Question

Use MATLAB to :

("j" is the imaginary number.) The term lo is the fundamental frequency of the periodic signal, 2/T, where T is the period. Frequencies nlo, where n is an integer, are the harmonics. This infinite sum is an exact representation of the original function. If we use a finite sum, where n goes from -N to N, we will get an approximation "X-(t)". In this problem we will calculate and plot the Fourier series representation of a square wave with period T, and compare it to the original function. In later classes you will learn how to derive the coefficients an. For now we will just give you the equation: n evenn n odd Procedure. Write a MATLAB program that will: a) Calculate the Fourier series coefficients an from equation (2) for a given N; b) Construct the Fourier series xF(t) from equation (1), and plot it for two periods; c) Plot two periods of the actual square wave x(t) on the same graph Note that the first step gives you an array of 2N+1 coefficients. The second step gives an array in t (use a small enough resolution to get a smooth plot) where each point in t is found by summing over n. This program can be done using array operations, or loops, or a combination of both There is not a single right way, but I think you will find array operations much more concise - and one of the great advantages of using MATLAB The square wave should have amplitude ±1 and T-1 s. Run your program with N = 10, 100 and 1000.

Answer 1