Chapter7

SamplingThe

effect

of

samplingThe

sampling

theoremPractical

use

of

samplingSamplingVery

important

step

for

digitalsignal

processing

!Widely

used

in

signal

recording,storage,

compression,

transmissi……SamplingUse

finite

points

to

express

a

continuous

cuTry

to

record

acurve

in

discrete

data

!SamplingCan

we

keep

the

information

insampling

process?Can

we

recover

the

continuouscurve

from

these

sampling

pointsTry

to

find

answer

in

frequencydomain

!Impulse-train

samplingSampling

periodSampling

frequencyImpulse-train

sampling

effectIn

time

domain,

signal

is

discrete

;In

frequency

domain,

signal

is

replicatedImpulse-train

sampling

effectOriginal

spectrum

and

its

mirrorsAnti-mirror

filterThe

sampling

theoremmust

be

a

band-limited

signalSampling

frequency

should

satisfy

theNyquist

conditionThe

Nyquist

ratecanbe

recovered

by

an

LPFThe

frequency

limit

for

signal

samplingFrequency

period

areaOver

samplingThe

recover

filter

can

be

made

easily

!Sampling

data

may

be

too

much

!Critical

samplingThe

recover

filter

must

be

ideal

LPF

!Sampling

data

is

less

!Under

samplingThe

spectrum

is

overlapped

with

mirrorThe

signal

can

not

be

recovered

fromsampling

data

!Practical

use

of

samplingSet

ananti-aliasing

filter

beforesampling

systemAn

analog

LPF

to

make

the

signal

band-limitSampling

with

a

zero-order

holdPractical

use

of

samplingSampling

with

a

zero-order

holdIf

sampling

condition

is

satisfied

,

the

sasignal

can

be

recovered

!(See

P.521)Practical

use

of

samplingSampling

for

narrow

band

signalsThe

sampling

condition:The

high

frequency

narrow

band

signal

can

bchanged

to

low