# Find amplitude-frequency characteristic of a discrete finite signal using Z-transform

I have a following signal given:

$$S(n) = [-1, 0, 2, -1]$$

I have to find the Z-transform of the signal and find amplitude-frequency characteristic and amplitude-phase characteristic of the signal.

So far I've managed to get to the point that the Z transform of the S(n) signal will be:

$$Z(z) = 2z^{-2} - z^{-3} - 1$$

However, I have no idea where to go from this. How do I find the characteristics?

• The offered bounty is too low for the level of the question.

• Very low bounty!

• I can provide you guidance and details of how to obtain the transform and the two characteristics, but cannot draw the plots. Let me know if that works. If you want the plots, they need to be plotted using the magnitude of the phase at different frequencies.

• That works for me

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Kav10
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• Can you correct your answer? There are a lot of question marks instead of actual symbols

• @ Kav10: Thank you for your very detailed solution. As Piotr mentioned, there were a lot of question marks in your solutions, which I guess was due to a copy/past from another editor. Matchmaticians editor runs automatically LaTeX. Writing solutions with LaTeX significantly improves readability of the solutions. I have edited your solution, and there are no questions marks/errors now. Please review the changes.

• @Piotr the question marks where dashes just to separate the three parts of the answer. Not sure why dashes were shown as question marks after submitting.

• @Walter thanks for editing the formulas, etc. It looks fine. I used my cellphone this time and it did not give me the LaTex option. I wrote the solution in “notes” and then added here, reviewed before submitting and it looked fine. Thanks again for editing.

• You can also type latex code with your phone, but it is much more convenient to type on a desktop.

• Agreed! Thanks.