连续时间信号样本表示采样定理英才chapter7 sampling.pdf

7Sampling

7.Sampling

1.RepresentationofaContinuous-timeSignalby

itsSamples:TheSamplingTheorem

1.Impulse-trainSampling

p(t)

(1)Sampling

xp(t)x(t)p(t)x(t)

x(t)p

1

Xp(j)[X(j)*P(j)]



2

wherep(t)T(t)(tnT)

n=

7Sampling

Time:

(7.2)

7Sampling

F

Frequency:x(t)⎯→X(j)

2

FT

p(t)⎯→P(j)

(k)

ss

k=

Fs

x(t)⎯→X(j)X(k)

pp2k=s

1

X(k)

Tk=s

7Sampling

Aliasing

7Sampling

(2)Samplingtheorem

Letx(t)beaband-limitedsignalwith

X(j)=0for||M.Thenx(t)isuniquely

determinedbyitssamples

x(nT),n=0,1,2,…,if

2,where=2/T.

sMs

2MiscalledNyquistRate.(Minimum

distortionlesssampl