# How to differentiate between two sets of data; one being a mixture of sinusoidal waves and other without any pattern

I have two sets of data; one is a mixture of different sinusoidal waves of different frequencies and amplitude while the other set does not have any regular pattern. I have the following questions:

1. How can one differentiate between these two sets of data in real time?
2. Can Fourier transform be used? If yes, how?
3. How effective are these methods to differentiate if there is noise in data?

## 1 Answer

The Fourier transform would seem to be what you want. If you have a finite set of data points then, more specifically, you want the Discrete Fourier Transform. There's plenty of information out there on it.

Discrete Fourier Transform at Wikipedia

Discrete Fourier Transform at Wolfram MathWorld

You will probably find many references to the Fast Fourier Transform, this is another algorithm which may be more efficient.

Fast Fourier Transform at Wolfram MathWorld