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Question I: Generate and plot the following signals using MATLAB: 1. X₁ (t) = u(t-4)-u(t-9) 2. A finite pulse (n(t)) with value = 4 and extension between 3 and 8 3. X₂(t) = u(t-4) +r(t− 6) - 2r(t − 9) + r(t - 11) in the time interval [022] Question II: 1. Generate and plot the signals y₁ (t) sin(200nt), and y₂ (t) = cos(750nt), then determine yl and plot the signals m(t) = +y2 and n(t) = y₁ - y₂. 2. Determine, using the MATLAB plots, if the sum and/or difference signals are periodic. In case a signal is periodic, determine its fundamental frequency.) Question III Write the programs that solve the following differential equations using zero initial conditions. dy(t) 1. 10 + 20y(t) = 10 dt dy 2. dy(t) + 2 + 4y(t) = 5 cos1000t dt² dt Question IV: Write the programs that determine the response of the linear time invariant system to the given input and the given initial conditions: 1. dy(t) + 5y(t) = 10u(t) y(0) = 3; dt 2. d²y(t) + 2 dy +2+2y(t) = 5 cos 2500t (y(0)=1, y'(0)=2); dt² dt Question V: Use Simulink (MATLAB) to simulate the following systems then show and plot the step response of the system. d¹y(t) + d²x(t) + 12x(t) 1.4 +6 dy(t)+8y(t) = 7 dt dt dt² 2. H(s) = 100(s+3) + 10 (Hint: transform to differential equation form) (s+1)*(s+4) (s+10) Question VI: Write a program that computes and plots the spectral representation of the function 1. y(t) = (10e-1¹0t)u(t) 2. y(t) = (10e-10t cos100t)u(t)

Question VII: Write a program that computes the Laplace and Fourier transforms of the function and plot the phase and amplitude spectra. 3. y(t) = (1010e-5t)u(t) 4. y(t) = (30 10e-8t cos 100t)u(t) Question VIII: Write a program that define the transfer functions and plots the zero-pole map of the systems 1. with poles (-1,-3) and zero (-6) 2. with poles (-1, 1+2j and 1-2j) and zero at (-3) Question IX: Write a program that determine the inverse Laplace and Fourier transforms of the transfer functions in VIII and plot their phase and magnitude spectra.