0
$\begingroup$

I have a x[n] = $\delta$[n]. By formula is should be

$$

X[k]= \sum_{n=0}^{N-1} \delta[n]W_N^{kn}

X[k]= \sum_{n=0}^{N-1} e^{-j2*pi*kn/N}

$$

The formulae isn't showing for some reason. I took a screenshot of what I got here: http://imgur.com/6j0Ibgu

basically why is the summation of an exponential term going to 1. $W_N=e^{-j*2*pi*k*n/N}$ in this case. I tried to prove it via $\sum\alpha^k=\frac{1-\alpha^N}{1-\alpha}$ but it doesn't work for me.

$\endgroup$
0
$\begingroup$

$X[k]= \sum_{n=0}^{N-1} \delta[n]W_N^{kn} \quad$, where $\>W_N^{kn}=e^{−j\,2\pi k\,n/N}$

HINT:

What is the value of $\delta[n]$ when $n \neq 0 \>$ ?

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.