Frequency analysis with unevenly distributed data in python

Question

I have a signal generated by a simulation program. Since the solver in this program has a variable time step, I have a signal with unevenly distributed data. I have two lists, a list with signal values ​​and another list with the time at which each value occurred. The data may be something like this

npts = 500 t=logspace(0,1,npts) f1 = 0.5 f2 = 0.6 sig=(1+sin(2*pi*f1*t))+(1+sin(2*pi*f2*t)) 

I would like to be able to perform frequency analysis of this signal using python. I can't seem to use the fft function in numpy because it requires evenly distributed data. Are there any standard functions that could help me find the frequencies contained in this signal?

Answer 1

The most common algorithm for solving such problems is called Least Squares Spectral Analysis. It looks like it will be in a future release of the scipy.signals package . Maybe there is a current version, but I can’t find it ... Also, there is some code from Astropython that I won’t copy it entirely, but it essentially creates a lomb class, which you can use the following code to get some values. What you need to do is the following:

 import numpy import lomb x = numpy.arange(10) y = numpy.sin(x) fx,fy, nout, jmax, prob = lomb.fasper(x,y, 6., 6.) 

Answer 2

Very simple, just find the formula for the Fourier transform and implement it as a discrete sum over your data values:

given a set of values f(x) for some set of x , then for each frequency k ,

 F(k) = sum_x ( exp( +/-i * k *x ) ) 

select k between 0 and 2*pi / min separation in x .

and you can use 2 * pi / max(x) as the increment size

For the test case, use something for which you know the correct answer, cf, one cos( k' * x ) for some k' or gauss.