Discrete Time Fourier Transformation (DTFT) Question

[Inquiring_M]

Hello all !

Homework Statement

I have the following problem.

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

Homework Equations

Fourier Transformations

The Attempt at a Solution

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


Is this alright so far ?

It is proven that 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 !

 

[anathema]

Thank you for your question. It seems like you have a good understanding of the concept of DTFT. You are correct in thinking that a DTFT is essentially a collection of DFTs calculated at different frequencies. In this case, since the signal x(n) is a simple step function, the DTFT can be calculated using the formula for the DTFT of a step function, which is 1/(1-e^(-jw)). This will give you a result that is a complex exponential function. You can then plot the magnitude and phase of this function to get a better understanding of the frequency components present in your signal. I hope this helps. Good luck with your calculations!