Fourier Series Synthesizer & FFT Analyzer
Synthesize periodic waveforms from harmonic components to observe Fourier series convergence, or analyze the FFT frequency spectrum of a noisy multi-tone signal.
Signal Generation
1 (Fundamental)50
Fourier Series Theory:
Any periodic electrical signal can be decomposed into and reconstructed from a sum of sinusoids (sin, cos). As the harmonic count approaches infinity, the synthesized waveform converges toward the ideal geometric shape.
Any periodic electrical signal can be decomposed into and reconstructed from a sum of sinusoids (sin, cos). As the harmonic count approaches infinity, the synthesized waveform converges toward the ideal geometric shape.
Synthesized Waveform (Time Domain)
Loading chart...
* Increasing the harmonic count shows convergence toward the ideal waveform. Near discontinuities, the Gibbs phenomenon (overshoot ringing) becomes visible.
Harmonic Amplitude Spectrum (Frequency Domain)
Loading chart...