Fourier Series Calculator

Calculate Fourier series expansions and harmonic coefficients for periodic waveforms.

Waveform Parameters

Waveform Type

Amplitude

Period

Evaluation Point (x)

Number of Harmonics: 10

Fourier Approximation (10 harmonics)

0.96824762

Exact Value

1.00000000

Approximation Error

3.1752e-2

Harmonic Coefficients

n=1bₙ=1.2732

n=3bₙ=0.4244

n=5bₙ=0.2546

n=7bₙ=0.1819

n=9bₙ=0.1415

n=11bₙ=0.1157

n=13bₙ=0.0979

n=15bₙ=0.0849

Fourier Series Formula

f(x) = a₀/2 + Σ[aₙcos(nωx) + bₙsin(nωx)]