HW1 – Introduction

• Read Chapter 0 in the text Signals and Systems Using MATLAB.
• Download and review the supplemental questions.
• Work the following problems 1, 2, and 3 below and submit your answers.
• Submit homework solutions via Assignment Upload Tool.  Show all work for full credit.

1. Complex Exponentials: Simply the following expression and give your answer both in polar and rectangular form.
   • c = -3e^jπ/4 + 4e^−jπ/2
2. Difference Equations:  Solve the following difference equation using recursion by hand (for n=0 to n=4)
   • y[n] + 0.5y[n-1] = 2x[n-1]; x[n] = δ[n], y[-1] = 0
3. Differential Equations:  Solve the following problem for y(t).

• dy/dt + 2y(t) = 2x(t); x(t) = u(t), y(0) = −1

Lab 1 – Introduction

1. Watch video entitled “Module 1 – Introduction to MATLAB”
2. Download and review the Matlab supplement on plotting signals.
3. Work the two problems below.
4. Include answers for Problems and include MATLAB coding along with any output plots that support solutions into one Word document entitled “Lab1_StudentID”.  Where your student id is substituted in the file name.
5. Upload file “Lab1_StudentID”.

In this lab, you will create and analyze a number of continuous and discrete-time sinusoids using MATLAB.

Activity 1:

Consider the discrete-time signal and assumen N=12.

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For M = 4, 5, and 10, plot x_M[n] on the interval 0 ≤ n ≤ 2N-1.  Use stem in MATLAB to create your plots, and be sure to appropriately label your axes.  (You can copy your plots by selecting Edit >  Copy Figure at the top of the figure pane.)  Using Insert –> Arrow at the top of the figure pane, insert an arrow to indicate the end of the first period and beginning of the next period.

Activity 2:

Consider the following two signals:

 

Assume N = 6 for signal x₁[n]. Plot each signal separately for the interval of 0 ≤ n ≤ 24.  Use stem and label your axes.

Question:

1. Are the signals periodic? Explain.

Please fill out and use the following Lab Report Template when submitting your lab work.

Please read and follow the guidelines given in the Solutions Template in submitting all of your lab work.