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SJSU EE 112 - Assignment 3

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San Jose State University Electrical Engineering Department EE112, Linear Systems MATLAB Assignment 3 “…we learn by doing…” Objective: In this lab we will explore the Fourier Series reconstruction of the periodic signal x(t), plot of the magnitude and phase spectrum using MATLAB. Assume signal x(t) has the following magnitude and phase Fourier series expressions: ⎩⎨⎧===,...3,1,/1,...4,2,0kkkckπ ⎩⎨⎧=−−==∠−,...3,1,2/]1)1[(,...4,2,02/)1(kkckkπ 1. Use MATLAB, plot the Magnitude and Phase spectrum of kC , for }10.....10{−∈k . Use the MATLAB command stem instead of plot to emphasize that the spectra are line spectra and not a continuous function of k. Label your axes and title your graphs. (see class-notes for similar examples) Hints: you can use the following commands Æ abs to compute ||kC Æ phase to compute phase angle of kC Æ Try to write a MATLAB function to compute kC for any k – this will be useful for solving next question. 2. We know that the original signal x(t) can be recovered from the Fourier series coefficients kC using the synthesis equationThis equation differs from the exact synthesis equation only in that the sum is now over a finite number of terms. The coefficients kC are unchanged. Use MATLAB to recover x(t). Show all work, in particular the function files used to implement the calculation of x(t) in the above equation. Produce plots for }4.....4{−∈t for each of the following cases: (a) 5max=k (b) 15max=k (c) 25max=k For all plots, use as the time axis t the Matlab vector ;4:01.0:4−=>> t Label all your axis and title all your plots 3. Your write up should include the following: a. Spectra of kC as two plots: ||kC and the phase angle of kC b. The three plots of truncated reconstructions of x(t) c. The script/function files that you wrote d. Use the same notations as conventions as stated in assignment 1 when naming your MATLAB files Helpful website


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SJSU EE 112 - Assignment 3

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