Timeline for Autocorrelation function of a filtered periodic signal
Current License: CC BY-SA 4.0
53 events
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| S Apr 18, 2023 at 14:49 | history | suggested | Maghreb_1911 | CC BY-SA 4.0 |
Removed some non necessary parts, cleaned the notation and corrected various mistakes
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| Apr 18, 2023 at 14:46 | review | Suggested edits | |||
| S Apr 18, 2023 at 14:49 | |||||
| Apr 17, 2023 at 22:46 | history | edited | Dan Boschen | CC BY-SA 4.0 |
fixed equation 13 to be "Z[kf_o=" as intended instead of "Y[kf_o]="
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| Apr 17, 2023 at 21:22 | history | edited | Dan Boschen | CC BY-SA 4.0 |
Reverted to earlier form where positive indexing Fourier series was introduced earlier in the solution
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| Apr 17, 2023 at 21:17 | history | edited | Dan Boschen | CC BY-SA 4.0 |
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| Apr 17, 2023 at 20:15 | history | rollback | Dan Boschen |
Rollback to Revision 28
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| Apr 17, 2023 at 20:13 | history | rollback | Dan Boschen |
Rollback to Revision 29
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| S Apr 17, 2023 at 14:38 | history | edited | lennon310 | CC BY-SA 4.0 |
Corrected some mistake due to the brief confusion between rectangular and exponential Fourier Series
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| S Apr 17, 2023 at 14:38 | history | suggested | Maghreb_1911 | CC BY-SA 4.0 |
Corrected some mistake due to the brief confusion between rectangular and exponential Fourier Series
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| Apr 17, 2023 at 13:29 | review | Suggested edits | |||
| S Apr 17, 2023 at 14:38 | |||||
| Apr 17, 2023 at 13:18 | history | edited | Dan Boschen | CC BY-SA 4.0 |
simplified by going to positive k indexing much earlier
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| Apr 17, 2023 at 12:38 | history | edited | Dan Boschen | CC BY-SA 4.0 |
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| Apr 17, 2023 at 11:59 | history | edited | Dan Boschen | CC BY-SA 4.0 |
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| Apr 17, 2023 at 11:52 | history | rollback | Dan Boschen |
Rollback to Revision 23
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| Apr 17, 2023 at 11:43 | history | edited | Dan Boschen | CC BY-SA 4.0 |
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| Apr 17, 2023 at 11:11 | history | edited | Dan Boschen | CC BY-SA 4.0 |
Fixed factor of 2 error in 14 and 16
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| Apr 17, 2023 at 10:43 | history | edited | Dan Boschen | CC BY-SA 4.0 |
no change, just make equation 14 look cleaner
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| Apr 17, 2023 at 10:27 | history | edited | Dan Boschen | CC BY-SA 4.0 |
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| Apr 17, 2023 at 10:09 | history | edited | Dan Boschen | CC BY-SA 4.0 |
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| Apr 17, 2023 at 9:59 | history | edited | Dan Boschen | CC BY-SA 4.0 |
fix sign error in equation 5
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| Apr 16, 2023 at 19:15 | history | edited | Dan Boschen | CC BY-SA 4.0 |
correcting errors caught by OP
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| Apr 16, 2023 at 18:49 | comment | added | Maghreb_1911 | Let us continue this discussion in chat. | |
| Apr 16, 2023 at 13:32 | comment | added | Dan Boschen | @Maghreb_1911 Thanks for the fun math "work-out" and your co-verification efforts. I feel like equation 16 could possibly reduce nicely to something to get rid of the summation but haven't pursued that. Plotting it may reveal what it converges to. | |
| Apr 16, 2023 at 13:19 | vote | accept | Maghreb_1911 | ||
| Apr 16, 2023 at 13:19 | comment | added | Maghreb_1911 | Yes, that seems a good idea. I'm going to close this one, then. Thank you very much for your help. | |
| Apr 16, 2023 at 11:34 | comment | added | Dan Boschen | @Maghreb_1911 not quite, there are caveats and more than I can explain in the comments- rather than make this longer, could we close this one out and post that as another question? I believe I can show cases for discrete in frequency with no periodicity in time but let’s see what others say too! | |
| Apr 16, 2023 at 8:32 | comment | added | Maghreb_1911 | Having a periodic signal means that in the frequency domain its representation consists of a certain number of Dirac deltas. So, if we have a discrete spectrum, there has to be a periodicity in the time domain. Is this what you are saying? And this fact continues to being true even if we remove a finite number of said deltas (which we call spectral components)? | |
| Apr 16, 2023 at 1:00 | comment | added | Dan Boschen | @Maghreb_1911 yes it is. Consider that each discrete frequency tone, on its own is periodic in time, and each of those tones in frequency are all integer harmonics of each other (important point to maintain periodicity). So the sum of that must also be periodic. If you remove any one or may of the frequencies, that shouldn't change the periodicity as provided by the sum of the rest. Does that make sense? | |
| Apr 15, 2023 at 23:15 | comment | added | Maghreb_1911 | Yes, you're right, sorry. There is only one thing I am not sure about: the formula you used to calculate the ACF is for periodic signals. Does that mean $ z (t) $ is still periodic, even if we have removed a part of it with the filter? | |
| Apr 15, 2023 at 22:50 | comment | added | Dan Boschen | @Maghreb_1911 $\cos(\pi/2 k)$ for $k = 2$ is $\cos(\pi) = -1$, and again for $k=6, 10, 14, \ldots$ right? (And = 1 for $k=4, 8, 12...$ | |
| Apr 15, 2023 at 19:46 | comment | added | Maghreb_1911 | So, since the expression of $Y_k$ is complicated, we try to find another way to describe the signal in the frequency domain (the rectangular coefficient $ a_k $ ) ? There may be a wrong sign in the number $ (6) $ , since $ cos( \frac{\pi}{2} \cdot k ) $ is always positive for even k. | |
| Apr 15, 2023 at 16:34 | comment | added | Dan Boschen | @Maghreb_1911 see my updates. | |
| Apr 15, 2023 at 16:32 | history | edited | Dan Boschen | CC BY-SA 4.0 |
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| Apr 15, 2023 at 16:22 | history | edited | Dan Boschen | CC BY-SA 4.0 |
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| Apr 15, 2023 at 15:55 | history | edited | Dan Boschen | CC BY-SA 4.0 |
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| Apr 15, 2023 at 15:38 | history | edited | Dan Boschen | CC BY-SA 4.0 |
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| Apr 15, 2023 at 14:33 | history | edited | Dan Boschen | CC BY-SA 4.0 |
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| Apr 15, 2023 at 12:41 | comment | added | Maghreb_1911 | Well, now we get the same result, but the original question remain unanswered: since we agree on part 1, is my $Z(f)$ correct? How do I calculate the ACF of $z(t)$? | |
| Apr 15, 2023 at 11:55 | history | edited | Dan Boschen | CC BY-SA 4.0 |
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| Apr 15, 2023 at 11:50 | history | edited | Dan Boschen | CC BY-SA 4.0 |
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| Apr 15, 2023 at 11:43 | history | edited | Dan Boschen | CC BY-SA 4.0 |
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| Apr 15, 2023 at 11:18 | history | edited | Dan Boschen | CC BY-SA 4.0 |
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| Apr 15, 2023 at 10:43 | history | edited | Dan Boschen | CC BY-SA 4.0 |
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| Apr 15, 2023 at 10:11 | comment | added | Maghreb_1911 | I added the way I computed the Fourier Transform of $y(t)$ . We get two slightly different results in the end, I think there are two mistakes in the $(7)$ , one of which is the application of the Time Scaling property of the Fourier transform. | |
| Apr 15, 2023 at 2:08 | history | edited | Dan Boschen | CC BY-SA 4.0 |
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| Apr 15, 2023 at 1:31 | history | edited | Dan Boschen | CC BY-SA 4.0 |
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| Apr 14, 2023 at 22:14 | history | edited | Dan Boschen | CC BY-SA 4.0 |
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| Apr 14, 2023 at 21:55 | history | edited | Dan Boschen | CC BY-SA 4.0 |
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| Apr 14, 2023 at 19:04 | comment | added | Maghreb_1911 | Do you get notified if I edit my question? | |
| Apr 13, 2023 at 13:11 | history | edited | Dan Boschen | CC BY-SA 4.0 |
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| Apr 13, 2023 at 12:30 | history | edited | Dan Boschen | CC BY-SA 4.0 |
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| Apr 13, 2023 at 12:11 | comment | added | Maghreb_1911 | Hello and thank you for your answer. $g(x)$ is $0$ when $x(t)$ is negative, so why is taking only the first half of the cosine's period (in which it is positive) wrong? | |
| Apr 13, 2023 at 11:58 | history | answered | Dan Boschen | CC BY-SA 4.0 |