# (Solved): SOLVE IT USING MATLAB PLEASE A continuous-time sinusoidal signal $$\mathrm{x}(\mathrm{t})$$ is ...

A continuous-time sinusoidal signal $$\mathrm{x}(\mathrm{t})$$ is obtained at the output of an ideal low-pass filter with cutoff frequency $$w_{c}=1000 \pi$$. (a) What is the maximum possible frequency $$w_{m}$$ of $$\mathrm{x}(\mathrm{t})$$ ? (b) What is the Nyquist rate of the signal $$\mathrm{x}(\mathrm{t})$$ ? (c) What is the requirement on sampling period Ts such that no aliasing will occur when recovering $$\mathrm{x}(\mathrm{t})$$ from its samples? If impulse-train sampling is performed on $$\mathrm{x}(\mathrm{t})$$, which of the following sampling periods guarantee that $$\mathrm{x}(\mathrm{t})$$ can be recovered from its sampled version using an appropriate lowpass filter? $\begin{array}{l} \text { Ts }=0.5 \times 10^{-3} \\ \text { Ts }=2 \times 10^{-3} \\ \text { Ts }=10^{-4} \end{array}$ - Write a MATLAB Code to validate your answer in both time and frequency. - Plot the signal with different sampling rates. - Determine if the is any aliasing.