Timeline for Restrictiveness of the condition that different signals give same autocorrelation sequence
Current License: CC BY-SA 4.0
7 events
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| Jun 9, 2021 at 13:27 | comment | added | mark leeds | Hi Hilmar: It's definitely confusing for me and at some point I just decided to consider them as two different concepts that happen to have the same The link below isn't bad. The only "negative" ( no pun intended ) is that something went with wrong with the latex so there should be negative signs in the definition of the sample autocorrelation, $\hat{\rho}_{k}$. statlect.com/fundamentals-of-statistics/autocorrelation | |
| Jun 8, 2021 at 19:34 | comment | added | Guru Aravind | Actually, I became more confused when I tried graphing the case of N=3 using some 3d graphing apps. I found that the only possible solutions, in that case, were the original sequence, its negation, its reverse and the reverse's negation. Then when I tried this code, I found that these deviations existed even though I had the same magnitude responses. | |
| Jun 8, 2021 at 19:30 | comment | added | Guru Aravind | @Hilmar: Thank you very much for the answer. I tried implementing the above idea in MATLAB by taking the fft of a known sequence and then multiplying the entire fft sequence by "i". Then I adjusted some of the constants to ensure the condition for realness after ifft, without changing the magnitude. After I took the ifft, I found the autocorrelation sequence of the newly formed sequence. But it varies from the original autocorrelation by a significant factor, especially at the trailing edge of the sequence. Could you give an idea as to what causes this deviation? | |
| Jun 8, 2021 at 11:28 | comment | added | Hilmar | Thanks for your comment. It certainly NOT a good idea to use the same word for two related concepts that are have substantial differences. Can you post a link to a crisp definition of what the statistical autocorrelation is. I googled some but most stuff I found was fluffy. | |
| Jun 7, 2021 at 21:52 | comment | added | mark leeds | Hi Hilmar: That's a lot for me to take in because of statistics background but, to anyone who comes here from statistics, the autocorrelation in your trivial example would not be the same. The autocorrelation at lag zero would be the same. Yet, the autocorrelation at lags 1 and 2 would be the exact opposite of each other in sign. But this is caused by a definition difference between statistics and dsp so I'm not saying anything that you said is incorrect. I'm just giving a heads up to any stat people who may find it puzzling. | |
| Jun 7, 2021 at 11:38 | vote | accept | Guru Aravind | ||
| Jun 7, 2021 at 11:34 | history | answered | Hilmar | CC BY-SA 4.0 |