Square wave by vector multiplication

I'm trying to build a square wave by using vector multiplication instead of using the "for" loop. It was suggested as multiply a 1xn vector with a nx1 vector. Here is my code constructing the square wave using the "for" loop:

N = 13;
f = 1000 * sin(2 * pi / (49 * N)); 
t = 0:0.0001:1; 
n = 100; 
A = 2;
square_wave = zeros(size(t)); 
for k = 1:n
  if mod(k, 4) == 1
    a_k = 4 * A / (k * pi);
  elseif mod(k, 4) == 3
    a_k = -4 * A / (k * pi);
  else 
    a_k = 0;
  end
  square_wave = square_wave + a_k * cos(k * 2 * pi * f * t);
end
plot(t, square_wave);
xlabel('Time (s)');
ylabel('Amplitude');
title('Square Wave Approximation');
grid on

Answer 1

[Voss]

k = (1:n).';
a_k = repmat([1;0;-1;0],n/4,1)*4*A./(k*pi);
square_wave = sum(a_k .* cos(k .* 2 * pi * f * t),1);

[David]

I tried to run the code above and it is reported error:

Error using .*

Matrix dimensions must agree.

square_wave = sum(a_k .* cos(k .* 2 * pi * f * t),1);

I assume the dimension of two matrices is not suitable for multiplication.

Do you have any idea how to fix this?

[Voss]

This runs for me:

N = 13;
f = 1000 * sin(2 * pi / (49 * N)); 
t = 0:0.0001:1; 
n = 100; 
A = 2;

k = (1:n).';
a_k = repmat([1;0;-1;0],n/4,1)*4*A./(k*pi);
square_wave = sum(a_k .* cos(k .* 2 * pi * f * t),1);

plot(t, square_wave)

Double-check that you are running the same code.