How to apply FFT on raw signal using Python

Question

I'm new in processing signals and need your help.

I have acquired a 10 seconds raw PPG (Photoplethysmogram) signal from my TI AFE4490. My hardware is calibrated and I'm using 250 samples per second to record those signal. I acquired 2500 points at the end.

You can see the image, the points and the code below.

Top: My raw PPG Signal - Bottom: Trying apply an FFT:

Code:

RED, IR, nSamples, sRate = getAFESignal()


period = 1/sRate

plt.figure(1)

plt.subplot(2,1,1)
x = np.linspace(0.0, nSamples*period, nSamples)
y = IR
plt.xlabel("Time (s)")
plt.ylabel("Voltage (V)")
plt.plot(x,y)

plt.subplot(2,1,2)
yf = fft(y)
xf = np.linspace(0.0, 1.0/(2.0*period), nSamples//2) 
plt.xlabel("Frequency (Hz)")
plt.ylabel("Gain")
plt.plot(xf, 2.0/nSamples * np.abs(yf[0:nSamples//2])) 

plt.grid()
plt.show()

The function getAFEsignal() is just a function to read a .txt file and put all into two numpy arrays.

Here you can find the .txt file: Raw signal file

As you can see, I didn't apply the FFT correctly, and I need this to discover which frequencies I need to filter. Do you know what I'm doing wrong, and if is possible to apply FFT on this signal?

Answer 1

The good news is that your computation of the FFT is fine. The data you show in the time domain has a fairly strong low frequency component. Correspondingly, your frequency-domain graph you get shows a significant spike near 0Hz.

The main problem lies in how you plot the results. To better see what you might expect to see in the frequency-domain based on an intuitive perception of the time-domain waveform you would need to readjust the scale of each axis. In particular, on the time scale shown you might expect to notice patterns with a duration of around 0.25 seconds up to maybe a few seconds. That would correspond to a frequency range of roughly 0-5Hz. It would then make sense to focus on that range instead of showing the entire 0-125Hz spectrum. This can be achieved by setting the x-axis limits as such:

plt.xlim(0,5) # set x-axis limits from 0 to 5Hz

Similarly for the y-axis, you need to consider that frequency components with small amplitudes (to the point of becoming harder to notice on a linear scale) can still have a very perceptible contribution on the time-domain signal. As such it is often desirable to show the frequency-domain amplitudes on a logarithmic decibel scale. This can be done as follows:

plt.plot(xf, 20*np.log10(2.0/nSamples * np.abs(yf[0:nSamples//2])))

Finally, if you want to better see the contribution of some specific frequency components without the interference from spectral leakage from other frequency component, you may want to consider pre-filtering your time-domain signal before computing the FFT. For example, if you want to eliminate the effect of the constant signal bias, the slow ~0.1Hz variation and the noises with frequency greater than 10Hz you might use something like the following:

import scipy.signal
b,a = signal.butter(4, [0.25/sRate, 10/sRate], btype='bandpass')
y = signal.filtfilt(b,a,signal.detrend(IR, type='constant'))