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:

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

  • 3
    $\begingroup$ Possible duplicate of z-transform of $2^k$ $\endgroup$
    – msm
    May 5, 2017 at 21:39
  • 2
    $\begingroup$ @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). $\endgroup$
    – Peter K.
    May 6, 2017 at 17:18
  • $\begingroup$ You are right @PeterK. I should have flagged the original question for lack of context as well. It seems qualified for closure. $\endgroup$
    – msm
    May 6, 2017 at 23:19
  • $\begingroup$ @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. $\endgroup$
    – Jack
    May 9, 2017 at 3:59


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