define gain and phase responsesexpressing hej in

Question

Define Gain and Phase Responses?

Expressing H(e^j?) in polar form as:  

H (e^j?) = G (?) e ^jφ(?)

G(?) is the "gain" of the discrete-time system and  φ(?) is the "phase". Both these quantities vary with ?.   

It may be shown that if the input to the system is a sinusoidal sequence {A cos (?n)}, the output will be: {G(?)A cos(?n + φ(?))}