- #1

Swapnil

- 459

- 5

My book on signal processing says that:

[tex] f(t) = \frac{1}{2\pi j} \int_{c-j\infty}^{c+j\infty} F(s) e^{st} ds = \lim_{\Delta s \to 0} \sum_{n = -\infty}^{\infty} \Big[ \frac{F(n\Delta s)\Delta s}{2\pi j} \Big] e^{n\Delta s t}[/tex]

I don't get this. How/Why can you write a integration over a complex variable as the above sum?

edit: I forgot a coefficient [tex]\frac{1}{2\pi j}[/tex] on the LHS. Sorry about that. Its fixed now.

[tex] f(t) = \frac{1}{2\pi j} \int_{c-j\infty}^{c+j\infty} F(s) e^{st} ds = \lim_{\Delta s \to 0} \sum_{n = -\infty}^{\infty} \Big[ \frac{F(n\Delta s)\Delta s}{2\pi j} \Big] e^{n\Delta s t}[/tex]

I don't get this. How/Why can you write a integration over a complex variable as the above sum?

edit: I forgot a coefficient [tex]\frac{1}{2\pi j}[/tex] on the LHS. Sorry about that. Its fixed now.

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