上海交通大学dsp实验指导书

ax)(t)=ax(t)M(t)ax(t)M(t)M(t)=∑∞−∞=nδ(t-nT)aX)jΩ)]([1SnamjXTΩ−Ω∑+∞−∞=TS/2π=Ωax(t)SΩax(t))(ωjeX∑+∞−∞=−nnjenxω)(1)(kjeXω∑−=−10)(Nnnjkenxω=kωπ2k/Mk=0,1,,M-1)(kjeXωy(n)h(n)x(n)y(n)=x(n)*h(n)=∑+∞−∞=−mmnhmx)()(h(n)x(n)y(n)L=N+M-1y(n)=x(n)*h(n))(ωjeY)(ωjeX•)(ωjeH)(nxaAnTeα−sin(0ΩnT)0n50α0Ω)(nxb)(nδ{01nn≠=00)(nxc)(nRN{01nNn10−≤≤)(nha)(10nR)(nhb)(nδ)1(−nδ)2(−nδ)3(−nδ2x(n)x(n)0)(nxaα2π0Ω2π)(txa)(ωjeX)(ΩjXa“”πω≤≤02/0Sff≤≤1.2.3.TT?x(n)h(n)y(n)=x(n)*h(n)?3)(ΩjXa)(txa)(nxb)(nhb)(nhb)(nxc)(nhay(n))(nxc)(nxaα0Ωα0Ω0Ωα0Ωh(n)x(n)h(n))(ωjeY)(ωjeX)(ωjeH|)(ωjeY4)(nxaα0Ω)(nhb)(kjeYω)(kjeYωaX)(kjeωbH)(kjeωdigitalsignalprocessingconvolutionidealsamplingverificationunitimpulserectangularspectralamplitudeFFTFFTFFTFFT5)(kXDFT[x(n)]∑−=10)(NnknNWnx10−≤≤Nkx(n)=IDFT[)(kX]∑−=−10)(NknkNWkX10−≤≤NnDFTFFTDFTDFTFFTL2DFTN)(nRNx(n)x(t)x(n)DFTDFTSfFFN=Sf/FFFTN=L2ptNTN/Sf1/FptFFT6FFTFFT)(nxa⎩⎨⎧−−0/)(2qpne150≤≤npq)(nxb⎩⎨⎧−02sinfnenπα150≤≤nαf)(nxc⎪⎩⎪⎨⎧−+081nn7430≤≤≤≤nn)(nxd⎪⎩⎪⎨⎧−−034nn7430≤≤≤≤nnFFT(A,N,IC)FFTAA(2i)A(2i+1)i=1,2,,NNICIC=0IC=1PL(X,N)XNp=8q=2,4,8qq=8p=8,13,14p)(nxbα=0.1,f=0.0625ff=0.43750.5625FFT)(nxc)(nxd7)(nxd)(nxc)(nxc)(nxdN=16FFTGaussserialTrig-waveserialDecayingsineserialInvertedTrig-waveserialIIRIIRButterworthChebyshevIIRNx(n)x(n)FFTX(k)=DFT[x(n)]8IIR)(sHaH(z)ButterworthChebyshevButterworthChebyshevNlg1101101.01.0−−SPαα)(SPΩΩN1−ch1101101.01.0−−PSαα1−ch)(PSΩΩ)(sHa∏=−ΩNkkNCss1)(πNk212−CksΩ=sin+jcos)(sHaε12−ΩNNP)]cossin([1kkNkkkPyjchxyshxs+Ω−∏=ε111−−=shNxkπNkyk212−==ΩCNSS2/11.0)110/(−Ωα=ΩCNPP2/11.0)110/(−Ωα1101.0−=Pαε1111−−+−=zzsssz−+=11sztg2arctgsωjeIIR9PfSfPαSαπω2=PPfπω2=SSf)2(PPtgω=Ω)2(SStgω=ΩCΩ)(sHa1111−−+−=zzs)(sHa1111−−+−=zzs)2(ωtg=Ω1111−−−+=zzs|)2(|ωctg=Ω11cos2202−+−=zzzsω|sincoscos|0ωωω−=ΩfTπω2=fT21210sinsin)sin(cosωωωωω++=1ω2ωIIRButterworth/ChebyshevTPfSfPαSα)(sHa)(sHa∑=Niiisb0)(sHaibi]/[][00∑∑==MiiiMiiizbzaiaibi10ChebyshevPfPαSfSαH(z)PfPαSfSαButterworthChebyshevButterworth1Pf2PfSfSαT=10sH(z)H(z)PfSfSαTNSΩ,N)(sHaH(z)H(z)IIR()11digitalfilterlow-passbilineartransformationhigh-passband-passorderprototypefrequencyresponseFIRFIRFIRh(n)FIR)(kHNkjezzH/2|)(π=∑−=−10)2()(NnknNjenhπk=0,1,,N1)(ωjdeHH(k))(kH)(/2NkjdeHπk=0,1,,N1FIRH(z)NzN−−1∑−=−−−1011)(NkkNzWkH)(ωjeH=∑−=−10)/2()(NkNkkHπωφ(4-4))(ωφ=)2/sin()2/sin(ωωNN2/)1(−−Njeω12)(ωjeH=2/)1(−−Njeω{)2/sin()2/sin()0(ωωNNHd++∑=MkdNkH1)([]2/)/2sin[(]2/)/2(sin[NkNkNπωπω−−+]2/)/2sin[(]2/)/2(sin[NkNkNπωπω++]}(4-5))(kHddHdHM={2/)1(2/−NNNNFIRh(n)H(k)h(n)N1∑−=10)(NknkNWkHn=0,1,,N1k=0M)(kHdh(n)h(n)=N1{)0(dH)]21(2cos[)(1−−∑=NnkNkHMkdπ})0(dHh(n)=N2∑=−−MkdNnkNkH1)]21(2sin[)(πFIRN13)(kHdk0ε0Sα1001FIRN=30h(n)N1ω2ωh(n)h(n)FIRIDFTh(n)h(n)samplingpassbandlinearphasestopbandimpulseresponserippleattenuationinterimpoint14N0ε0Sα1n2n)(kHd,k=0,1,,Mh(n),n=0,1,,N1h(n)