Vibrato

Vibrato: a wavering of pitch.

• occurs in the singing voice and musical instruments (e.g. violin, wind instruments, the theremin, etc.)
• often due to human control after note onset;
• center frequency $f_c$ is modulated by a sinusoid with frequency $f_m$ yielding osc~ frequency:
  $$f_i = f_c + d\sin(2\pi f_m t),$$
  where $d$ is the frequency deviation from $f_c$.

• example: $f_c = 220$ Hz, $f_m = 3$ Hz, and $d = 3$: