Functions {wave function} can be waves.
series
Periodic functions can be trigonometric series. If period is T, series is: a0 + sum over i of (ai * cos(2n * pi * tau / T) + bi * sin(2n * pi * tau / T)), where a0 = (1/T) * (integral from -T/2 to T/2 of f(t) * dt), ai = (2/T) * (integral of f(t) * cos(2n * pi * t / T)), and bi = (2/T) * (integral of f(t) * sin(2n * pi * t / T)).
Sine or cosine can be zero. Even periodic function uses cosine. Odd periodic function uses sine.
period
For function over interval with width x, period T is twice interval length x: T = 2*x.
jump
Term coefficients depend on differences {jump} between left-hand and right-hand function limits, derivatives at jump points, and second derivatives at jump points.
analyzer
Harmonic analyzer can find first 20 coefficients from function graph and areas. Integrator circuits can calculate area.
Mathematical Sciences>Algebra>Function>Kinds>Trigonometric
3-Algebra-Function-Kinds-Trigonometric
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Date Modified: 2022.0224