Asking for help: how to represent differential equation of DPSK signals correctly in MATLAB

Hi,

I am currently struggling with the problem of FFT of
non-return-to-zero DPSK signals (differential equation in time domain
is more easily solved by FFT in frequency domain). The main question
is I do not quite understand how to represent correctly the PHASE OF
THE CARRIER after FFT and IFFT.

I just thought to extract the phase right at the center (0th
frequency component) but it seems not convince myself.

I am looking forward to hearing from your valuable suggestions or
instructions. I really appreciate your time and your assistance.

Regards,
.

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