# Discrete Time Fourier Transformation (DTFT) Question

#### Inquirer

Joined Oct 29, 2012
2
Hello all I have the following problem.

I have to calculate the DTFT of this : x(n)=u(n)-u(n-4).

So far , from what I have studied I have understood, that DTFT , is actually many DFT's calculated for different omega values lets say in an interval from -pi to pi , with step 0.2 .

Is this so far correct ?

we know that (it is proven) x(n) = 1

So finally have this: Now my main problem, how can I continue from that step ? Am I supposed to get some arithmetic result ?

Thanks for you help !

#### blah2222

Joined May 3, 2010
582
If you plot out x[n] you get a step function that lasts from n = 0 to n = 3 where it holds the value of '1' and is '0' everywhere else. This simplifies the expression:

$$X(\omega) = \sum_{n=-\infty}^{\infty}x[n]e^{-jwn} X(\omega) = \sum_{n=0}^{3}(1)e^{-jwn} X(\omega) = 1 + e^{-j\omega} + e^{-j2\omega} + e^{-j3\omega}$$

Plotting the magnitude of X(w) in MATLAB (-4pi:4pi) an infinite response: