summation without using any loop algorithm

Hello,

I am trying to implement the summation for a square wave without the use of loops. I have the following code:

sona = sin((2*k - 1)'*t)./(2*k - 1);

but keep getting the error: "Error using * Inner matrix dimensions must agree"

Can you please explain what the problem is and how I can fix this error?

Thanks, monkey_matlab

[Geoff Hayes]

monkey_matlab - how have you defined k and t?

[monkey_matlab]

k = 1:3;
t = linspace(0, 4*pi, 100);

Answer 1

[Walter Roberson]

Suppose that your k is a row vector of 1:n

k = 1:n;

and suppose that your t is a row vector of length L

L = 50;
t = linspace(0,20,L);

then

(2*k-1)' * t

would be well defined and would be of size n x L. You can sin() that and the result will stay n x L. Now you are trying to divide it by the row vector (2*k-1). An n x L matrix cannot be divided by a 1 x n row vector. So you need to extend the 1 x n row vector into an n x L matrix in order to do the division:

repmat((2*k-1)', 1, L)

now you can do element-by-element division, and that is going to give you an n x L result. If you now sum along the first dimension, you would get a 1 x L result:

    n = 16;        %number of harmonics
    startat = 0;   %start and stop times
    endat = 20;
    L = 50;        %how many time points

    k = 1:n;
    k21 = 2*k - 1;
    t = linspace(0,20,L);
    sona = sum(sin(k21' * t) ./ repmat(k21', 1, L), 1);

    plot(t, sona)