The frequency response of an ideal filter is given by :
Where K and 
are constants (not functions of 
).
Question : Why should the phaseshift 
with constant ?
Answer : So that different frequencies in the passband have the same time delay
so the shape of a signal is unmodified by the filter (in the passband).
Discussion
If there are N samples per period, a phase shift 
through the system produces a time delay :
So if 
then 
independent of .