𝐹𝑔.𝑚(𝜃, 𝜃𝑚) = 𝐹𝑃𝑀 ∞∑ 𝑚=𝑜𝑑𝑑 1𝑚 cos(𝑚𝑍 𝑟 (𝜃 − 𝜃 𝑚 )

How to apply fourier series on this equation at matlab to draw a graph.

Answer 1

[TED MOSBY]

Hi,

This is the Fourier series of a periodic even-symmetric square wave. As this series is already written as a fourier series, so it doesn't need any further fourier analysis so we can simply evaluate and plot it in MATLAB as below:

Zr      = 3;         % Constant
theta_m = 0;       
N       = 50;        % Number of odd harmonics to include

% Evaluation range
theta = linspace(0, 2*pi, 1000);  

% Fourier series: sum of 1/m * cos(m * Zr * (theta - theta_m))
m = 1:2:(2*N - 1);                       
series_sum = zeros(size(theta));          

for k = 1:length(m)
    series_sum = series_sum + (1/m(k)) * cos(m(k) * Zr * (theta - theta_m));
end

plot(theta, series_sum, 'LineWidth', 1.5)
xlabel('\theta (rad)')
ylabel('Fourier Series Value')
title(['Sum_{m=1,3,...,' num2str(m(end) ) '} (1/m) * cos(m Z_r (\theta - \theta_m))'])
grid on

The output should look like this:

Hope this helps!