Timeline for fourier transform on an interval?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 5, 2015 at 22:27 | vote | accept | Qiao | ||
| Mar 11, 2012 at 19:43 | answer | added | Bazin | timeline score: 4 | |
| Jun 15, 2011 at 12:49 | comment | added | André Henriques | From the previous answers, you have seen that there are MANY different ways of defining this ill-defined Fourier transform. You say: "I have to do these computations". So you haveto make a choice. Please make sure that you know how to justify your choice. In other words, it's not enough justify the computation after the fact by saying "it provided the answer that I wanted to get". You need to understand why the particular choice that you made is the correct one to make. | |
| Jun 15, 2011 at 11:00 | comment | added | S. Carnahan♦ | Alternatively, you can analytically continue these functions to complex functions on the complex line minus some branch cuts. You should end up with a tempered distribution that depends on your choice of branch. | |
| Jun 15, 2011 at 5:52 | comment | added | Yemon Choi | If the function $(10-x^2)^{-1/2}$ arises in some physical model, the chances are that this is implicitly understood to vanish outside the interval $[-\sqrt{10},\sqrt{10}]$, in line with what Zen suggests. On the other hand, sometimes one observes values on a finite interval but knows for some physical reason that it should be periodic (e.g. electric potential from a mains socket) and so in that case one should use Fourier series. | |
| Jun 15, 2011 at 4:52 | comment | added | Zen Harper | Why not just define the function to be zero outside the interval? Or, if the interval is bounded, why not use Fourier series instead? You need to specify in more detail why you want to use the Fourier transform; it changes certain functions into certain other functions, but without knowing what properties you seek, it is difficult to know exactly what you should be looking for. | |
| Jun 15, 2011 at 4:15 | history | asked | Qiao | CC BY-SA 3.0 |