Discrete Time Fourier Transformation (DTFT) Question

Discussion in 'Homework Help' started by Inquirer, Oct 29, 2012.

1. Inquirer Thread Starter New Member

Oct 29, 2012
2
0
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 !

2. blah2222 Well-Known Member

May 3, 2010
574
36
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:

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