Timeline for Hartley Transform vs Fourier Transform
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Nov 30, 2021 at 13:05 | comment | added | Laurent Duval | Not so sure on the finite number. Convergence issues (notably in the discrete case) seem complicated to me. | |
| Nov 29, 2021 at 23:26 | comment | added | robert bristow-johnson | oh c'mon, there are really a finite number of theorems and properties. it's one reason that i like the unitary form: $$ X(f) \triangleq \mathscr{F}\Big\{ x(t) \Big\} = \int\limits_{-\infty}^{+\infty} x(t) \, e^{-j 2 \pi f t} \ dt $$ $$ x(t) \triangleq \mathscr{F}^{-1}\Big\{ X(f) \Big\} = \int\limits_{-\infty}^{+\infty} X(f) \, e^{+j 2 \pi f t} \ df $$ so that i can take advantage of the similarity of forward and inverse, of $-j$ and $+j$. it makes duality, parseval's and convolution theorems and the such easy to remember. | |
| Nov 29, 2021 at 22:15 | comment | added | Laurent Duval | @robertbristow-johnson I truly appreciate your concern. Yet I really feel that even in 1D, I need a couple of years to get more insights, especially on its discretizations and its phase properties | |
| Nov 28, 2021 at 18:48 | comment | added | robert bristow-johnson | Laurent it's hard for me to believe that you do not understand the Fourier Transform. | |
| Jan 10, 2021 at 22:35 | history | edited | Laurent Duval | CC BY-SA 4.0 |
added details
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| Oct 9, 2016 at 8:30 | history | edited | Laurent Duval | CC BY-SA 3.0 |
added an historical note
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| Oct 9, 2016 at 8:17 | comment | added | Laurent Duval | I am glad not being alone in such a gross coming-out. Without the appropriate level in maths, I am becoming semi-Platonist. Some tools might be unreasonably efficient because of intricate relationships pertaining to analysis, algebra or topology. If I have a lot of free time, I will dive into category theory, to take a step above the landscape, and see what emerges | |
| Oct 9, 2016 at 4:24 | comment | added | Marcus Müller | "I still don't" <- same here. If I happen to end up with too much spare time on my hands, I might do some functional analysis, ~ theory and group theory... and knowing that those people that took matching courses during their math studies have less of a practical understanding of the FT ("huh, you use that for what? What's frequency? It was just one of the examples on one of our exam sheets for the less interesting class of linear integral transforms..."), I probably still won't understand it, just more of its structural foundation... | |
| Oct 8, 2016 at 21:54 | history | answered | Laurent Duval | CC BY-SA 3.0 |