What is the mathematical formula to generate a sine wave, which changes its period sinusoidally?
E.g. a sinusoidal signal, with sinusoidal change of frequency.

  • It might be better to ask this on the Math.SE site. They have MathJax over there that will make it easier to write mathematics. Commented Oct 17, 2015 at 5:07
  • Basically, you're looking for y=sin([sin(ax)+e]x). You have to play with the constants a lot to make it work the way you want. Commented Oct 17, 2015 at 5:23
  • I’m voting to close this question because it's a question about a mathematical formula which is off-topic.
    – n00dles
    Commented Feb 8, 2023 at 18:59

1 Answer 1


I'm presuming you mean something like this (the blue waveform): -

enter image description here

The red waveform is amplitude modulation and the blue waveform is frequency modulation.

This should be the formula you need: -

enter image description here

  • y(t) is the FM output
  • fc is the unmodulated carrier frequency
  • f(delta)/fm is the modulation index - see this wiki article
  • fm is the modulating frequency
  • t is time