fourier series for odd triangle function in matlab

To plot the Fourier series for an odd triangle wave function in MATLAB, you can follow these steps:

Define the triangle wave function using a combination of the sawtooth and abs functions. Since we want an odd triangle wave function, we can use the sawtooth function with a period of pi and a phase of -pi/2, and take the absolute value of the result. Here is an example implementation:


main.m
% Define triangle wave with period 2*pi
period = 2*pi;
triangle = @(t) abs(sawtooth(t - pi/2, 0.5));

% Plot the triangle wave from -2*pi to 2*pi
t = linspace(-2*pi, 2*pi, 1000);
plot(t, triangle(t));
xlim([-2*pi, 2*pi]);
ylim([-0.2, 1.2]);
xlabel('t');
ylabel('f(t)');
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Define the Fourier coefficients for the triangle wave. Since the triangle wave is odd, the Fourier series only includes sine terms. The nth coefficient can be calculated using the formula:


main.m
B_n = (2/period) * integral(f(t) * sin(n * pi * t / period), t, -period/2, period/2)
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In the case of the odd triangle wave function, we can use the formula for the Fourier series of a sawtooth wave:


main.m
B_n = (-1)^{n+1} * (2/(n * pi))
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Here is an example implementation:


main.m
% Define Fourier series coefficients
n_max = 10;
B = zeros(1, n_max);
for n = 1:n_max
    B(n) = (-1)^(n+1) * (2/(n * pi));
end
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Calculate the Fourier series for the triangle wave. We can use a loop to iteratively add up each sine term in the series using the Fourier coefficients. Here is an example implementation:


main.m
% Calculate Fourier series
y = zeros(size(t));
for n = 1:n_max
    y = y + B(n) * sin(n * t);
end

% Plot Fourier series
hold on;
plot(t, y);
legend({'Triangle wave', 'Fourier series (n=10)'});
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Here's the full code:


main.m
% Define triangle wave with period 2*pi
period = 2*pi;
triangle = @(t) abs(sawtooth(t - pi/2, 0.5));

% Plot the triangle wave from -2*pi to 2*pi
t = linspace(-2*pi, 2*pi, 1000);
plot(t, triangle(t));
xlim([-2*pi, 2*pi]);
ylim([-0.2, 1.2]);
xlabel('t');
ylabel('f(t)');
hold on;

% Define Fourier series coefficients
n_max = 10;
B = zeros(1, n_max);
for n = 1:n_max
    B(n) = (-1)^(n+1) * (2/(n * pi));
end

% Calculate Fourier series
y = zeros(size(t));
for n = 1:n_max
    y = y + B(n) * sin(n * t);
end

% Plot Fourier series
plot(t, y);
legend({'Triangle wave', 'Fourier series (n=10)'});
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