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SOLVE IT USING MATLAB PLEASE

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.

Here as asked in question we need to solve it using MATLAB . So , providing MATLAB code only here in this step and calculation in other steps -: title