How to Extract the following Frequency-domain Features in Python?

Question

Please feel free to point out any errors/improvements in the existing code

So this is a very basic question and I only have a beginner level understanding of signal processing. I have a 1.02 second accelerometer data sampled at 32000 Hz. I am looking to extract the following frequency domain features after having performed FFT in python -

Mean Freq, Median Freq, Power Spectrum Deformation, Spectrum energy, Spectral Kurtosis, Spectral Skewness, Spectral Entropy, RMSF (Root Mean Square Freq.), RVF (Root Variance Frequency), Power Cepstrum.

More specifically, I am looking for plots of these features as a final output.

The csv file containing data has four columns: Time, X Axis Value, Y Axis Value, Z Axis Value (The accelerometer is a triaxial one). So far on python, I have been able to visualize the time domain data, apply convolution filter to it, applied FFT and generated a Spectogram that shows an interesting shock

To Visualize Data

#Importing pandas and plotting modules

import numpy as np
from datetime import datetime
import pandas as pd
import matplotlib.pyplot as plt

#Reading Data
data = pd.read_csv('HelicalStage_Aug1.csv', index_col=0)
data = data[['X Value', 'Y Value', 'Z Value']]
date_rng = pd.date_range(start='1/8/2018', end='11/20/2018', freq='s')

#Plot the entire time series data and show gridlines
data.grid=True
data.plot()

enter image description here

Denoising

# Applying Convolution Filter

mylist = [1, 2, 3, 4, 5, 6, 7]
N = 3
cumsum, moving_aves = [0], []

for i, x in enumerate(mylist, 1):
    cumsum.append(cumsum[i-1] + x)
    if i>=N:
    moving_ave = (cumsum[i] - cumsum[i-N])/N
    #can do stuff with moving_ave here
    moving_aves.append(moving_ave)
np.convolve(x, np.ones((N,))/N, mode='valid')

result_X = np.convolve(data[["X Value"]].values[:,0], np.ones((20001,))/20001, mode='valid')
result_Y = np.convolve(data[["Y Value"]].values[:,0], np.ones((20001,))/20001, mode='valid')
result_Z = np.convolve(data[["Z Value"]].values[:,0],

np.ones((20001,))/20001, mode='valid')
plt.plot(result_X-np.mean(result_X))
plt.plot(result_Y-np.mean(result_Y))
plt.plot(result_Z-np.mean(result_Z))

enter image description here

FFT and Spectogram

import numpy as np
import scipy as sp
import scipy.fftpack
import pandas as pd
import matplotlib.pyplot as plt
%matplotlib inline

df = pd.read_csv('HelicalStage_Aug1.csv')
df = df.drop(columns="Time")
df.plot()
plt.title('Sensor Data as Time Series')

signal = df[['Y Value']]
signal = np.squeeze(signal)

Y = np.fft.fftshift(np.abs(np.fft.fft(signal)))
Y = Y[int(len(Y)/2):]
Y = Y[10:]

plt.figure()
plt.plot(Y)

enter image description here

    plt.figure()
powerSpectrum, freqenciesFound, time, imageAxis = plt.specgram(signal, Fs= 32000)
plt.show()

enter image description here

If my code is correct and the generated FFT and spectrogram are good, then how can I graphically compute the previously mentioned frequency domain features?

I have tried doing the following for MFCC -

import numpy as np
import matplotlib.pyplot as plt
import scipy as sp
from scipy.io import wavfile
from python_speech_features import mfcc
from python_speech_features import logfbank

# Extract MFCC and Filter bank features
mfcc_features = mfcc(signal, Fs)
filterbank_features = logfbank(signal, Fs)

# Printing parameters to see how many windows were generated
print('\nMFCC:\nNumber of windows =', mfcc_features.shape[0])
print('Length of each feature =', mfcc_features.shape[1])
print('\nFilter bank:\nNumber of windows =', filterbank_features.shape[0])
print('Length of each feature =', filterbank_features.shape[1])

Visualizing filter bank features

#Matrix needs to be transformed in order to have horizontal time domain

mfcc_features = mfcc_features.T
plt.matshow(mfcc_features)
plt.title('MFCC')

enter image description here enter image description here

Answer 1

I think your fft taking procedure is not correct, fft output is usually peak and when you are taking abs it should be one peak, as , probably you should change it to Y = np.fft.fftshift(np.abs(np.fft.fft(signal))) to Y=np.abs(np.fft.fftshift(signal)