### Linearity of the DTFT

(3.9) |

or

(3.10) |

where are any

*scalars*(real or complex numbers), and are any two

*discrete-time signals*(real- or complex-valued functions of the integers), and are their corresponding continuous-frequency

*spectra*defined over the unit circle in the complex plane.

*Proof: *
We have

One way to describe the linearity property is to observe that the Fourier transform ``commutes with mixing.''

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Time Reversal

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Existence of the Fourier Transform