Raised-Cosine Filter - calculating phase response I want to compute phase response of an raised-cosine FIR filter. I have trouble finding the complex transfer function of the filter in literature (there is a real valued transfer function of frequency).

I have found formula for magnitude for raised-cosine filter (paper “Raised Cosine Equalization Utilizing Log Scale Filter Synthesis”, D. McGrath, J. Baird, B. Jackson) but there is no mention of phase response. I have read the IEEE paper “Generalized Raised-Cosine Filters” by N. S. Alagha, P. Kabal, but did not find the clear way how to calculate the phase response. In the first mentioned paper the phase is not linear and it's said that it is minimum phase filter. Here is the plot from McGrath at al. paper, page 8:



What is the way to calculate phase response for an raised-cosine FIR filter? I don't want to use MATLAB, I need to implement the solution in C++.
Just like the sinc pulse, a raised cosine pulse with zero delay (centered around $t=0$) has a real Fourier transform. You can find its expression in section 11.4 of "Telecommunications Breakdown" by Johnson and Sethares (a free draft version is available here).

For a time-shifted pulse, you can apply the time-shift property of the Fourier Transform.