7 Sampling
7.1 Representation of a Continuous-time Signal by
its Samples,The Sampling Theorem
7,Sampling

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(1) Sampling
7 Sampling
Time domain:



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7 Sampling














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Frequency domain:
7 Sampling
7 Sampling
(2) (Shannon) Sampling theorem
Let x(t) be a band-limited signal with X(j?)=0 for
|?|>?M,Then x(t) is uniquely determined by its
samples x(nT),n=0,?1,?2,…,if
s>2?M,where?s=2?/T,
2?M is called Nyquist Rate.
( Minimum distortionless sampling frequency )
7 Sampling
(3) Recovery
System for sampling and reconstruction:
7 Sampling
7 Sampling
7.1.2 Sampling with a Zero-order Hold
(1) Sampling system construction:
7 Sampling
7 Sampling
(2) Signal Recovery
7 Sampling
7.3 The Effect of Undersampling,Aliasing
s=6?0
s=3?0
7 Sampling
s=1.5?0
s=1.2?0
7 Sampling
Problems,7.1 7.2 7.3 7.6 7.9