## Thursday, April 3, 2014

### Alternative to Fourier Transform

I noticed if you have a plot, like this:
you can easily find some frequency information with this formula:
Where d is the number of divisions of the interval you want to analyze and r /d is the rightmost point... a slight modification could be made to shift the interval being analyzed from starting at 0.
So for the values from the first image, with x of 100 and d of 10, if we vary s we get:

It appears the most interesting values are 2.5, 3, and 4.75... the original function I used to generate the data points was in fact:
The reason it works is pretty simple, no matter what your original wave is, if you add it together with a simple sine and cosine wave at a particular frequency and take the absolute value as per the formula, the result will be much larger on average over the interval if the original wave contains that frequency, as the waves "resonate" and reinforce each other making a larger value over the interval.
It seems much simpler than the Fourier transform, though it is somewhat less exact because there is noise in the result potentially making it more difficult to find the peaks.