Trying to plot an approximation of x(t)

I am trying to answer this question where a=3 and b=2

and here is my code I have made so far

syms x k n;
b = @(f,x,k) int(f*cos(k*pi/2*x)/2,x,-3,1);
c = @(f,x,k) int(f*sin(k*pi/2*x)/2,x,-3,1);
xt = @(f,x,n) b(f,x,0) + symsum(b(f,x,k)*cos(k*pi/2*x)+c(f,x,k)*sin(k*pi/2*x),k,1,n); 
time = -2:0.5:2;
f= sawtooth(pi*time);
numTerms=1; %1,10,25,50
ezplot(xt(f,x,numTerms),-2,2)

but I keep getting an error when i run it and I'm not exactly sure what I'm doing wrong.

Answer 1

[Abraham Boayue]

clear variables close all

M = 250; % The length of each function a =3; b =2; x = -2:4/(M-1):2;

y = (a/b)*x;

f1 = zeros(1,M); f2 = f1; f3 = f2; f4 = f3; f5 = f4;

for k = 1 ck = (-1)^(k-1)/(pi*k); f1 = f1+3*ck.*sin(pi*k*x); p1 = abs(mean(y-f1)); end

for k = 1:3 ck = (-1)^(k-1)/(pi*k); f2 = f2+3*ck.*sin(pi*k*x); p2 = abs(mean(y-f2)); end

for k = 1:5 ck = (-1)^(k-1)/(pi*k); f3 = f3+3*ck.*sin(pi*k*x); p3 = abs(mean(y-f3)); end

for k = 1:15 ck = (-1)^(k-1)/(pi*k); f4 = f4+3*ck.*sin(pi*k*x); p4 = abs(mean(y-f4)); end

for k = 1:100 ck = (-1)^(k-1)/(pi*k); f5 = f5+3*ck.*sin(pi*k*x); p5 = abs(mean(y-f5)); end

figure plot(x,f1,'linewidth',2,'color','r') hold on; plot(x,f2,'linewidth',2,'color','g') plot(x,f3,'linewidth',2,'color','b') plot(x,f4,'linewidth',2,'color','k') plot(x,f5,'linewidth',2,'color','m')

a = legend('f1:N =1','f2:N =3','f3:N =5','f4:N =15','f5:N =100'); set(a,'fontsize',14) a= title('f(t) : Sine fourier series'); set(a,'fontsize',14); a= xlabel('x [-2\pi 2\pi]'); set(a,'fontsize',20); a = ylabel('y'); set(a,'fontsize',20); a = zlabel('z'); set(a,'fontsize',20); grid

% Disply the residual average power disp('1. Average ridual power for N = 1') disp(p1) disp('2. Average ridual power for N = 3') disp(p2) disp('3. Average ridual power for N = 5') disp(p3) disp('4. Average ridual power for N = 15') disp(p4) disp('5. Average ridual power for N = 100') disp(p5)

[Abraham Boayue]

Hi, I thought wise to do the math and then use the result for the coding, hope this helps.