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I've constructed a figure containing 3 different plots representing a position of 3 different masses over some time range. I want to find the period of each. I'm not familiar with the FFT function that I've come across while searching for ways to find the period online. How do I go about this? Below is the kernel for the plot and the figure; I won't include the code used to build all these variables as it would be quite extensive.

I know I code just start making vertical lines and then estimate by eye, but I'd much rather do it through coding than with that method.

#using the times in days
T9 = 500
dt9 = 0.5
num9 = T9/dt9
times9 = np.linspace(0, T9, num9)
xpos_q9_m1_AU_new = xpos_q9_m1_AU[:-1]
xpos_q9_m2_AU_new = xpos_q9_m2_AU[:-1]
xpos_q9_m3_AU_new = xpos_q9_m3_AU[:-1]
plt.plot(times9, xpos_q9_m1_AU_new)
plt.plot(times9, xpos_q9_m2_AU_new)
plt.plot(times9, xpos_q9_m3_AU_new)
plt.xlabel('Time (days)')
plt.ylabel('X Positions (AU)')
plt.title('X Position of the Kepler 16 System over Time')
plt.legend(['Body 1', 'Body 2', 'Body 3'])
plt.savefig('q9_plot.png');

X Position of Masses over Time

Elijah Shepherd
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1 Answers1

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What you're looking for is a Fourier Transform. This function determines what frequencies make up a wave. Scipy has a module that does this for you nicely:

from scipy.fft import fft
# Number of sample points
N = 600
# sample spacing
T = 1.0 / 800.0
x = np.linspace(0.0, N * T, N)
y = np.sin(50.0 * 2.0 * np.pi * x)
yf = fft(y)
xf = np.linspace(0.0, 1.0 / (2.0 * T), N // 2)
import matplotlib.pyplot as plt
plt.plot(xf, 2.0 / N * np.abs(yf[0:N // 2]))
plt.grid()
plt.show()

Frequency distribution of np.sin(50.0 * 2.0 * np.pi * x) showing spike at 50

This gives you a graph showing the predicted frequency.

Krish
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