Timeline for Are complex exponentials the only eigenfunction for arbitrary LTI systems?
Current License: CC BY-SA 4.0
10 events
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| Nov 11, 2023 at 11:53 | history | edited | Matt L. | CC BY-SA 4.0 |
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| Nov 11, 2023 at 11:52 | comment | added | Matt L. | @David: That's of course true, but from the question it appears that the OP is aware that specific LTI systems can have many more eigenfunctions than just the complex exponentials. The way I understood the question is if complex exponentials are the only eigenfunctions in the most general case, i.e. for all possible LTI systems. | |
| S Nov 11, 2023 at 11:44 | history | edited | Matt L. | CC BY-SA 4.0 |
elaborated answer by copying comment in
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| S Nov 11, 2023 at 11:44 | history | suggested | roobee | CC BY-SA 4.0 |
elaborated answer by copying comment in
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| Nov 10, 2023 at 18:29 | comment | added | David | If you consider a trivial system with an impulse response of a scaled delta function. Then every input function is an eigenfunction, since the output is simply a scaled version of the input. | |
| Nov 10, 2023 at 16:31 | vote | accept | roobee | ||
| Nov 10, 2023 at 16:30 | review | Suggested edits | |||
| S Nov 11, 2023 at 11:44 | |||||
| Nov 10, 2023 at 16:28 | comment | added | roobee | Thanks! I tried to find whether exponential function was the only one that satisfied f(x+y) = f(x)f(y) previously but I couldn't find it. I'll edit the comment into the answer and accept it | |
| Nov 10, 2023 at 14:32 | comment | added | Brian61354270 | Also worth noting that exponential functions are the only continuous functions that satisfy $x(t-\tau) = x(t)x(-\tau)$ (with some qualifications). Related question from Math.SE: A function with a property $f(x+y)=f(x)f(y)$ | |
| Nov 10, 2023 at 10:52 | history | answered | Matt L. | CC BY-SA 4.0 |