Define gain and phase responses, Electrical Engineering

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Define Gain and Phase Responses?

Expressing H(ej?) in polar form as:  

H (ej?) = 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(?))}


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