Matlab report 2 (due April 11 to 15)
Gibbs Phenomenon





1-     Use Matlab to calculate the Fourier series coefficients for the sequence given in example 3.5 in textbook for T=1 sec and T1=0.25sec.

2-     Compare the Coefficients obtained in 1 above with the exact coefficients given in equation 3.44. Draw both sets of coefficients on the same figure using the plot command.

3-     Using the exact coefficients (equation 3.44) do the following

a.     Construct the signal xN(t) (equation 3.47) by taking the partial sum of the Fourier series summation as explained in page 200 of the textbook for N=3, 19, 99, and 999 . Take the step for drawing xN(t) to be step =0.01 and 0.001. (The output here is 8 curves)

b.    Compare between the graphs of xN(t) for the different N and steps. Comment on your result.

c.     Draw the error signal eN(t)=x(t)-xN(t) for different N and step

d.    Calculate the energy in eN(t) for different N and step.

e.     Calculate the peak value of xN(t) for different N and step. (hint : use the matlab command max to find the peak)