I have plotted the magnitude and the phase responses of an M-point moving average filter, the following are the plots when M = 10:
We can observe that corresponding to every lobe in the magnitude spectrum we have a line in the phase spectrum - a linear phase response is observed corresponding to every lobe. (See the below picture)
I tried to observe the magnitude and phase responses for different values of M and observed a similar pattern.
Is there any reason behind this pattern? Is there any significance for this?