7 Sampling 7. Sampling 7.1 Representation of a Continuous-time Signal by its Samples: The Sampling Theorem 7. 1.1 Impulse-train Sampling (1) Sampling p(t) ()=x(t)p() 3[X(j)*P(m) x() where ∑ d(t-nT) n=-07 Sampling 7.1 Representation of a Continuous-time Signal by its Samples: The Sampling Theorem 7. Sampling      = = [ ( )* ( )] 2 1 ( ) ( ) ( ) ( )    X j X j P j x t x t p t p p 7.1.1 Impulse-train Sampling x(t) p(t) xp (t)  + =− = = − n T where p(t)  (t)  (t nT) (1) Sampling