I have a bandpass signal, I do IQ demodulation meaning:
$IQ(t) = x(t)*exp(-2\pi f_ct)$
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?