DTFT & z-Transform

This demo shows the Discrete-Time Fourier Transformation (DTFT) \(X(\mathrm{e}^{\mathrm{j}\Omega})\) as well as the z-Transform \(X(z)\) of a cosine signal \(x[k] = a^k \cos(\omega k)\cdot\varepsilon[k]\). Adjust \(\omega\in[0,\pi]\) and \(a\in[0,2]\) to see the time sequence, DTFT magnitude, and pole-zero plot.

Normalized frequency \(\omega/\pi\): 0.25 Decay \(a\): 0.9 Recompute