I have to make code for the following but don't know how to use put sigma into matlab

I have to make code for the following but don't know how to use put sigma into matlab

[C.J. Harris]

Maybe that's why your homework is suggesting you use a for-loop instead...

Answer 1

[Abraham Boayue]

This might help, try to understand how the for loop works, it is the basis of programming.
clear variables
close all
x = -5:0.1:5;
N = length(x);
y_sinx = zeros(1,N);
y1 = y_sinx;
y2 = y1;
y3 = y2;
M = [1 2 5 10];

% Although you were asked to use double for loops, but this is totally 
% inefficient for such a simple problem.

for k = 1:N
    sum = 0;
      for n = 1:M(1)
          sum = sum +((-1)^(n-1))*(x(k)^(2*n-1))/(factorial(2*n-1)); 
      end
      y_sinx(k) = sum;
end

for k = 1:N
    sum = 0;
      for n = 1:M(2)
          sum = sum +((-1)^(n-1))*(x(k)^(2*n-1))/(factorial(2*n-1)); 
      end
      y1(k) = sum;
end

for k = 1:N
    sum = 0;
      for n = 1:M(3)
          sum = sum +((-1)^(n-1))*(x(k)^(2*n-1))/(factorial(2*n-1)); 
      end
      y2(k) = sum;
end

for k = 1:N
    sum = 0;
      for n = 1:M(4)
          sum = sum +((-1)^(n-1))*(x(k)^(2*n-1))/(factorial(2*n-1)); 
      end
      y3(k) = sum;
end

figure
subplot(221)
plot(x,y_sinx,'linewidth',2,'color','m')
legend('M = 1')
a= title('y(x) = sin(x)');
set(a,'fontsize',14);
a= xlabel('x [-5 5]');
set(a,'fontsize',20);
a = ylabel('y');
set(a,'fontsize',20);
a = zlabel('z');
set(a,'fontsize',20);
grid
subplot(222)
plot(x,y1,'linewidth',2,'color','g')
legend('M = 2')
a= title('y(x) = sin(x)');
set(a,'fontsize',14);
a= xlabel('x [-5 5]');
set(a,'fontsize',20);
a = ylabel('y');
set(a,'fontsize',20);
a = zlabel('z');
set(a,'fontsize',20);
grid

subplot(223)
plot(x,y2,'linewidth',2,'color','b')
legend('M = 5')
a= title('y(x) = sin(x)');
set(a,'fontsize',14);
a= xlabel('x [-5 5]');
set(a,'fontsize',20);
a = ylabel('y');
set(a,'fontsize',20);
a = zlabel('z');
set(a,'fontsize',20);
grid
subplot(224)
plot(x,y3,'linewidth',2,'color','r')
legend('M = 10')
a= title('y(x) = sin(x)');
set(a,'fontsize',14);
a= xlabel('x [-5 5]');
set(a,'fontsize',20);
a = ylabel('y');
set(a,'fontsize',20);
a = zlabel('z');
set(a,'fontsize',20);
grid

% A much better for loop. ( This is recommended)

% sum = zeros(1,N);
% for n = 1:M(3)
%   sum = sum +((-1)^(n-1))*(x.^(2*n-1))/(factorial(2*n-1)); 
% end

% figure
% plot(x,sum,'linewidth',2,'color','r')
% a= title('y(t) : sum of sine wave');
% set(a,'fontsize',14);
% a= xlabel('x [-5 5]');
% set(a,'fontsize',20);
% a = ylabel('y');
% set(a,'fontsize',20);
% a = zlabel('z');
% set(a,'fontsize',20);
% grid