I would appreciate it very much if someone would be able to provide some clarity on plotting phase responses.
For instance, given that the frequency response of a filter can be written as H(exp(j*Ω))=cos(Ω), how would I go about determining the phase response?
The answer key demonstrates a piecewise solution:
This is what I understand so far:
-cos(omega) is strictly real, so the phase carries values of 0, or +/- pi
-between the values of -pi/2 and pi/2, cos(ω) is positive, so the phase is 0
-I understand since the function cos(ω) is strictly real, phases where the function is not positive should either be pi/-pi (as opposed to -pi/2/pi/2, for when it's imaginary), but how do you know for which range it's pi, and for which range it's -pi?
This might be a stupid question, but I've spent a lot of time thinking it through, so I'm thinking I'm missing something, and would appreciate any clarity.
Thank you so much!