# DTFT of a cosine

We plot the Discrete Time Fourier Transform of a sinusoidal signal $x[n] = \cos(2\pi \nu n),$ given by $X(\nu) = \frac{1}{2} \sum_{n\in\mathbf Z} \delta_{\nu - n} + \delta_{-\nu + n}.$

By comparing with the continuous time sinusoidal signal $$x_c(t) = \cos(2\pi \nu t),$$, we observe spatial aliasing.