Given a sinusoid (y(t)=A cos left(Omega_{mathrm{c}} t ight)), using Equation (1.170), show that if (y(t)) is sampled

Given a sinusoid \(y(t)=A \cos \left(\Omega_{\mathrm{c}} t\right)\), using Equation (1.170), show that if \(y(t)\) is sampled with a sampling frequency slightly above the Nyquist frequency (that is, \(\Omega_{\mathrm{s}}=2 \Omega_{\mathrm{c}}+\epsilon\), where \(\epsilon \ll \Omega_{\mathrm{c}}\) ), then the envelope of the sampled signal will vary slowly, with a frequency of \(\pi \epsilon /\left(2 \Omega_{\mathrm{c}}+\epsilon\right) \mathrm{rad} / \mathrm{sample}\). This is often referred to as the Moiré effect. Write a MatLaB program to plot 100 samples of \(y(n)\) for \(\epsilon\) equal to \(\Omega_{\mathrm{S}} / 100\) and confirm the above result.