Discrete fourier transformation from a list of x-y points

Question

What I\'m trying to do is, from a list of x-y points that has a periodic pattern, calculate the period. With my limited mathematics knowledge I know that Fourier Transformat

Answer 1

For samples that are not evenly spaced, you can use scipy.signal.lombscargle to compute the Lomb-Scargle periodogram. Here's an example, with a signal whose dominant frequency is 2.5 rad/s.

from __future__ import division

import numpy as np
from scipy.signal import lombscargle
import matplotlib.pyplot as plt


np.random.seed(12345)

n = 100
x = np.sort(10*np.random.rand(n))
# Dominant periodic signal
y = np.sin(2.5*x)  
# Add some smaller periodic components
y += 0.15*np.cos(0.75*x) + 0.2*np.sin(4*x+.1)
# Add some noise
y += 0.2*np.random.randn(x.size)

plt.figure(1)
plt.plot(x, y, 'b')
plt.xlabel('x')
plt.ylabel('y')
plt.grid()

dxmin = np.diff(x).min()
duration = x.ptp()
freqs = np.linspace(1/duration, n/duration, 5*n)
periodogram = lombscargle(x, y, freqs)

kmax = periodogram.argmax()
print("%8.3f" % (freqs[kmax],))

plt.figure(2)
plt.plot(freqs, np.sqrt(4*periodogram/(5*n)))
plt.xlabel('Frequency (rad/s)')
plt.grid()
plt.axvline(freqs[kmax], color='r', alpha=0.25)
plt.show()

The script prints 2.497 and generates the following plots:

Answer 2

As starting point:

• (I assume all coordinates are positive and integer, otherwise map them to reasonable range like 0..4095)
• find max coordinates xMax, yMax in list
• make 2D array with dimensions yMax, xMax
• fill it with zeros
• walk through you list, set array elements, corresponding to coordinates, to 1
• make 2D Fourier transform
• look for peculiarities (peaks) in FT result

Answer 3

This page from Scipy shows you basic knowledge of how Discrete Fourier Transform works: http://docs.scipy.org/doc/numpy-1.10.0/reference/routines.fft.html

They also provide API for using DFT. For your case, you should look at how to use fft2.