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sci.fourier-series-sawtooth Calculator
Calculates Fourier series coefficients and partial sum approximation of a sawtooth wave from harmonic number and amplitude. The Gibbs phenomenon causes 9% overshoot at discontinuities regardless of how many Fourier terms are included — this is a fundamental property of Fourier series at jump discontinuities.
Inputs
Frequency Hz
Cycles per second (Hz). Audible sound: 20 Hz – 20 kHz. Make sure units match what the formula expects.
Num Harmonics
Count of items or occurrences.
Time Ms
Duration of the process. Make sure units match the rate inputs (seconds, minutes, or hours).
Results
Fourier series value at t
The computed numeric or monetary value.
exact sawtooth value
The computed numeric or monetary value.
approximation error
The difference between the computed result and the exact or true value — a measure of approximation accuracy.
sawtooth FS: 2/π Σ(-1)^(n+1) sin(2πnft)/n
Sample size or count used in the calculation.
Gibbs phenomenon
pH of the solution. Below 7: acidic. 7: neutral. Above 7: basic (alkaline).