數(shù)字信號(hào)實(shí)驗(yàn)報(bào)告 IIR數(shù)字濾波器設(shè)計(jì)

實(shí)驗(yàn)報(bào)告課程名稱______數(shù)字信號(hào)處理___________實(shí)驗(yàn)項(xiàng)目______IIR數(shù)字濾波器設(shè)計(jì)_____實(shí)驗(yàn)二IIR數(shù)字濾波器設(shè)計(jì)一、實(shí)驗(yàn)?zāi)康?、熟悉用雙線性變換法設(shè)計(jì)IIR數(shù)字濾波器的原理與方法。2、掌握數(shù)字濾波器的計(jì)算機(jī)軟件實(shí)現(xiàn)方法。3、通過觀察對(duì)實(shí)際心電圖信號(hào)的濾波作用，學(xué)習(xí)數(shù)字濾波器在實(shí)際中的應(yīng)用。二、實(shí)驗(yàn)儀器及材料計(jì)算機(jī)，MATLAB軟件三、實(shí)驗(yàn)內(nèi)容及要求1．設(shè)計(jì)巴特沃斯低通數(shù)字濾波器對(duì)人體心電信號(hào)進(jìn)行濾波(1)人體心電圖信號(hào)在測(cè)量過程中會(huì)受到工業(yè)高頻干擾，所以必須經(jīng)過低通濾波處理，才能作為判斷心臟功能的有用信息。以下為一個(gè)實(shí)際心電圖信號(hào)采樣序列x(n)，其中存在高頻干擾，采樣周期T=1秒。在實(shí)驗(yàn)中，以x(n)作為輸入序列，濾除其中干擾成分。x(n)=[-4,-2,0,-4,-6,-4,-2,-4,-6,-6,-4,-4,-6,-6,-2,6,12,8,0,-16,-38,-60,-84,-90,-66,-32,-4,-2,-4,8,12,12,10,6,6,6,4,0,0,0,0,0,-2,-4,0,0,0,-2,-2,0,0,-2,-2,-2,-2,0]對(duì)序列x(n)用FFT做頻譜分析，生成x(n)的頻譜圖。(2)用沖激響應(yīng)不變法設(shè)計(jì)一個(gè)巴特沃斯低通IIR數(shù)字濾波器H(z)。設(shè)計(jì)指標(biāo)參數(shù)為：在通帶內(nèi)頻率低于0.2π時(shí)，最大衰減小于1dB；在阻帶內(nèi)[0.3π,π]頻率區(qū)間上，最小衰減大于15dB。寫出數(shù)字濾波器H(z)的表達(dá)式，畫出濾波器的幅頻響應(yīng)曲線。(3)用所設(shè)計(jì)的濾波器對(duì)實(shí)際心電圖信號(hào)采樣序列進(jìn)行濾波處理，編寫程序,計(jì)算H(z)對(duì)心電圖信號(hào)采樣序列x(n)濾波后的序列y(n)，并分別畫出濾波前后的心電圖信號(hào)波形圖和頻譜圖。2．用help查看內(nèi)部函數(shù)cheb1ord.m及cheby1.m，了解調(diào)用格式，并用此函數(shù)設(shè)計(jì)一個(gè)數(shù)字切貝雪夫帶通濾波器。設(shè)計(jì)指標(biāo)參數(shù)為：抽樣頻率fs=2kHz；在200Hz≤f≤400Hz時(shí)，最大衰減小于2dB；在f≤100Hz，f≥600Hz，最小衰減大于40dB。編程設(shè)計(jì)，求數(shù)字濾波器H(z)的表達(dá)式，畫出濾波器的幅頻響應(yīng)曲線。四、思考題1．對(duì)比實(shí)驗(yàn)內(nèi)容1中濾波前后心電圖信號(hào)x(n),y(n),說明濾波器的作用。2．雙線性變換與沖激不變法比較有何優(yōu)缺點(diǎn)？五、實(shí)驗(yàn)報(bào)告要求1．列出本實(shí)驗(yàn)編寫的所有文件及各項(xiàng)實(shí)驗(yàn)結(jié)果曲線，加注必要的說明；2．對(duì)實(shí)驗(yàn)結(jié)果作理論計(jì)算，解釋實(shí)驗(yàn)結(jié)果；3．回答思考題；4．總結(jié)實(shí)驗(yàn)體會(huì)及實(shí)驗(yàn)中存在的問題。六、參考本實(shí)驗(yàn)所用的MATLAB函數(shù)：x=rand(r,c):用MATLAB隨機(jī)生成輸入信號(hào)x（n），范圍為0～1,r行,c列。y=conv(x1,x2):將序列x1(n)與序列x2(n)做線性卷積，結(jié)果賦給序列y(n)。y=fft(x,L):將序列x(n)做L點(diǎn)快速傅立葉變換，結(jié)果賦給序列y(n)。y=ifft(x,L):將序列x(n)做L點(diǎn)快速傅立葉反變換，結(jié)果賦給序列y(n)。stem(x,y):以x為橫坐標(biāo)，y為縱坐標(biāo)畫離散曲線。LENGTH(X)：returnsthelengthofvectorX.ItisequivalenttoMAX(SIZE(X))fornon-emptyarraysand0foremptyones.[N,Wn]=BUTTORD(Wp,Ws,Rp,Rs)returnstheorderNofthelowestorderdigitalButterworthfilterwhichhasapassbandrippleofnomorethanRpdBandastopbandattenuationofatleastRsdB.WpandWsarethepassbandandstopbandedgefrequencies,normalizedfrom0to1.BUTTERButterworthdigitalandanalogfilterdesign.[B,A]=BUTTER(N,Wn)designsanNthorderlowpassdigitalButterworthfilterandreturnsthefiltercoefficientsinlengthN+1vectorsB(numerator)andA(denominator).Thecoefficientsarelistedindescendingpowersofz.ThecutofffrequencyWnmustbe0.0<Wn<1.0,with1.0correspondingtohalfthesamplerate.IMPINVARImpulseinvariancemethodforanalogtodigitalfilterconversion.[BZ,AZ]=IMPINVAR(B,A,Fs)createsadigitalfilterwithnumeratoranddenominatorcoefficientsBZandAZrespectivelywhoseimpulseresponseisequaltotheimpulseresponseoftheanalogfilterwithcoefficientsBandAsampledatafrequencyofFsHertz.TheBandAcoefficientswillbescaledby1/Fs.FILTEROne-dimensionaldigitalfilter.Y=FILTER(B,A,X)filtersthedatainvectorXwiththefilterdescribedbyvectorsAandBtocreatethefiltereddataY.Thefilterisa"DirectFormIITransposed"implementationofthestandarddifferenceequation:a(1)*y(n)=b(1)*x(n)+b(2)*x(n-1)+...+b(nb+1)*x(n-nb)-a(2)*y(n-1)-...-a(na+1)*y(n-na)FREQZDigitalfilterfrequencyresponse.[H,W]=FREQZ(B,A,N)returnstheN-pointcomplexfrequencyresponsevectorHandtheN-pointfrequencyvectorWinradians/sampleofthefilter:jw-jw-jmwjwB(e)b(1)+b(2)e+....+b(m+1)eH(e)=----=------------------------------------jw-jw-jnwA(e)a(1)+a(2)e+....+a(n+1)egivennumeratoranddenominatorcoefficientsinvectorsBandA.ThefrequencyresponseisevaluatedatNpointsequallyspacedaroundtheupperhalfoftheunitcircle.IfNisn'tspecified,itdefaultsto512.BILINEARBilineartransformationwithoptionalfrequencyprewarping.[Zd,Pd,Kd]=BILINEAR(Z,P,K,Fs)convertsthes-domaintransferfunctionspecifiedbyZ,P,andKtoaz-transformdiscreteequivalentobtainedfromthebilineartransformation:H(z)=H(s)||s=2*Fs*(z-1)/(z+1)思考題：1．對(duì)比實(shí)驗(yàn)內(nèi)容1中濾波前后心電