2.Sequenee"网=⑵彳一2-2』,1二+』3,3+2』},,耐the南京理工大学课程考试
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(学生考试用)课程教学大纲编号:04027704学分:3.5试卷编号:—001—满分分值:100分课程名称:数字信号处理(英)考试方式:闭卷笔试考试时间:120分钟组卷年月:.组卷教师:审定教师:—Notice!3.Someusefulequations:如竺沁[切二迟沿咒M-UAlltheanswersshouldbewrittenintheanswersheet!Thefollowingmaybeusedforyouranswers:Propertiesofcommonwindowfunctions:RectangularBartlettHanning1Hamming1BlackmanWidthofmainlobe4p/(M+1)8p/M8p/M8p/M12p/MPeakapproximationerror(dB)-21-25-44-53-74II对-1恥]<叱皿]=乔可咖呼;0<«<27-1I+ro忑⑵"[曲]]=E非]厂4.Someusefulsigns:----modularoperation;——N-pointcircularconvolution*convolutionsumBasicconcepts:(40')1.8.Considerthefollowingsystems(a)to(d),wherey[n]aretheoutputsequences,x[n]aretheinputsequences.Thelinearsystemsinclude;theshift-invariantsystemsinclude;thecausalsystemsinclude;thestablesinclude.⑻畑=2核[«];(b严]=2班-川+2];J网一召恥[(d严]=恥-2]Foreachofthefollowingsystems,wherey[n]aretheoutputsequenee,x[n]aretheinputsequenee.Thelinearsystemsare;theshift-invariantsystemsare;thecausalsystemsare;thestablesare.⑻M=2椅[«];(b严]=2班-总+2];『网一召班(d严]=恥-2];andtheconjugateeonjugatesymmetricsequenee心卜antisymmetriesequenee-Asignalhasaeontinuousandperiodfrequencyspeetrum.Let疋国](0乞总乞1)[幻(0thenx[<«+3>^](0<2^-1)^^x[<-«>^](0JJT>_.8j丽”坯闵3<^
N],0£n£N-1.DeterminetheN-pointDFTY[k],0£k£N-1;(2)Letsequenee日期一("兀闵,determinetheN-pointDFTZ[k],0£k£N-1;{x[w];nisevenQ刑isoddiw>-6,0£n£N-1,determinetheN-pointDFTW[k],0£k£N-1;Analysisanddesign:(40')(8)AeausalIIRLTIdiserete-timesystemiseharaeterizedbytheinput-outputrelation:尹[旳]=恥]-0尼1兄"-2]DeterminethesystemfunetionH(z);Sketehthemagnituderesponse|H(ejw)|andphaseresponsej(w).(9')AeausalLTIdiserete-timesystemiseharaeterizedbysystemfunetion:jV(z)=(2+z_1)(1+2z_1)(1-+尹)Determinetheimpulseresponseh[n]ofthissystem;Provethatthesystemhasalinearphaseresponse;Plotthelinearphasestruetureflowgraphtorealizethissystem.◎=—TV(10')(1)Aeausalanalogsystemfunetionis,Designaeorrespondingdigitalfilterbybilineartransformmethod(assumeT=2),determinethedigitalsystemfunetionH(z);(2)DesignahighpassFIRfilterwiththesmallestlengthusingthewindow-basedapproaehandmeetingthespeeifieations:®=0.35jt,些=0.55jt,=0.01;(5^=0.05Seleetasuitablewindowfunetionw[n],determinethefilterlengthNandimpulseresponseh[n].(13')UseDIT-FFTalgorithmtoeomputetheN-pointDFTX[k],0£k£N-1,ofalength-Nsequeneex[n],0£n£N-1,