iq demodulation

iq_demod.py

import matplotlib.pyplot as plt
import numpy as np
from scipy import signal


# Source: https://github.com/guillaume-chevalier/filtering-stft-and-laplace-transform
def butter_lowpass_filter(data, cutoff_freq, sampling_freq, order=4):
    nyq_freq = 0.5 * sampling_freq
    normal_cutoff = float(cutoff_freq) / nyq_freq
    b, a = signal.butter(order, normal_cutoff, btype='lowpass')
    y = signal.filtfilt(b, a, data)
    return y
    

# helper, multiply with this to convert deg to rad    
rad = np.pi/180

# these are the parameters of our transmitted signal.
# a * np.cos(2*Pi*freq * t - phi)
phi = 45 * rad
a = 1
freq = 50


# this is the 'receiver' side, it needs to 'sample' the signal we are sending:
sampling_freq = 2000
t = np.linspace(0,1,sampling_freq)
omega = 2*np.pi*freq

signal_received = a * np.cos(omega * t - phi)

# we can also add some noise if we want:
# noise =  1 + 0.5 * np.random.uniform(-0.5, 0.5, sampling_freq)
# signal_received = signal_received * noise


# get i and q with a multuplication and a lowpass filteR:
signali = signal_received * np.sin(omega*t)
signali = butter_lowpass_filter(signali, freq, sampling_freq)

signalq = signal_received * np.cos(omega*t)
signalq = butter_lowpass_filter(signalq, freq, sampling_freq)


# we can get the amplitude back with this:
magnitude = 2 * np.sqrt(signali**2 + signalq**2)
plt.plot(magnitude, label="magnitude")

# we can get the 'angle' back with this:
freq = np.arctan2(signali, signalq)
plt.plot(freq / rad, label="angle")

plt.legend()
plt.show()

That's how it looks. You get back the 45 degress and the amplitude (1) that we are transmitting, there is some wiggling at the beginning and the end of the 'transmission' because of the low pass filter.

Setting a=10, and adding some noise:

This is the schematics of an sdr, you can find the multiplication and filtering towards the output.

These are the equations I used, you can check them using the rules for sin(x+y) and cos(x+y)

two more for completeness:

Let's hope I didn't make a mistake somewhere.