User Tools
notes:cft
Differences
This shows you the differences between two versions of the page.
| Both sides previous revisionPrevious revisionNext revision | Previous revision | ||
| notes:cft [2020/11/24 16:57] – cjj | notes:cft [2020/11/25 19:43] (current) – [Fourier integral theorem and Dirac δ-function] cjj | ||
|---|---|---|---|
| Line 13: | Line 13: | ||
| e^{-i\pi m}D_m\propto\sum_{k=0}^{N-1}\exp\left(-2\pi i\frac{km}{N}\right)e^{i\pi k}\tilde{D}_k | e^{-i\pi m}D_m\propto\sum_{k=0}^{N-1}\exp\left(-2\pi i\frac{km}{N}\right)e^{i\pi k}\tilde{D}_k | ||
| \end{equation} | \end{equation} | ||
| + | =====Fourier integral theorem and Dirac δ-function===== | ||
| + | {{ : | ||
| + | [[https:// | ||
| + | \[ | ||
| + | \int_{-\infty}^\infty dx \frac{\sin(xL)}{x} = \pi | ||
| + | \] | ||
| + | As $L$ goes to infinity, the integrand becomes more and more like a δ-function. | ||
| + | |||
| + | - [[http:// | ||
notes/cft.1606237038.txt.gz · Last modified: by cjj
Page Tools
Except where otherwise noted, content on this wiki is licensed under the following license: CC Attribution-Noncommercial-Share Alike 4.0 International
