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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?


1 Answer 1


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 $|a|$.


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