CODEWITHSUNDEEP
pythonfftfrequencyaccelerometer
Chanski
Chanski

Reputation: 63

Fast Fourier Transform for an accelerometer in Python

I have data from the accelerometer in m/s2 (Y-axis) for a time period in seconds (X-axis). I would like to convert this data real-time so that I get the value of an acceleration related to the frequency in Hz. I know that, for example, there is an FFT function in numpy, but I have no idea at all how to use it. I would appreciate, if somebody could provide an example code to convert the raw data (Y: m/s2, X: s) to the desired data (Y: m/s2, X: Hz). It should not be necessarily exactly this function. Thanks!

Upvotes: 2

Views: 7671

Answers (1)

lnogueir
lnogueir

Reputation: 2085

First, let's create a time-domain signal.

For simplicity, I will create a sine wave with frequency components 12Hz and 24Hz and you can assume the unit of the values are m/s^2:

import numpy as np
import matplotlib.pyplot as plt

# This would be the actual sample rate of your signal
# since you didn't provide that, I just picked one
# big enough to make our graphs look pretty
sample_rate = 22050

# To produce a 1-second wave
length = 1

# The x-axis of your time-domain signal
t = np.linspace(0, length, sample_rate * length)

# A signal with 2 frequency components
# - 12Hz and 24Hz
y = np.sin(12 * (2 * np.pi) * t) + 0.5*np.sin(24 * (2 * np.pi) * t) 

# Plot time domain signal
plt.plot(t, y)
plt.xlabel("Time (s)")
plt.show()

This will output:

Time-domain signal

Now, we continue on with the script by taking the Fourier transform of our original time-domain signal and then creating the magnitude spectrum (since that gives us a better way to visualize how each component is contributing than the phase spectrum):

# This returns the fourier transform coeficients as complex numbers
transformed_y = np.fft.fft(y)

# Take the absolute value of the complex numbers for magnitude spectrum
freqs_magnitude = np.abs(transformed_y)

# Create frequency x-axis that will span up to sample_rate
freq_axis = np.linspace(0, sample_rate, len(freqs_magnitude))

# Plot frequency domain
plt.plot(freq_axis, freqs_magnitude)
plt.xlabel("Frequency (Hz)")
plt.xlim(0, 100)
plt.show()

So now we can visualize the frequency-domain:

Frequency-domain signal

Notice how the magnitude of the 24Hz component is about half of the 12Hz component. That is because I purposely timed the 24Hz component by 0.5 on the time-domain signal, so the 24Hz component 'contributes' less to the overall signal, hence we get this halved spike for that component.

Note, also, that the y-axis of our output signal is not really in m/s^2 per Hz as you wanted. But you could compute the actual m/s^2 values by taking the integral over your desired frequency band.

I'll leave the jupyter notebook I created available here, feel free to use it and open issues if you have any problems with it.

Upvotes: 5

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