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II. Project Description The project considers different signal processing techniques to analyze signals in both time and frequency domains. The project is divided into three parts namely: Numerical signal simulations using MATLAB, Fourier series and Fourier transform analysis and simulations, and oral presentation. In the first part, students will be more familiar how to use a numerical tool (e.g. MATLAB) to simulate a time domain signal. In the second part, analysis and simulations for Fourier series and Fourier transform are conducted in both time and frequency domains. Last part of the project considers your skills in presenting your work and measures the teamwork performance. Part A In this part, a numerical analysis tool (e.g. MATLAB or Octave) will consider to help students to simulate different signals in time domain. The target of this part is to let student be more familiar with signal's parameters mapping to MATLAB. Consider the signal $x(t)$ that is an input to the system $h(t)$ given as $\begin{cases} 0 & t < 0\\ 1 & 0 \le t \le 2\\ 0 & t > 2 \end{cases}$ $h(t) = \begin{cases} 0 & t < 0\\ e^{-2t} & t \ge 0 \end{cases}$ The output of the system $y(t)$ is the convolution of $x(t)$ and $h(t)$ given as y(t) = x(t) * h(t) a. Given x(t) and h(t), explain two methods to find the output y(t). b. Explain how to define the time vector for x(t) and h(t) in MATLAB and justify your selection. c. Write a MATLAB code to plot x(t) and h(t) and show all details on the figure d. Write a MATLAB code to find the output y(t) without using any MATLAB built-in functions e. Write a MATLAB code to find the output y(t) using MATLAB built-in functions f. Plot the output signal y(t) obtained in part (d) and (e) in one figure and comment on the results

          II.
Project Description
The project considers different signal processing techniques to analyze signals in both time and
frequency domains. The project is divided into three parts namely: Numerical signal simulations using
MATLAB, Fourier series and Fourier transform analysis and simulations, and oral presentation. In the
first part, students will be more familiar how to use a numerical tool (e.g. MATLAB) to simulate a time
domain signal. In the second part, analysis and simulations for Fourier series and Fourier transform are
conducted in both time and frequency domains. Last part of the project considers your skills in
presenting your work and measures the teamwork performance.
Part A
In this part, a numerical analysis tool (e.g. MATLAB or Octave) will consider to help students to simulate
different signals in time domain. The target of this part is to let student be more familiar with signal's
parameters mapping to MATLAB.
Consider the signal $x(t)$ that is an input to the system $h(t)$ given as
$\begin{cases} 0 & t < 0\\ 1 & 0 \le t \le 2\\ 0 & t > 2 \end{cases}$
$h(t) = \begin{cases} 0 & t < 0\\ e^{-2t} & t \ge 0 \end{cases}$
The output of the system $y(t)$ is the convolution of $x(t)$ and $h(t)$ given as
y(t) = x(t) * h(t)
a. Given x(t) and h(t), explain two methods to find the output y(t).
b. Explain how to define the time vector for x(t) and h(t) in MATLAB and justify your selection.
c. Write a MATLAB code to plot x(t) and h(t) and show all details on the figure
d. Write a MATLAB code to find the output y(t) without using any MATLAB built-in functions
e. Write a MATLAB code to find the output y(t) using MATLAB built-in functions
f. Plot the output signal y(t) obtained in part (d) and (e) in one figure and comment on the results

II.
Project Description
The project considers different signal processing techniques to analyze signals in both time and
frequency domains. The project is divided into three parts namely: Numerical signal simulations using
MATLAB, Fourier series and Fourier transform analysis and simulations, and oral presentation. In the
first part, students will be more familiar how to use a numerical tool (e.g. MATLAB) to simulate a time
domain signal. In the second part, analysis and simulations for Fourier series and Fourier transform are
conducted in both time and frequency domains. Last part of the project considers your skills in
presenting your work and measures the teamwork performance.
Part A
In this part, a numerical analysis tool (e.g. MATLAB or Octave) will consider to help students to simulate
different signals in time domain. The target of this part is to let student be more familiar with signal's
parameters mapping to MATLAB.
Consider the signal x(t) that is an input to the system h(t) given as
0 t < 0
1 0 ≤ t ≤ 2
0 t > 2
h(t) = 0 t < 0
e^-2t t ≥ 0
The output of the system y(t) is the convolution of x(t) and h(t) given as
y(t) = x(t) * h(t)
a. Given x(t) and h(t), explain two methods to find the output y(t).
b. Explain how to define the time vector for x(t) and h(t) in MATLAB and justify your selection.
c. Write a MATLAB code to plot x(t) and h(t) and show all details on the figure
d. Write a MATLAB code to find the output y(t) without using any MATLAB built-in functions
e. Write a MATLAB code to find the output y(t) using MATLAB built-in functions
f. Plot the output signal y(t) obtained in part (d) and (e) in one figure and comment on the results

Added by Juan Manuel P.

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