南京理工大学数字信号处理(英)考试试卷

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试卷（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,