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The Discrete Fourier Transform (DFT) is a mapping between a finite set of discrete points in a (primal) domain (time, space) and the dual frequency domain. DFT requires an input sequence which is discrete, such as a sampling from an analogue audio signal.

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Problem observing the correctness of a Fourier transform property

I'm studying "Signals & Systems" by Oppenheim et al. On page 391, for a real-valued $x[n]$ whose Fourier transform is $X(e^{j\omega})$: $$x[n] \leftrightarrow X(e^{j\omega})$$ $$\mathcal{Ev}\{x[n]\} …