The spectrum as a recipe (with live audio)

f_k (Hz)

A_k

φ_k (rad)

Window (ms)

Delay t_d (ms)

Preset

Fundamental f₀ Period T₀ Harmonic numbers

Set an amplitude to 0 to remove a component (try removing the lowest one of a harmonic set, then Play: the pitch stays). Phase changes the waveform but not the sound.