Question

HW1 Description The MATLAB script accompanying this assignment simulates the approximation of the periodic function f() defined below using a Fourier series of N harmonics (including the fundamental frequency). In the script do, and the best a, and by coefficients are computed using their analytical expressions (corresponding to this definition of f(t) of course). There is also a parameter N that controls the maximum nth harmonic to approximate the signal. Definition Sketch flt) f(t) = - SEST ((t + 2tk) ->tt > T, K EZ Requirements Your goal for this assignment is to write a report where you cover (answer, discuss and comply with) the following: • Report length (minimum): 500 words • Your report must be typed using a word editor. • What is the period and the fundamental frequency of the function f(c)? Include the units of course. • What is the DC Component (Offset)? Justify why. • Select any four values for N in increasing order between 1 and 100. Compare the approximations you get when using those four different values. Add screenshots from the figures generated by the MATLAB script to your report. When we say compare, you must, among other things, include an analysis of the differences observed between approximations and why we observed those differences. Your comparison must include analysis for both, time domain and frequency domain (discrete spectrum). . What is the highest frequency your approximation will have for N = 200? Explain. • What is the resulting approximation if you use N = 0? Explain. • What happens with the approximation if we use the negative of all coefficients b, instead? Explain. Notes At any point in the report you can include figures and/or graphs to support your explanations. Make sure you add a caption to any figure/graph in your report. This must be a numbered caption with a summarized explanation of what the figure is all about.
please step by step

the main three question are the last three one thank you

Answer 1

(1) f(t) obtained by using fourier series of N-harmonics is

                                   

f(t) = do + an cos(nwst) + bn sin(nwet) n=1 n=1

Here time period is

                                                                  

T, = 21

So

                                                                      

21 W = = = lrad/s

Highest frequency (in rad/s) is

                                                           

mar = Nws = 200 rad)s

(2) For N = 0,

                                                                                  

f(t) = ac

Here a₀ is the DC value of the signal. From graph, we can see that average value of signal = 0. So we will get

                                                                          

f(t) = 0

(3) New f_new(t) is

                                   

N frey(t) = -10 + -an cos(nwgt) + -on sin(nwgt) n=1

We know from (2) that a₀ = 0. Since f(t) is symmetric about t = 0, so it will not have any cos component. So

a_n = 0. So we get

                                                            

にい arrows - (05

and

                                                          

fnew(t) = -bn sin(nwgt) na

Or

                                            

N fnew(t) = bn sin(-nwgt) n=1

Or

                                          

N freu(t) = bn sin(nws(-+)) n=1

Or

                                                                

freu(t) = f(-1)

So new approximation will be time reversed form of original signal.