- #1

arcTomato

- 105

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- TL;DR Summary
- Fourier transform

Dear all.

I'm learning about the discrete Fourier transform.

##I(\nu) \equiv \int_{-\infty}^{\infty} i(t) e^{2 \pi \nu i t} d t=\frac{N}{T} \sum_{\ell=-\infty}^{\infty} \delta\left(\nu-\ell \frac{N}{T}\right)##

this ##i(t)## is comb function

##i(t)=\sum_{k=-\infty}^{\infty} \delta\left(t-\frac{k T}{N}\right)##.

I would like to see how to derive ##I(ν)##.(Especially the part about transformation to ##lN/T from kT/N)

If you can teach me, please.

Thank you.

I'm learning about the discrete Fourier transform.

##I(\nu) \equiv \int_{-\infty}^{\infty} i(t) e^{2 \pi \nu i t} d t=\frac{N}{T} \sum_{\ell=-\infty}^{\infty} \delta\left(\nu-\ell \frac{N}{T}\right)##

this ##i(t)## is comb function

##i(t)=\sum_{k=-\infty}^{\infty} \delta\left(t-\frac{k T}{N}\right)##.

I would like to see how to derive ##I(ν)##.(Especially the part about transformation to ##lN/T from kT/N)

If you can teach me, please.

Thank you.

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