Determine power and energy for the following signals
i)x(t)=3cos 5\(\Omega_0t.\)
ii)\(X[n]=(\dfrac{1}{4})^n u[n]\)

Determine Fourier series representation of the following signals:

For a continuous time signal x(t)=8cos 200πt
Find (1)Minimum sampling rate.
(2)If f_s=400Hz,what is discrete time signal?
(3)If f_s=150Hz,what is the discrete time signal?
(4)Comment on result obtained in 2 and 3 proper justification.

Determine the inverse z transform of the function using Residue method:
\(X(z) =\dfrac{3-2z^{-1}+z^{-2}}{1-3z^{-1}+2z^{-2}}.\)

Two LTI system in cascade have impulse response h₁[n] and h₂[n]
\(h_{1}[n]=(0.9)^{n}u[n]-0.5(0.9)^{n-1}u[n-1]\)
\(h_{2}[n]=(0.5)^{n}u[n]-0.5(0.5)^{n-1}u[n-1]\)
Find the equivalent response h[n]of the system.

A casual LTI system is described\( y[n]=\dfrac{3}{4}y[n-1]-\dfrac{1}{8}y[n-2]+x[n]\)
Where y[n]response of the system and x[n]is excitation to the system.

• Determine impulse response of the system.
• Determine step response of the system.
• Plot pole zero pattern and state whether system is stable.

Determine the inverse z-transform for the function:\(X[Z]=\dfrac{z^{2}+z}{z^{2}-2z+1}\space\space ROC>|z|\)

Find the response of a system with transfer function \(H(s) =\dfrac{1}{s+5}R_{e}>-5\).

Input \( x(t)=e^{-t}u(t)+e^{-2t}u(t)\)

For the given LTI system,described by the differential equation:
\(\dfrac{dy^{2}(t)}{dt^{2}}+\dfrac{3dy(t)}{dt}+2y(t)=x(t)\)
Calculate output y(t) if input\( x(t)=e^{-3t}u(t)\)is applied to the system.