Chapter 7 Sampling
1 Chapter 7 Sampling
Chapter 7 Sampling Continuous sampling Discrete Code Digital Signal Signal 1g Signal Continuous D/A Signal DSP x2() x() T 0 T 2T t x1(n)=x2(n7)=x(mr) x1()≠x2(t)≠x()
2 Chapter 7 Sampling Continuous Signal Discrete Signal sampling Code Digital Signal DSP Continuous D/A Signal -T 0 T 2T t x (t) 1 x (t) 2 x (t) 3 ( ) ( ) ( ) 1 2 3 x nT x nT x nT = = ( ) ( ) ( ) 1 2 3 x t x t x t
Chapter 7 Sampling 57.1 The Sampling Theorem 57. 1.1 Impulse-Train Sampling () p()=∑(-n7) x(7)x(2T n=-00 3T-2T-T0T 2T 3T 4T
3 Chapter 7 Sampling §7.1 The Sampling Theorem §7.1.1 Impulse-Train Sampling -3T -2T -T 0 T 2T 3T 4T t x(t) x(0) x(T) x(2T) x(t) x (t) p p(t) (t nT ) n = − + =−
Chapter 7 Sampling Sampling Theorem: Let x() be a band-limited signal with X(o)=0, o>OM then x(t) is uniquely determined by its samples x(nT)n=0,+1 if 2兀 0s>2OM where p()=∑6(-m7) HGo) P Hojo OM<oc<os=om 4
4 Chapter 7 Sampling Sampling Theorem: Let be a band-limited signal with then is uniquely determined by its samples if where ( ) M x(t) X j = 0 , x(t) x(nT),n = 0,1, s 2 M T s 2 = x (t) p x(t) x(t) p(t) (t nT ) n = − + =− H(j) M c s − M 0 T −c H(j) c
Chapter 7 Sampling he reconstruction of the signal nT HlO n=-00 P x Hojo 0 O<0.<0.-0 M x(()=>x(nT)sa on(t-nT) 5
5 Chapter 7 Sampling The reconstruction of the signal x (t) p x t r ( ) x(t) p(t) (t nT ) n = − + =− H(j) M c s − M 0 T −c H(j) c ( ) ( ) a H ( ) n x t x nT S t nT + =− = −