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 $?


closed as off-topic by Stanley Pawlukiewicz, MBaz, lennon310, jojek Jul 10 '18 at 13:40

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    $\begingroup$ I'm voting to close this question as off-topic because no effort shown $\endgroup$ – Stanley Pawlukiewicz Jul 5 '18 at 17:27

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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