UsefulVerse
Language · English

Free to use, no account

Fourier Series Calculator

Estimate a real Fourier series from uniformly spaced samples across one period. Choose how many harmonics to keep, inspect the coefficients, and compare the reconstructed curve with your samples.

Enter 4–128 equally spaced sample values, one per line or separated by semicolons. Do not repeat the endpoint.

Use one consistent time unit. Frequency is the reciprocal of this period and is shown per time unit.

The limit depends on the number of samples to avoid exceeding the usable frequency range.

This is a finite-sample approximation, not an audio analyzer. More samples and harmonics can improve a smooth-signal fit; discontinuities may show Gibbs overshoot. The result depends on uniform sampling and one correctly chosen period.

Real Fourier series: DC = (1/N)Σxⱼ; aₙ = (2/N)Σxⱼcos(2πnj/N); bₙ = (2/N)Σxⱼsin(2πnj/N); f(t) = DC + Σ[aₙcos(2πnt/T) + bₙsin(2πnt/T)], 0 ≤ t < T.

How does this Fourier series calculator work?

Enter 4–128 equally spaced values for one complete period, the period length, and a harmonic count. The calculator estimates real Fourier coefficients with a discrete sum and reconstructs the signal from the selected harmonics.

Frequently asked questions

How does this Fourier series calculator work?

Enter 4–128 equally spaced values for one complete period, the period length, and a harmonic count. The calculator estimates real Fourier coefficients with a discrete sum and reconstructs the signal from the selected harmonics.

Are my samples uploaded?

No. The calculation and chart run in this browser. Your samples are not uploaded or saved by this tool.

What does the DC component mean?

It is the average value of all samples in one period. A constant input therefore has only DC, with all higher coefficients equal to zero within rounding tolerance.

How many samples and harmonics should I use?

Use enough uniform samples to represent the waveform. The calculator limits the harmonic count to the usable range of those samples; more harmonics can capture sharper changes but may create overshoot near jumps.

Why can the reconstructed curve overshoot near a jump?

A truncated Fourier series can show Gibbs oscillation around a discontinuity. Increasing the harmonic count narrows the affected region but does not remove the overshoot entirely.