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Programming Problems: 1. [CO2] (10 points) A system S is represented by its impulse response: \begin{equation} h(t) = \frac{1}{4} \left( e^{-2t} - e^{-t} \right) u(t) \end{equation} (5) a) (5 pts) Find the response of the system, if the input is $x(t) = \cos(t)u(t)$. Plot the signals $x(t)$, $h(t)$ and $y(t)$ for $t = [0, 20]$. b) (5 pts) Find the response of the system if $h(t) = \frac{1}{2} \left( e^{-t} - e^{-4t} \right) u(t)$ and $x(t) = e^{-t}\sin(t)u(t)$. Plot the signals $x(t)$, $h(t)$ and $y(t)$ for $t = [0, 20]$.

          Programming Problems:
1. [CO2] (10 points) A system S is represented by its impulse response:
\begin{equation}
h(t) = \frac{1}{4} \left( e^{-2t} - e^{-t} \right) u(t)
\end{equation}
(5)
a) (5 pts) Find the response of the system, if the input is $x(t) = \cos(t)u(t)$. Plot the signals $x(t)$, $h(t)$ and $y(t)$ for $t = [0, 20]$.
b) (5 pts) Find the response of the system if $h(t) = \frac{1}{2} \left( e^{-t} - e^{-4t} \right) u(t)$ and $x(t) = e^{-t}\sin(t)u(t)$. Plot the signals $x(t)$, $h(t)$ and $y(t)$ for $t = [0, 20]$.

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Programming Problems:
1. [CO2] (10 points) A system S is represented by its impulse response:

h(t) = (1)/(4)( e^-2t - e^-t) u(t)

(5)
a) (5 pts) Find the response of the system, if the input is x(t) = cos(t)u(t). Plot the signals x(t), h(t) and y(t) for t = [0, 20].
b) (5 pts) Find the response of the system if h(t) = (1)/(2)( e^-t - e^-4t) u(t) and x(t) = e^-tsin(t)u(t). Plot the signals x(t), h(t) and y(t) for t = [0, 20].

Added by Lisa M.

University Physics with Modern Physics

Hugh D. Young 14th Edition

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Solved by Expert Ronald Prasad

Step 1

First, let's define the given impulse response h(t) = 2(e^(-t) - e^(-4t))u(t) and the input signal x(t) = cos(t)u(t). Show more…

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This is a programming question to be solved in MATLAB. (Do not use the conv() function for convolution operation) We need to perform convolution using mathematical equations. A clear solution with an explanation using comments is required for both sub-questions. Programming Problems: 1. [CO2] (10 points) A system S is represented by its impulse response: (5) a) (5 pts) Find the response of the system if the input is x(t) = cos(t)u(t). Plot the signals x(t), h(t), and y(t) for t = [0,20]. b) (5 pts) Find the response of the system if h(t) = 2(e^(-t) - e^(-4t))u(t) and x(t) = e^(-t)sin(t)u(t). Plot the signals x(t), h(t), and y(t) for t = [0,20].

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