Timeline for Why do singularities on the imaginary axis affect the Fourier transform differently than the Laplace transform?
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 17, 2024 at 3:35 | vote | accept | Mikayla Eckel Cifrese | ||
| Jan 14, 2024 at 20:39 | comment | added | Dan Boschen | offering this as a comment ( as Ahsan has a nice answer) for additional intuition if Fourier Series expansion is understood: Consider the Fourier Series expansion of a constant: it is an impulse a $f=0$ (DC). Now consider the Fourier Series expansion of a step: it would have all frequencies, going down at $1/f$. This is the difference between Fourier and (unilateral) Laplace: Fourier is a correlation with functions constant for all time, so would converge to an impulse. Laplace is a correlation with functions that step at $t=0$. That step smears out what would have otherwise been impulses. | |
| Jan 14, 2024 at 17:14 | history | became hot network question | |||
| Jan 14, 2024 at 8:41 | answer | added | Ahsan Yousaf | timeline score: 2 | |
| Jan 14, 2024 at 5:05 | history | asked | Mikayla Eckel Cifrese | CC BY-SA 4.0 |