Timeline for PDF of $z = \exp(j\varphi)$, where $\varphi \sim \mathcal{U}[-a, +a]$
Current License: CC BY-SA 4.0
19 events
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| Dec 28, 2019 at 11:43 | comment | added | Felipe Augusto de Figueiredo | @IosifPinelis, thanks for your reply. I totally agree with your comment. You have given the answer to the question and the other one would be a totally different question and the answer as you said is quite straightforward to get to. Have a nice 2020! | |
| Dec 27, 2019 at 16:08 | vote | accept | Felipe Augusto de Figueiredo | ||
| Dec 26, 2019 at 0:11 | comment | added | Iosif Pinelis | Felipe: Your question was about the pdf of $z$ (not about the pdf's of the real and imaginary parts of $z$), and that question was answered. The real-and-imaginary question is a different one and should be asked separately, to keep things in good order, even though it is not hard to answer that question either. | |
| Dec 25, 2019 at 14:58 | comment | added | Felipe Augusto de Figueiredo | @IosifPinelis, I was expecting something like two distinct distributions, one for the real and another for the imaginary parts of $Z$. However, it seems the final result is a unified PDF (and quite complex, at least for me, expression). | |
| Dec 25, 2019 at 14:30 | comment | added | Iosif Pinelis | Felipe: Again, if you can specify what seems unclear to you, then I can try to further help you. | |
| Dec 25, 2019 at 13:52 | comment | added | Felipe Augusto de Figueiredo | @IosifPinelis, thanks for your reply. To be honest, I still don't get what is the PDF of $Z$. | |
| Dec 24, 2019 at 23:56 | comment | added | Michael Engelhardt | @GeraldEdgar - but $j$ is the current density! Quoth the physicist ... | |
| Dec 24, 2019 at 20:26 | comment | added | Gerald Edgar | We commonly see $j$ in electrical engineering (and perhaps also other engineering). They say they do not want to collide with $i$ which is used for current. | |
| Dec 24, 2019 at 19:31 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Dec 24, 2019 at 17:42 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Dec 24, 2019 at 16:44 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Dec 24, 2019 at 16:15 | comment | added | Iosif Pinelis | Dear Michael, I am glad this issue got resolved. Best wishes to you too! | |
| Dec 24, 2019 at 16:14 | comment | added | Iosif Pinelis | @FelipeAugustodeFigueiredo : As usual, I have tried my best to present the answer. So, at this point I don't know how to improve/detail it, unless you tell me at what specific junctions you have difficulties. Perhaps those junctions include the notions of the push-forward measure and determining/defining a measure $\mu$ by integrals $\int g\,d\mu$. Is that so? | |
| Dec 24, 2019 at 16:02 | comment | added | Michael Engelhardt | Dear Iosif, I'm not genuinely offended, and I'm not surprised that there might be some $j$s in physics papers (although I would never do that myself). Happy holidays! | |
| Dec 24, 2019 at 15:57 | comment | added | Felipe Augusto de Figueiredo | @IosifPinelis, sorry but I haven't followed you. Could you explain better how p(c) is the PDF of z, please? | |
| Dec 24, 2019 at 15:53 | comment | added | Iosif Pinelis | @MichaelEngelhardt : I am sorry if this hurt your feelings. I did not think this could offend anyone. I believe I did see $j$ in place of $i$ in some physics papers. Anyhow, I have removed the mention of physics. | |
| Dec 24, 2019 at 15:52 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Dec 24, 2019 at 15:41 | comment | added | Michael Engelhardt | I take umbrage at the suggestion, and strenuously deny, that physicists write $j$ instead of $i$. | |
| Dec 24, 2019 at 15:15 | history | answered | Iosif Pinelis | CC BY-SA 4.0 |