数字信号处理08A_答卷.doc

浙江科技学院考试试卷

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浙江科技学院考试试卷

专业班级学号姓名

………………………………………………………………………装订线……………………………………………………………………………………
浙江科技学院
2012-2013学年第一学期考试试卷A卷
考试科目数字信号处理考试方式闭完成时限2小时
拟题人审核人批准人2012年12月18日
信息与电子工程学院2010年级电子信息工程（互联网方向）专业

SolutionsforReferenceandItsScoreCriteria
PartoneFundamentals(Total8QuestionsinThisPart,EachQuestionIsMarkedoutof8)

Question1(8Marks)
Discrete-timesystemdifferentialequationisgivenby

wherex(n)andy(n)arethesystem’sinputandoutputrespectively,determinethelinearityofthesystem.

SolutionforReference
Supposethesystemprovidestwooutputsy1(n)andy2(n)giventheinputsofx1(n)andx2(n)respectively,thenwehave

Thus,itisnonlinearsystem（3Marks+3Marks+2Marks）

Question2(8Marks)
Determinetheinversez-transformsofthefollowingz-transforms.
(a),ROC（5Marks）
(b)（3Marks）.
SolutionforReference：
(a)Apartial-fractionexpansionofX(z)isthenoftheform
(2Marks)
TheROCofX(z)includes，thereforeisacausalsequence.
Theinversez-transformoftheaboveisgivenby(1Marks)
（2Marks）
（b）
Thez-transformofadiscretesequencex(n),expressedasX(z),isdefinedas
Thustheinversez-transformofX(z)canbegivenby
（1Mark+2Marks）

Question3(8Marks)
ConsidertheconnectionofthreeLTIsystemsasfollows:
Let,and,thendetermineunitsampleresponseofthewholesystem.

SolutionforReference：
Theunitsampleresponseofthewholesystemisoftheform

（3Marks）
(2Marks)
(3Marks)

Question4(8Marks)
Letthecontinuous-timesignalis
DeterminetheNyquistfrequencyof(4Marks).
IfissampledatthedoublerateoftheNyquistfrequency,whatisthesamplingperiodTsofsinewaveinthesampledsequence.?Whatisthesampledsignal?(4Marks)

SolutionforReference：
(a)Thefrequencyofsignalis325Hz(1Mark)
Thefrequencyofsignalis360Hz(1Mark)
Thus,thehighestfrequencyofis360Hz(1Mark)
AndtheNyquistfrequencyofis360Hz(1Mark)

(b)Thesamplingfrequencyfs=360Hz*2=720Hz,andthesamplingperiodTs=1/720s(2Marks)
Thesampledsignalcanbegivenby

(2Marks)

Question5(8Marks)
Letx(n)bealength-3sequencedefinedby

(a)DeterminetheDTFTofx(n)(4Marks).
(b)DeterminetheN-pointDFTofx(n)(4Marks).
SolutionforReference：
(a)TheD