Given a signal $ x \left[ n \right] $ and its DTFT $ X \left( {e}^{j \omega} \right) $.
Which property of the DTFT allows you to easily compute the inverse DTFT of $ \frac{4 X \left( {e}^{j \omega} \right)}{\pi} - 2 $?
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3$\begingroup$ I'm voting to close this question as off-topic because no effort shown $\endgroup$– user28715Jul 5, 2018 at 17:27
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$\begingroup$ For my understanding, what would be some imrovements that would make this question meet the standards? Thank you $\endgroup$– Sau001Jun 25, 2021 at 17:35
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1 Answer
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The property is the Linearity of the DTFT.
Linearity means that if your input is a linear combination of signals the output will be the same linear combination of each input by itself:
$$ \operatorname{DTFT} \left( \alpha x \left[ n \right] + \beta y \left[ n \right] \right) = \alpha \operatorname{DTFT} \left( x \left[ n \right] \right) + \beta \operatorname{DTFT} \left( y \left[ n \right] \right) $$
This also holds for the Inverse DTFT.
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