Sampling (L 11-18)
This demo shows signals in the time and frequency domain before and after sampling with the sampling frequency \(\omega_\mathrm{a}\) as described in Chapter 11. As an example, the input signal \(x(t)\) is \[ x(t) = \frac{\omega_\mathrm{g}}{2\pi}\,\mathrm{si}^2\!\left(\frac{1}{2}\omega_\mathrm{g}t\right), \] with the spectrum \(X(\mathrm{j}\omega)\), calculated as \[ X(\mathrm{j}\omega) = \Lambda\!\left(\frac{\omega}{\omega_\mathrm{g}}\right) = \frac{1}{\omega_\mathrm{g}}\cdot\mathrm{rect}\!\left(\frac{\omega}{\omega_\mathrm{g}}\right) \ast \mathrm{rect}\!\left(\frac{\omega}{\omega_\mathrm{g}}\right). \] The input signal \(x(t)\) is sampled, resulting in \(x_\mathrm{a}(t)\) (c.f. L 11-13 to 11-14), and reconstructed to obtain \(y(t)\) (c.f. 11-16 to 11-18). You can view \(x_\mathrm{a}(t)\) and \(y(t)\) and their respective spectra \(X_\mathrm{a}(\mathrm{j}\omega)\) and \(Y(\mathrm{j}\omega)\) in time and frequency domain, and optionally display the individual \(\mathrm{si}\)-functions that sum up to \(y(t)\). Adjust the sampling frequency \(\omega_\mathrm{a}\) and the cutoff frequency \(\omega_\mathrm{g}\) to see the effect of aliasing.