# DTFT of $f[k] = 3^k u(-k-1)$

Find the Discrete-time Fourier transform of $f[k] = 3^k u(-k-1)$ (then sketch it and find its magnitude & angle).

It doesn't fit any templates on the Fourier table, and I don't see how one could re-arrange this expression to solve it. So, how?

Also for $\mathcal Z$-transform, how does one solve:

you have $\displaystyle H(z) = \frac{1}{1 - \frac 12 z^{-1}}$ and input to that is $f[k] = 2^k$

How do you find $y(t)$?

The general formula of $\mathcal Z$-transform is:

$$F(z) = \sum_{k=\infty}^{0} f[k] z^{-k}$$

• Possible duplicate of z-transform of $2^k$
– msm
May 5 '17 at 21:39
• @msm Except that doesn't have an answer either. I can't close a question as duplicate if the "duplicate" is not answered (well, I can, I just think it's nonsensical).
– Peter K.
May 6 '17 at 17:18
• You are right @PeterK. I should have flagged the original question for lack of context as well. It seems qualified for closure.
– msm
May 6 '17 at 23:19
• @msm what lack of context? you simply chose to ignore my last question. Please don't offer that kind of "help" if you fail to follow up with a response.
– Jack
May 9 '17 at 3:59