### 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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