Using MATLAB and the matlab template below provided please write a code for this problem:

The equation from the link :

Template:

%Create the vector of t values %Use array operations to calculate the three approximations and the %exact function as given in the assignment

%If using the checker, store the results in these variables

t = [];

y1 = []; y2 = []; y3 = []; y_exact =[];

%Plot all four functions on the same graph; add all necessary annotations

(= {4, 147, 2T(t) = 10. \t\ > IA. 4. Harmonic Analysis A fundamental technique of engineering analysis is Fourier decomposition - representing a periodic function as a sum of sine or cosine functions at multiples of the fundamental frequency. For example, a periodic square wave can be written as a sum of cosines as shown here. Using the cosine series given in the link, calculate the first five non-zero terms (including the DC term) of the series for 50 % duty cycle over the domain t = [-2 , 2 T], taking 0. = 1 and A = 1. Choose the step size so that you get a smooth plot (see plotting instructions below). Create one graph containing plots of: a. The fundamental term +DC offset (= 0.5) b. The sum of the first 3 terms (DC, fundamental, and 3rd harmonic) C. The sum of the first 5 terms (DC, fundamental, 3rd, 5th and 7th harmonic) d. The exact function, which can be calculated using the MATLAB built-in function square () as follows: Yuexact = 0.5+square (x + pi/2)/2; You can use the app on the linked web page to check that your plotted functions are correct. . For all assignments, always follow good graphing practices, including: a. Distinguish each series clearly (i.e., with different line types, and don't forget to include a legend). b. Title your plot. Note: your title should be more informative than simply Y vs X. C. Label all axes with a name and units. (When there are no units, indicate 'unitless'). For this particular problem, assume that the time unit is milliseconds, and the amplitude unit is centimeters. (= {4, 147, 2T(t) = 10. \t\ > IA. 4. Harmonic Analysis A fundamental technique of engineering analysis is Fourier decomposition - representing a periodic function as a sum of sine or cosine functions at multiples of the fundamental frequency. For example, a periodic square wave can be written as a sum of cosines as shown here. Using the cosine series given in the link, calculate the first five non-zero terms (including the DC term) of the series for 50 % duty cycle over the domain t = [-2 , 2 T], taking 0. = 1 and A = 1. Choose the step size so that you get a smooth plot (see plotting instructions below). Create one graph containing plots of: a. The fundamental term +DC offset (= 0.5) b. The sum of the first 3 terms (DC, fundamental, and 3rd harmonic) C. The sum of the first 5 terms (DC, fundamental, 3rd, 5th and 7th harmonic) d. The exact function, which can be calculated using the MATLAB built-in function square () as follows: Yuexact = 0.5+square (x + pi/2)/2; You can use the app on the linked web page to check that your plotted functions are correct. . For all assignments, always follow good graphing practices, including: a. Distinguish each series clearly (i.e., with different line types, and don't forget to include a legend). b. Title your plot. Note: your title should be more informative than simply Y vs X. C. Label all axes with a name and units. (When there are no units, indicate 'unitless'). For this particular problem, assume that the time unit is milliseconds, and the amplitude unit is centimeters