low-pass-filtering.py

#! /usr/bin/env python3

# Low-pass:
# voltage divider:  gain = Xc/(Xc+R) = 1/(1+R/Xc) = 1/(1+jωCR)
# At 3db, freq ωₒ: R = |Xc| = 1/ωₒC  thus  CR = 1/ωₒ
# gain = 1/(1+jω/ωₒ) = 1/(1+jf/fₒ)

import numpy
import matplotlib.pyplot as plt

# define input waveform as 010100 trapezoid
lo = numpy.array( [0] * 200 )
hi = numpy.array(list(range(10)) + [10] * 200 + list(range(9,-1,-1))) / 10.0
wave = numpy.concatenate( [lo,hi,lo,hi,lo,lo] )

# Func for low-pass RC filter of waveform
def low_pass( waveform, freq, f3db, hue, offset ):
  fftwaveform = numpy.fft.rfft(waveform)
  harmonics = numpy.arange(len(fftwaveform))
  gains = 1.0 / (1.0 + 1j * (harmonics * freq) / f3db)
  fftfiltered = fftwaveform * gains
  filtered = numpy.fft.irfft(fftfiltered)
  plt.plot(filtered * 0.8 + offset, color=hue, lw=2.0)

# input_waveform, base_freq, RC_filter_freq, screen_colour, screen_offset
low_pass(wave, 1, 1e10, "black", 4)
low_pass( wave, 1, 20, "green", 3)
low_pass( wave, 1, 6, "blue", 2)
low_pass( wave, 1, 3, "red", 1)
low_pass( wave, 1, 1.2, "orange", 0)

plt.savefig("low-pass-filtering.png")
plt.show()