Math · Signal Analysis

Fourier Series Calculator

Decompose a periodic waveform into its harmonic components — coefficients a0, an and bn, amplitudes and phases.

Fourier series
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Fundamental frequency ω0
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DC component a0
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Total RMS of harmonics
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Dominant harmonic
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Even / odd symmetry
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n Frequency (rad/s) an bn Amplitude An Phase φn (deg)
Fourier series: f(t) = a0 + Σn=1..∞ [ an·cos(nω0t) + bn·sin(nω0t) ]
Coefficients: a0 = (1/T)∫f dt,   an = (2/T)∫f·cos(nω0t) dt,   bn = (2/T)∫f·sin(nω0t) dt.

Five classic waveforms

Square, triangle, sawtooth, half-wave and full-wave rectified signals built in.

Harmonic table

Every coefficient with amplitude and phase angle, ready for filter or audio design.

Symmetry hints

Odd/even symmetry instantly tells you which coefficients should vanish.

Series preview

See the truncated Fourier formula built from your harmonic limit.

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