Python FFT for feature extraction

Question

I am looking to perform feature extraction for human accelerometer data to use for activity recognition. The sampling rate of my data is 100Hz.

From the various sources I have researched an FFT is a favourable method to use. I have the data in a sliding windows format, the length of each window is 256. I am using Python to do this with the NumPy library. The code I have used to apply the FFt is:

import numpy as np

def fft_transform (window_data):

    fft_data = []
    fft_freq = []
    power_spec = []

    for window in window_data:

        fft_window = np.fft.fft(window)
        fft_data.append(fft_window)

        freq  = np.fft.fftfreq(np.array(window).shape[-1], d=0.01)
        fft_freq.append(freq )

        fft_ps = np.abs(fft_window)**2
        power_spec.append(fft_ps)

    return fft_data, fft_freq, power_spec

This give output which looks like this:

fft_data

array([  2.92394828e+01 +0.00000000e+00j,
        -6.00104665e-01 -7.57915977e+00j,
        -1.02677676e+01 -1.55806119e+00j,
        -7.17273995e-01 -6.64043705e+00j,
         3.45758079e+01 +3.60869421e+01j,
         etc..

freq_data

array([  0.      ,   0.390625,   0.78125 ,   1.171875,   1.5625  , etc...

power_spectrum

array([  8.54947354e+02,   5.78037884e+01,   1.07854606e+02,
         4.46098863e+01,   2.49775388e+03,   etc...

I have also plotted the results using this code - where fst_ps is the first array/window of power_spectrum and the fst_freq is the first window/array of the fft_freq data.

import matplotlib.pyplot as plt
fig = plt.figure(figsize=(width, height))

fig1= fig.add_subplot(221)
fig2= fig.add_subplot(222)
fig1.plot(fst_freq, fst_ps)
fig2.plot(fst_freq, np.log10(fst_ps))
plt.show()

I am looking for some advice on what my next step is for extracting features. Thanks

Answer 1

So, as you decomposed signal into spectrum, next step you could try to understand which frequencies is relevant for your application. But it's quite bit difficult to get it from single spectrum picture. Remember, that one frequency bin in the spectrum - it's the same basic signal bounded by narrow frequency range. Some frequencies could not be important for your task.

Better way, if you could try STFT method to understand your signal features in the frequency-time domain. For example, you may read this article about STFT approach on Python. Usually this method applied for searching some kind of time-frequency patterns, which can be recognized as features. For example, in human voice pattern (as in the article) you may see sustainable floating frequencies with duration and frequency bound features. You need to get STFT for your signal to find some patterns on the sonogram to extract features for your task.