This way you will have multiple plots on Figure 1. # B.3 Run the code that results from B.2 for N_TERMS = 10,20 and 30 without closing the Figure each time you run. f zeros (1, length (t)) for n 1 : 2 : 201 f f + (4/pi). Insert a legend on your plot describing the two signals: name the ideal square wave f(x) and the approximation f'(x). Consider the number of terms N_TERMS - 7.

* B.1 Write a brief description of how CODE 2 implements the Fourier series described by Equation (1) *B.2 Using the command hold on, plot the graph produced by CODE 1 and CODE 2 on the same picture. % CODE 2 clc, syms nx I = pi N_TERMS = input ('Number of terms: ') n = 1:N_TERMS & Calculating the coefficients of the Fourier Series % tic a0 = (1/L) *int(1, X, 0, pi) an = (1/L) *int (1*cos (n*x), x, 0, pi) bn = (1/L) int(1+sin(n*x), X, 0, pi) * Plugging the coefficient values in the Fourier Series f = 0 for n = 1:N_TERMS f = ft (an(n) *cos (n*x) + bn(n) *sin(n+x)) end % toc fprintf('Approximation using d terms ', n) f_approx = (a0/2) + f ezplot(F_approx, (-10,10]) title('Fourier Series Approximation') xlabel('x') ylabel('F(x) approximated') To do so, the following MATLAB code can be used. The Fourier series for a shifted square wave with amplitude A, period T, and phase p is as follows: (1) f ( t) n 1 N ( a ( n) cos ( n t) + b ( n) sin ( n t)) where. (x a) 1 2 ej ( x a) tdt lim n 1 2 n k nejk ( x a) ( sin(n + 1 2)(x a) 2sinx a 2), where j is a unit vector in positive vertical direction on the complex plane, so j2 1. This general mathematical result says you can calculate a signal's power in either the time domain or the frequency domain.Part B: Approximation of a square wave using the Fourier series The following MATLAB code can be used to plot a square wave: & CODE 1 & Ideal square wave t=-10:0.0001:10 x=0.5+ (square (t) +1) plot(t, x) By means of a weighted sum of sines and cosines, let us try to approximate the square wave plot produced by the code above. Here are two important applications of Fourier series: cos(asinx) J0(a) + k 1J2k(a)cos(2kx). Start by forming a time vector running from 0 to. The complex Fourier series obeys Parseval's Theorem, one of the most important results in signal analysis. This example shows how the Fourier series expansion for a square wave is made up of a sum of odd harmonics.

Square wave fourier series matlab