MATLAB

Department of Electrical and Computer Engineering, Tuskegee University

EENG 0323: Signals and Systems, Fall 2018

Project-2

Total Points: 100, Due Date: 12-05-2018

Project Statement/Problem

A 100Hz symmetrical square wave varies between 5V and -5V.

a) Plot the square wave using MATLAB. b) Use the expression of complex exponential Fourier series coefficients, 𝐶𝑘, from the table, to

calculate the coefficients using MATLAB for k = 0 to 20. Note that some of the coefficients

may be zero.

c) Obtain the combined trigonometric Fourier series coefficients for the above case using the

complex exponential Fourier series coefficients, 𝐶𝑘, of part a, and plot (‘stem’ plot) double- sided amplitude spectrum for the coefficients of part b using MATLAB.

d) Reconstruct/approximate the signal (square wave) by adding the following number of combined trigonometric Fourier series components, and plot the reconstructed signal for each

case:

i) First 5 components (i.e., up to 𝑘 = 5) ii) First 10 components (i.e., up to 𝑘 = 10) iii) First 20 components (i.e., up to 𝑘 = 20)

e) Compare and comment about the above three cases/options considering the following: i) Relative amplitudes of the calculated coefficients ii) Similarity and any distortion compared to the original signal. iii) Economic considerations iv) Environmental considerations

Other Instructions

• The project should be done in groups. Each group will have 4 members. You will be forming/choosing your groups. Each group must email the names of the members by 3:00PM

11-28-2018 Wednesday to the instructor.

• Create one single m-file and include the coding for all steps in the same file. Save your m-file as Project2_GroupNo.m.

• Run the file to generate the outputs/plots. Remember to include ‘grid’, and appropriate/relevant ‘axes labels’ and ‘title’ in each plot.

• Put the complete code and the corresponding outputs (plots) in a Word document. Include figure captions, as/if needed.

• Submit the printed/paper version of the word document (project report) with a cover page within the deadline.

• Email the m-file (actual MATLAB code) to the instructor within the deadline.

Warning

• Each group must do its own project. Each member must participate actively in the project tasks and should be able to answer any questions related to the project.

• Any trace of copying/plagiarism (from other groups or from internet) will result in zero points/credit in the project.

• If two or more projects (codes, report) can be identified as having traces of copying/plagiarism from each other, all those project works/reports will get zero points/credit.