequencies" but since a discrete signal is periodic in frequency, that doesn't work. Related reading: andrewduncan.net/air | |
| Aug 1, 2021 at 20:14 | history | edited | OverLordGoldDragon | CC BY-SA 4.0 |
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| Aug 1, 2021 at 20:14 | comment | added | OverLordGoldDragon |
@PeterK. I seek to "qualify" $x$ for zero autocorrelation by only looking at it in time domain. Possible I'm missing something but I've not found much in Hilbert transform as aid; sure one can test x == analytic(x.real), but that doesn't reveal any properties like symmetry/norm. I suppose my actual goal is sufficient criteria for $A \neq B$.
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| Aug 1, 2021 at 18:01 | comment | added | OverLordGoldDragon | @PeterK. I'm unfamiliar with time-domain form of Hilbert transform, but suppose I'll find insights there - will look into. Also I'm uncertain regarding criterion 1, might be L1 norm instead, and unsure if there's such a relation for $A \neq B$; I'll revisit bit later. | |
| Aug 1, 2021 at 17:48 | comment | added | Peter K.♦ | Interesting question. What's wrong with the usual "the imaginary part is the Hilbert transform of the real part" ? It doesn't explicitly go to the frequency domain, though perhaps that implies something in the frequency domain. | |
| Aug 1, 2021 at 17:33 | history | edited | OverLordGoldDragon | CC BY-SA 4.0 |
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| Aug 1, 2021 at 17:24 | history | edited | OverLordGoldDragon | CC BY-SA 4.0 |
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| Aug 1, 2021 at 17:15 | history | edited | OverLordGoldDragon | CC BY-SA 4.0 |
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| Aug 1, 2021 at 17:07 | history | asked | OverLordGoldDragon | CC BY-SA 4.0 |