# Phase response distortion due to IQ demodulation

I have a bandpass signal, I do IQ demodulation meaning:

first step:

$$IQ(t) = x(t)*exp(-2\pi f_ct)$$

second step:

low pass using $$filtfilt$$ function in MATLAB. (in order to avoid phase distortion)

Here, $$F_c=5 MHz$$ and $$F_S=40 MHz$$

For low-pass filter I use this:

[b,a] = butter(5,2*Fc/Fs) ;
IQ(t) = filtfilt(b,a,IQ(t))*2; The plot shows frequency response of $$x(t)$$, $$real(IQ(t))$$ a.k.a $$I$$, $$imag(IQ(t))$$ a.k.a $$Q$$ and $$IQ(t)$$, respectively.

When I reconstruct this signal again to the original bandpass signal:

$$x'(t) = IQ(t)*exp(+2\pi f_ct)$$

The magnitude, phase response and power spectrum of the original and reconstructed signal is a follows: note: To plot phase response I use matlab's $$unwrap$$ function.

The frequency spectrum of original and reconstructed signal:

The phase response of the $$x'(t)$$ seems distorted at $$2f_c = 10MHz$$ .

Question1: Is this normal?

Question2: Does this happen because low-pass filter is not reversible?

Question3: Can I recover that phase response?

• You could try using a linear phase FIR filter for the lowpass filtering. Comparing the original with the reconstructed bandpass signal should only have a linear phase difference between the two. Note - if you're examining the phase where the magnitude is near zero - then the phase calculation isn't very meaningful. – David Jan 28 at 12:38