Alright, after seeing it for a few time in my courses, I am still confused on how to actually calculate this function. I know that the arg function describes the phase of a signal, and that's all fine and dandy, but I would like some sort of mathematical equation to calculate it. I know it has something to do with an arctan. For example, in my DSP book, these transfer functions are given: H1(z) = (z+b)/(z+a) 0<|a|<1 H2(z) = (bz+1)/(z+a) 0<|b|<1 It then goes on to calculate the arg without showing any steps: arg[H1(e^jw)] = arctan(sin w/(b+cos w)) - arctan(sin w/(a+cos w)) and arg[H2(e^jw)] = arctan(b*sin w/(1+b*cos w)) - arctan(sin w/(a+cos w)) Could anyone explain to me how this is calculated? Thanks.