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math.fourier-series-coefficients Calculator
Computes Fourier series coefficients for square, triangle, and sawtooth waves, and plots the partial sum approximation. Any periodic signal can be decomposed into Fourier components — this is the mathematical basis of audio compression (MP3) and signal filtering.
Inputs
Function Type
Reference formula or conversion factor shown for context.
Amplitude
Maximum displacement from equilibrium. Energy carried by a wave is proportional to amplitude squared.
Harmonics
Count of items or occurrences.
Frequency Hz
Cycles per second (Hz). Audible sound: 20 Hz – 20 kHz. Make sure units match what the formula expects.
Results
RMS value
The computed numeric or monetary value.
fundamental b₁
Sample size or count used in the calculation.
3rd harmonic b₃
Sample size or count used in the calculation.
5th harmonic b₅
Sample size or count used in the calculation.
type
The classification or type assigned based on the inputs.