Using the fourier series to approximate a triangular wave.

I want to approximate a triangular waveform, with the Fourier Series. The triangular waveform has an amplitude of 1 and a frequency of 30 Hz.

and N-values of 1, 5, 10, and 20 number of Fourier terms for approximation.

The only function that I can think of is the sawtooth function. I was wondering if there is a more fitting function for this.

[John D'Errico]

A sawtooth does exactly what you want. So what is the problem?

Answer 1

[Sulaymon Eshkabilov]

Here is one simple code how to generate sawtooth approximation using different Fourier series:

t = linspace(0, 10, 1000);
Phase_shift = pi;
ST = sawtooth(2*pi*t*.5+Phase_shift);
plot(t, ST, 'm', 'LineWidth', 2.5, 'DisplayName', 'SawTooth'), hold on
t = linspace(0, 10, 1000);
N = 1;
FS1 = (2/pi)*sin(pi*t*N);
plot(t,FS1, 'r', 'LineWidth', 2, 'DisplayName','N=1')
N=5;
F=0;
for ii = 1:N
    F = F+(-1)^(ii+1)*sin(pi*t*ii)*(1/ii);
    FS5 = (2/pi)*F;
end
plot(t,FS5, 'g', 'LineWidth', 2, 'DisplayName','N=5')
hold on
N=10;
F=0;
for ii = 1:N
    F = F+(-1)^(ii+1)*sin(pi*t*ii)*(1/ii);
    FS10 = (2/pi)*F;
end
plot(t,FS10, 'b', 'LineWidth', 2 , 'DisplayName','N=10')
hold on
N=20;
F=0;
for ii = 1:N
    F = F+(-1)^(ii+1)*sin(pi*t*ii)*(1/ii);
    FS10 = (2/pi)*F;
end
plot(t,FS10, 'k', 'LineWidth', 1.5, 'DisplayName','N=20')
hold off
legend("show")
xlabel("Time, [s]")
ylabel('x(t)')
grid on
title('Sawtooth Approximation with Fourier Series: N = [1, 5, 10, 20]')
xlim([0, 5.5])

[Gidel]

The script does not display the figure showed, sorry.

[Walter Roberson]

@Gidel

The figure you see in @Sulaymon Eshkabilov Answer is the result of running the posted code inside the Answers facility itself. The figure was not inserted as an image: that is actual R2023a output.