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Linearity of the DTFT

(3.9) 
or

(3.10) 
where
are any scalars (real or complex
numbers),
and
are any two discretetime signals
(real or complexvalued functions of the integers), and
are their corresponding continuousfrequency 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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