- #1

- 9

- 0

## Homework Statement

Given is [itex]\sum_{n=-N}^{N}e^{-j \omega n} = e^{-j\omega N} \frac{1-e^{-j \omega (2N+1)}}{1 - e^{-j\omega}}[/itex]. I do not see how you can rewrite it like that.

## Homework Equations

Sum of a finite geometric series: [itex]\sum_{n=0}^{N}r^n=\frac{1-r^{N+1}}{1-r}[/itex]

## The Attempt at a Solution

Or is the above result based on this more general equation: [itex]\sum_{n=0}^{N}ar^n=a\frac{1-r^{N+1}}{1-r}[/itex]? Although I think the equation in (2) is just this equation for a=1, right?

So, I know how to get to the 2nd term in (1), i.e., [itex]\frac{1-e^{-j \omega (2N+1)}}{1 - e^{-j\omega}}[/itex], but I have no idea why it is multiplied by the term [itex]e^{-j\omega N}[/itex].