how to calculate first n terms of the sawtooth Fourier series and plot the results in figure?

Answer 1

[Gautam]

Hi Ismita

To calculate the Fourier series coefficients and plot the Fourier series approximation for the given sawtooth function, follow these steps:

1. Define the sawtooth function and its range and period.
2. Calculate the Fourier series coefficients (an and bn).
3. Create a Fourier series approximation using the calculated coefficients.
4. Plot and compare the original function with its Fourier series approximation.

You can modify the code below which shows calculation and plotting of a fourier series approximated function using the first 10 terms

% Define the period and the range for x
T = 2*pi;      % Period of the periodic function
x = linspace(-T/2, T/2, 1000); % Range of x values
% Define the given piecewise function
f = @(x) ((-1/2)*(pi+x).*(x >= -pi & x <0) + (1/2)*(pi-x).*(x>=0 & x<=pi));
% Number of terms in the Fourier series
N = 10;
% Calculate the Fourier series coefficients (an and bn)
a0 = (1/T) * integral(@(x) f(x), 0, T);
an = zeros(1, N);
bn = zeros(1, N);
for n = 1:N    
    an(n) = (1/T) * integral(@(x) f(x).*cos(n*pi*x/2), 0, T);
    bn(n) = (1/T) * integral(@(x) f(x).*sin(n*pi*x/2), 0, T);
end
% Create the Fourier series approximation
F = a0/2;
for n = 1:N
    F = F + an(n) * cos(n*pi*x/2) + bn(n) * sin(n*pi*x/2);
end
% Plot the original function and its Fourier series approximation
figure;
plot(x, F);
xlabel('x');
ylabel('f(x)');