The Sampling Theorem X() Band-limited signal X(=0, forall f, I f2w Bandwidth W Sampling Theorem: If we sample the signal at intervals Ts where Ts < 1/2W then signal can be completely reconstructed from its samples using the formula x0)=∑27xm)id27-m月 n=-∞ Where, wswok I W Witht (=>x(n7 )sin c(-n)I x(0)=>x()sinc[2W(t-a)The Sampling Theorem X f () • Band-limited signal X f () = 0, for all f ,| f | ≥ W – Bandwidth < W -w w Sampling Theorem: If we sample the signal at intervals Ts where Ts <= 1/ 2W then signal can be completely reconstructed from its samples using the formula ∞ x t() = ∑ 2 W© Ts x(n Ts)sin c[2 W© (t − n Ts)] n=−∞ Where, W ≤ W©≤ 1 − W Ts ∞ 1 t With T = => x t s () = ∑ x(n Ts)sin c[( − n)] 2 W T n=−∞ s ∞ n n () = ∑ x t x( )sin c W[2 (t − )] 2 W 2 W n=−∞ Eytan Modiano Slide 9