# Can I decompose a sine signal into its component sine waves?

If I have a sine signal that was composed of the sum of multiple other sine waves, is there any way that i can decompose the sine signal into its component sine waves without knowing any of the component sine waves or how many sine waves were summed to get the signal?

For example, if I create a signal be summing the following waves together: sin(x) + sin(3x) + sin(3x) + sin(4x), then can i take this signal, and without knowing the sine waves that were summed to create it or how many sine waves were summed to create it, can i decompose it into the sines that were used to create it (sin(x) + sin(3x) + sin(3x) + sin(4x) in this case)?

## 2 Answers

If I have a sine signal that was composed of the sum of multiple other sine waves,

No. Either it's a sine, or it's a sum of other sines.

I take it you want to say "I've got a signal that's a sum of sines".

is there any way that i can decompose the sine signal into its component sine waves without knowing any of the component sine waves or how many sine waves were summed to get the signal?

Yes, the Fourier transform does exactly that. It's the standard thing that you'll need to understand, no matter what you do in signal decomposition, so: get reading!

• I've read about Fourier Transform before and I may be mistaken, but doesn't the fourier transform decompose a sine signal into an into an infinite number of component sine waves that can be summed to create the sine signal? If it does, then it is not ideal for my application because I only need to decompose a sine signal into the finite number of sine waves that were summed to create it. – CCS May 5 at 6:54
• no, a sine signal is composed of exactly 1 (one) sine, and thus, the Fourier transform yields exactly that. – Marcus Müller May 5 at 10:25

Curve fitting is another option after Fourier transform, you can fit a sum of sine function to your signal and the fitting coefficients show the amplitude and frequency of the signal. Check this: https://stackoverflow.com/questions/38832474/curve-fitting-in-matlab-for-a-sinusoidal-function-with-more-than-8-terms