sci-com-exercise-4

% Manual increment
% increment = (2 * pi) / 100
% x = [-pi:increment:pi]
x = linspace(-pi, pi, 101);
N = 1000;
empty_mat = zeros(N+1, 101);
for i = 0:N
   expression = (sin((2*i+1).* x)) / (2*i + 1);
   % disp(size(expression))
   % empty_mat(i+1)
   empty_mat(i+1, :) = expression;
end
SNf1 = empty_mat .* (4 / pi);
% disp(SNf1)
SNf = sum(SNf1);
f = [0:100];
f(find((x < 0) & (x >= -pi))) = -1;
f(find((x <= pi) & (x >= 0))) = 1;
% Error
E = abs(f - SNf);
% Plotting x against SNf and x against err
plot(x, SNf)
title("x-values against partial sum (SNf)");
xlabel("x-values");
ylabel("SNf");
% Plotting x against SNf
plot(x, E)
title("x-values against partial sum (SNf)");
xlabel("x-values");
ylabel("SNf");
% Plotting x against err
plot(x, E)
title("x-values against E (absolute error between Fourier series of f and N-th partial sum)");
xlabel("x-values");
ylabel("E");
% Maximum and average error
disp(["Maximum error:", max(E)])
disp(["Average error:", mean(E)])