Question

The given input signal for 2.7.2 is:   x(t) = 3 cos(2 π t) + 6 sin(5 π t).

Plz explain steps.

Given a causal LTI system described by the differential equation find \(H(s),\) the \(\mathrm{ROC}\) of \(H(s),\) and the impulse response \(h(t)\) of the system. Classify the system as stable/unstable. List the poles of \(H(s) .\) You should the Matlab residue command for this problem.

(a) \(y^{\prime \prime \prime}+3 y^{\prime \prime}+2 y^{\prime}=x^{\prime \prime}+6 x^{\prime}+6 x\)

2.7.2 The signal \(x(t)\) in the previous problem is filtered with a continuous-time LTI system having the following frequency response. Find the output \(y(t) .\)

2.7.3 Consider the cascade combination of two continuous-time LTI systems.

The frequency response of SYS 1 is

$$ H_{1}^{f}(\omega)=\left\{\begin{array}{ll} 1 & \text { for }|\omega|<6 \pi \\ 0 & \text { for }|\omega| \geq 6 \pi \end{array}\right. $$

The frequency response of SYS 2 is

$$ H_{2}^{f}(\omega)=\left\{\begin{array}{ll} 0 & \text { for }|\omega|<4 \pi \\ 1 & \text { for }|\omega| \geq 4 \pi \end{array}\right. $$

(a) Sketch the frequency responses of each of the two systems.

(b) If the input signal is

Answer 1