8月30日 的 FourierSeries 應用程式分析

Fourier Series Lab is an interactive learning app for exploring how periodic signals are rebuilt with Fourier series. Choose preset waveforms—square, triangle, or sawtooth—or enter your own expression using standard math syntax such as sin(x) + 0.5*sin(3*x). The app numerically integrates over one period to compute coefficients a₀, aₙ, and bₙ, then plots the original function alongside the partial sum so you can see convergence in real time.  On the Lab tab, adjust the number of terms with a slider or stepper, tune integration accuracy, and play an animation that steps through harmonics one by one. Toggle harmonic overlays, residual curves, and live error metrics including mean squared error and maximum absolute error. The Spectrum tab breaks down each harmonic with bar charts for cosine, sine, and magnitude components, plus phase readouts. The Reference tab keeps standard formulas, study notes on topics like the Gibbs phenomenon, and a live coefficient table synced with your current session.