Fourier Series Online Simulator

Many engineering and scientific phenomena are periodic in nature, such as current and voltage in AC circuits. Fourier analysis allows these periodic signals to be expressed in terms of their fundamental and harmonic components. A Fourier series represents a periodic function as a sum of sine and cosine waves, enabling any periodic signal to be modeled using trigonometric functions.

Fourier Series Calculator

Choose a Signal

Rectangular Wave Square Wave (50% Duty) Sawtooth Wave Triangular Wave Sine Wave (Example)

Parameters

Amplitude A: Period T: Pulse Width (for rectangular only): Number of Harmonics (N):

MATLAB Code

syms t n

% Parameters
T = 4; % period
w0 = 2*pi/T; % fundamental frequency
n = 1:7; % harmonic index (symbolic sum up to 7)

% Define the sine wave
f = sin(w0 * t);

% Fourier coefficients
a0 = (1/T) * int(f, t, 0, T)

an = (2/T) * int(f * cos(n*w0*t), t, 0, T)

bn = (2/T) * int(f * sin(n*w0*t), t, 0, T)

    

Output

a0 =
0

an =
[0, 0, 0, 0, 0, 0, 0]

bn =
[1, 0, 0, 0, 0, 0, 0]

    

Further Reading