# FTT Features to use after time-domain is transformed to frequency-domain

Please forgive the question if it sounds trivial/naive, I am from computer science background, not electrical/computer engineering.

I work with GPS trajectory dataset for classification. Data was collected at sampling rate of 1-second per sample.

time-domain:

Currently, I considered working with time-domain features only, so I extracted two point-level features:

• speed: (rate of distance between consecutive locations with time), and
• acceleration: (rate of speed with time).

I then divided each user's trip into fixed-length segments of 100 time steps (100 data points per segment). I finally calculated 11 statistics of each feature (min, max, mean, median, st-dev, etc) in the fixed-length segment, making a total of 22 features per segment. This I used to train a classifier (decision tree) for classification.

frequency-domain:

But I wanted to try combination of time-and-frequency features in building my model, to see the impact, so using fast Fourier transform, I proceeded in the following way:

1. Take the original 2-featured segments (the 100 fixed data point segments).
2. Use scipy.fft.fft to obtain the corresponding frequency spectrum of each feature, thus:
 import numpy as np
from scipy.fft import fft
N = 100  # number of samples in a segment
T = 1    # sample spacing ( 1 second)

def fft_transform(data):
"""
compute the FFT of each segment's feature in features's dimension
"""
fourier = fft(data, axis=2)
magnitude = np.abs(fourier)

return magnitude

The figure below illustrates an example input in time and frequency domains.
3. Take only the positive frequencies values of the FFT (since FFT of real-valued input is symmetric).
4. Add the frequency-domain values of each feature to its time-domain. The result is 11 time-domain features for speed (similarly acceleration) and 50 frequncy-domain features for speed (similarly acceleration). Total: 122 features per input. The new results obtained yielded significant negative impact on the overall model performance, evaluated on the usual metrics (precision, recall, f1).

In the next round of experiment, I would like to consider significant FFT descriptors to add as frequency features instead of using the whole FFT values as explained above. I initially thought of computing same feature statistics as I did for the time-domain, but was advised that wouldn't make a good features for FFT spectrum (that doing so may also lead to discard of important features/pattern).

I can testify to that, as the results I obtained doing so even worsen the model performance. Some classes never get correctly predicted even for 1 sample.

• What constitute a good FFT descriptors to select and add to time-domain instead the similar statistics as used for time features?