// multi-utility computation suite · offline · instant · precise
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math.fourier-coefficients Calculator
Calculates Fourier series coefficients (a₀, aₙ, bₙ) for a periodic function and reconstructs the waveform from a given number of harmonics. Every periodic waveform decomposes into a sum of sinusoids — this is why audio equalizers can boost specific frequency bands.
Inputs
N Terms
Reference formula or conversion factor shown for context.
Period
Time for one complete cycle (s). Period = 1 / frequency. A 50 Hz signal has a 20 ms period.
Amplitude
Maximum displacement from equilibrium. Energy carried by a wave is proportional to amplitude squared.
Waveform
Reference formula or conversion factor shown for context.
Results
fundamental frequency (1/T)
Sample size or count used in the calculation.
angular frequency (rad/s)
Sample size or count used in the calculation.
RMS amplitude
Reference formula or conversion factor shown for context.