数字信号处理(英文版)课后习题答案4 .pdfVIP

(Partial)SolutionstoAssignment4

pp.81-82

DiscreteFourierSeries(DFS)

DiscreteFourierTransform(DFT)

,k=0,1,...N-1

,n=0,1,...N-1

DiscreteTimeFourierTransform(DTFT)

isperiodicwithperiod=2π

FourierSeries(FS)

FourierTransform(FT)

2.1ConsiderasinusoidalsignalQ2.1Considerasinusoidalsignal

F

thatissampledatafrequency=2kHz

s

a).Determineanexpressoinforthesampledsequence,anddetermineits

discretetimeFouriertransform

b)Determine



c)Re-computeX()fromX(F)andverifythatyouobtainthesameexpression

asin(a)

a).ans:

=

whereand

Usingtheformular:

b)ans:

where

c).ans:

Letbethesamplefunction.

TheFouriertransformofis

Usingtherelationshipor

where

Consideronlytheregionwhere(or

therefore

where

END

2.3Foreachshown,determinewhere

isthesampledsequence.Thesamplingfrequenceisgivenforeach

case.

(b)Hz

(d)Hz

theory:therelationshipbetweenDTFTandFTis

where

or

b.ans:

d.ans:

omitted(usingthesamemethodasabove)

2.4Inthesystemshown,letthesequencebeandthe

samplingfrequencybekHz.Alsoletthelowpassfilterbeideal,withbandwidth

(a).Determineanexpressionfor