Question

Write an Octave program to generate Fourier Synthesis of Sawtooth Wave (for up to 13 harmonics)

Answer 1

To generate the Fourier synthesis of a sawtooth wave using Octave, you can use the built-in FFT function. This involves summing individual harmonics of the wave and scaling their amplitudes.

Step-by-step explanation:

To generate the Fourier synthesis of a sawtooth wave using Octave, you can use the built-in FFT function. Here's an example program:

x = 0:0.01:2*pi;
A = 1;
frequencies = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13];

sawtooth_wave = zeros(size(x));

for n = 1:length(frequencies)
sawtooth_wave = sawtooth_wave + (A / (2 * n - 1)) * sin((2 * n - 1) * x);
end

plot(x, sawtooth_wave);

This program uses a loop to sum the individual harmonics of the sawtooth wave. The amplitude of each harmonic is scaled by 1/(2n-1), where n is the index of the harmonic. The resulting waveform is then plotted using the plot function.