0
$\begingroup$

enter image description here

When I am in the DT Fourier Domain, and I want to come back to the time domain, which pair do I use? Asking because both pairs have the exact same "form" in the Fourier domain, and that is what is tripping me up. Do I just use pair 2 when I want to go into the Fourier domain and then I have to use pair 1 when I want to come back?? Or is there more to it than that?

$\endgroup$
1
$\begingroup$

I would really recommend that you compute the DTFT of the sequences $x_1[n]=a^nu[n]$ and $x_2[n]=-a^nu[-n-1]$. This is very straightforward if you use the formula for the geometric series:

$$\sum_{n=0}^{\infty}q^n=\frac{1}{1-q},\qquad |q|<1\tag{1}$$

It will be important to consider the magnitude of $a$. Note that it's not for nothing that the table in your question specifies a condition on $|a|$.

$\endgroup$

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.