Square wave by vector multiplication

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David
David 2024-3-30
编辑： Voss 2024-4-1
Ran in:
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

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采纳的回答

Voss
Voss 2024-3-30
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);
  2 个评论
David
David 2024-4-1
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
Voss 2024-4-1
编辑：Voss 2024-4-1
Ran in:
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.

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