Properties of DTFT to Infer the Inverse DTFT of Altered Data
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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