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Pavoo
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Homework Statement
My book writes the following: using pair for the Discrete Time Fourier Transform:
[itex]-a^{k}u[-k-1] <---(DTFT)---> \frac{1}{1-ae^{-iw}} for \left | a \right | > 1[/itex]
Homework Equations
Well, for the simple similar pair such as:
[itex]a^{k}u[k] <---(DTFT)---> \frac{1}{1-ae^{-iw}} for \left | a \right | < 1[/itex]
The calculation is pretty straightforward regarding the GP series.
In the above however, I get lost where they get the result from.
The Attempt at a Solution
I've come to here, coming from DTFT definition and simplifying the unitstep boundaries to the sum of:
[itex]\sum_{1}^{\infty}a^{-k}e^{iwk}[/itex]
The question is, how do I get from here to the above?
[itex]a^{k}u[k] <---(DTFT)---> \frac{1}{1-ae^{-iw}} for \left | a \right | < 1[/itex]
I am thankful for any walk through you can give, since I spent way too much time on this problem. Is there something obvious I don't see about this one, or is the calculation of GP series I am mistaken about?
Thanks in advance!