國(guó)立臺(tái)灣大學(xué)機(jī)器人實(shí)驗(yàn)室

MATLABSignalProcessingToolbox報(bào)告日期:2009/3/11指導(dǎo)老師:黃漢邦教授報(bào)告者:黃子豪

OutlineTimeresponse,ConvolutionFourier,Laplace,Z-transformDTFTandFFTIIRandFIRfiltersSignalProcessingToolboxExampleFDAtoolExample波形產(chǎn)生Wihtenoise---randn(t)Squarefunction---square(t)Sinc函數(shù)---sinc(t)鋸齒波---sawtooth(t)步階響應(yīng)與脈衝響應(yīng)差分方程式y(tǒng)(n)+1.2y(n-1)+0.25y(n-2)=x(n),求出在n=0時(shí)的步階響應(yīng)與脈衝響應(yīng)filter指令格式輸出信號(hào)(yn)=filter(輸入信號(hào)係數(shù)bm，輸出信號(hào)係數(shù)ak,輸入信號(hào)xn)

步階響應(yīng)與脈衝響應(yīng)clear;closeall;t=-5:120;n0=0;%impulsestartingpointa=[11.20.25];%y(n)coefficientb=[1];%x(n)coefficient%stepsignalx_step=(t>=n0);%impulsesignalx_imp=(t==n0);%checkresponsestp_rep=filter(b,a,x_step);imp_rep=filter(b,a,x_imp);%plotfiguresubplot(211)stem(t,x_step);xlabel('timesequence(n)');ylabel('inputsignalx');title('Stepinputsignal')subplot(212)步階響應(yīng)與脈衝響應(yīng)stem(t,stp_rep);line(t,zeros(1,length(t)));xlabel('timesequence(n)');ylabel('outputsignaly(n)');title('Stepresponse')figuresubplot(211)stem(t,x_imp);xlabel('timesequence');ylabel('inputsignalx');title('Impulseinputsignal')subplot(212)stem(t,imp_rep);line(t,zeros(1,length(t)));xlabel('timesequence(n)');ylabel('outputsignaly(n)');title('Impulseresponse')線(xiàn)性摺積運(yùn)算輸出性號(hào)y(n)可由將輸入訊號(hào)x(n)與系統(tǒng)脈衝響應(yīng)T(n)作線(xiàn)性摺積而求得

函式:c=conv(a,b)c的向量長(zhǎng)度為length(a)+length(b)-1範(fàn)例:c=conv([111],[111])c=12321線(xiàn)性摺積運(yùn)算差分方程式y(tǒng)(n)+1.2y(n-1)+0.25y(n-2)=x(n),x(n)=0.5u(n),求出系統(tǒng)的響應(yīng)%CHECKlinearconvolutionANDfullresponseclear;closeall;t=-5:20;n0=0;%impulsestartingpointa=[11.20.25];%y(n)coefficientb=[1];%x(n)coefficient%stepsignalx_step=(t>=n0);x_in=(0.5.^t).*x_step;%(0.5)^n*u(n)%impulsesignalx_imp=(t==n0);%impulseresponsestp_rep1=filter(b,a,x_imp);%convolutionstp_rep2=conv(x_in,stp_rep1);%輸入信號(hào)與脈衝響應(yīng)的摺積%checkresponse

stp_rep3=filter(b,a,x_in);%使用filter指令求出系統(tǒng)響應(yīng)與stp_rep2的結(jié)果比較%plotfiguresubplot(211)stem(t,x_in);xlabel('timesequence(n)');ylabel('inputsignalx');title('Inputsignal')subplot(212)stem(t,stp_rep1);line(t,zeros(1,length(t)));xlabel('timesequence(n)');ylabel('impulseresponsey(n)');title('Impulseresponse')線(xiàn)性摺積運(yùn)算

線(xiàn)性摺積運(yùn)算figuresubplot(211)stem(t,stp_rep2(6:length(t)+5));line(t,zeros(1,length(t)));xlabel('timesequence(n)');ylabel('outputsignaly(n)');title('Convolution')subplot(212)stem(t,stp_rep3);line(t,zeros(1,length(t)));xlabel('timesequence(n)');ylabel('outputsignaly(n)');title('fullresponse')FouriertransformVariablex(預(yù)設(shè)設(shè)輸入入變數(shù)數(shù)符號(hào)號(hào)),w(預(yù)設(shè)設(shè)輸出出變數(shù)數(shù)符號(hào)號(hào))symstwInverseFourierTransformVariablew(預(yù)設(shè)設(shè)輸入入變數(shù)數(shù)符號(hào)號(hào)),x(預(yù)設(shè)設(shè)輸出出變數(shù)數(shù)符號(hào)號(hào))離散傅傅立葉葉轉(zhuǎn)換換%sinsignalclear;closeall;w1=0.5*pi;%analoguesignalfrequencyto=1/w1;%analoguesignalperiodts=0.5*0.5*to;%samplingperiodtd=0:ts:4;%timesequencex_sin=sin(w1.*td);%fouriertransformw=0:pi/50:2*pi;fori=1:length(w)fork=1:length(x_sin);x_ff(k)=x_sin(k)*exp(-j*w(i)*k);%傅立立葉轉(zhuǎn)轉(zhuǎn)換公公式endx_f(i)=sum(x_ff(:));end離散傅傅立葉葉轉(zhuǎn)換換%plotsinfiguresubplot(211)stem(td,x_sin);%plotthex-axisline(td,zeros(1,length(td)));xlabel('timesequencen');ylabel('Samplingsin(nt)');title('SamplingsignalofSin')subplot(212)plot(w/pi,abs(x_f));xlabel('piunit');ylabel('Magnitude');line(w/pi,zeros(1,length(w/pi)));title('Fouriertransformofsin')離散傅傅立葉葉轉(zhuǎn)換換—使使用fft指令令FFT是一一種計(jì)計(jì)算DFT的方方法，，可降降低計(jì)計(jì)算時(shí)時(shí)間範(fàn)例:clear%時(shí)間間向量量與訊訊號(hào)產(chǎn)產(chǎn)生t=(0:1/100:10-1/100);%Timevectorx=sin(2*pi*15*t)+sin(2*pi*40*t);%Signal%FFT轉(zhuǎn)轉(zhuǎn)換y=fft(x);%ComputeFFTofxm=abs(y);%Magnitudep=unwrap(angle(y));%Phase(使使相位連續(xù)續(xù))f=(0:length(y)-1)*99/length(y);%Frequencyvector離散傅立葉葉轉(zhuǎn)換%畫(huà)出振幅幅圖plot(f,m);title('Magnitude');%畫(huà)出相位位圖set(gca,'XTick',[15406085]);figure;f=(0:length(y)-1)*99/length(y);plot(f,p*180/pi);title('Phase');set(gca,'XTick',[15406085]);逆離散傅立立葉轉(zhuǎn)換---使用用ifft指令%時(shí)間向量量與訊號(hào)t=(0:1/255:1);x=sin(2*pi*120*t);figure;plot(t,x);title('xsignal');%比較原始始訊號(hào)x與與重建訊號(hào)號(hào)yy=real(ifft(fft(x)));figure;plot(t,y);title('ysignal');LaplaceTransformVariablet(預(yù)設(shè)輸輸入變數(shù)符符號(hào)),s(預(yù)設(shè)輸輸出變數(shù)符符號(hào))InverseLaplaceTransformVariables(預(yù)設(shè)設(shè)輸入變數(shù)數(shù)符號(hào)),t(預(yù)設(shè)輸出出變數(shù)符號(hào)號(hào))ZTransformVariablen(預(yù)設(shè)設(shè)輸入變數(shù)數(shù)符號(hào)),z(預(yù)設(shè)輸出出變數(shù)符號(hào)號(hào))範(fàn)例:>>Symszn>>f=n^4;>>ztrans(f)ans=z*(z^3+11*z^2+11*z+1)/(z-1)^5InverseZtransformVariablez(預(yù)設(shè)設(shè)輸入變數(shù)數(shù)符號(hào)),n(預(yù)設(shè)輸出出變數(shù)符號(hào)號(hào))範(fàn)例:>>symszn>>f=2*z/(z-2)^2;>>iztrans(f)ans=2^n*n零點(diǎn)-極點(diǎn)點(diǎn)分析%求解根b=[234];a=[1331];zer=roots(b)pol=roots(a)k=b(1)/a(1)%化回多項(xiàng)式式bb=k*poly(zer)aa=poly(pol)zplane(zer,pol)SignalProcessingToolboxExample1--設(shè)計(jì)一一帶通濾波器器在commandwindow下執(zhí)行>>playshowfiltdem1.三個(gè)頻率5,15,30Hz的sine波波SignalProcessingToolboxExample12.設(shè)計(jì)一10~20Hz帶帶通之IIR帶通濾波器器SignalProcessingToolboxExample13.5與30Hzsin波波被濾掉，剩下下15HzSignalProcessingToolboxExample14.比較濾波前後後的頻率響應(yīng)SignalProcessingToolboxExample2---比較較濾波器差異異在commandwindow下執(zhí)行>>playshowfiltdem21.畫(huà)出理想的濾濾波器頻率響應(yīng)SignalProcessingToolboxExample22.設(shè)計(jì)一YULEWALK八階的IIRfilterSignalProcessingToolboxExample23.設(shè)計(jì)一ButterworthandChebyshevIIRfilterSignalProcessingToolboxExample24.頻率率響應(yīng)圖FDATool(FilterDesignandAnalysisTool)MATLAB命令令視窗鍵入入fdatool指指令>>fdatool1.選擇濾濾波器2.選擇濾濾波器設(shè)計(jì)方法3.指定濾濾波器階數(shù)數(shù)4.輸入濾濾波器頻率率規(guī)格5.輸入訊訊號(hào)衰減程程度與漣波規(guī)格格設(shè)計(jì)一最少少階次帶通通等漣波FIR濾波波器取樣頻率(Fs)=2000Hz第一個(gè)阻帶帶結(jié)束頻率率(Fstop1)=200Hz通帶開(kāi)始的的頻率(Fpass1)=300Hz通帶結(jié)束的的頻率(Fpass2)=700Hz第二各阻帶帶開(kāi)始的頻頻率(Fstop2)=800Hz第一各阻帶帶衰減大小小(Astop1)=75dB通帶漣波大大小(Apass)=0.1dB第二阻帶衰衰減大小(Astop2)=75dB帶通濾波，，等漣波FIR帶通等漣波FIR濾波器器輸入帶通之之頻率範(fàn)圍圍輸入振幅衰衰減的程度度與漣波的的振幅勾選Minimumorder按下DesignFilter分析濾波器器選擇上圖之之分析工具具列振幅圖相位圖將濾波器係係數(shù)輸出到到workspaceFile->Export將濾波器係係數(shù)輸出成成C標(biāo)頭檔檔TargetsGenerateCHeaderconstintBL=64;constint32_TB[64]={80690,-1072542,-2939985,5461255,6950698,-5912941,-1602054,-5104533,-11144430,12287884,6241733,6077793,18813071,-23835745,-15696747,-5156699,-29284886,42299228,32893668,454314,43788106,-72822941,-65058054,12465656,-67152964,133647322,139847119,-51918454,129068678,-362675861,-580944589,712218408,712218408,-580944589,-362675861,129068678,-51918454,139847119,133647322,-67152964,12465656,-65058054,-72822941,43788106,454314,32893668,42299228,-29284886,-5156699,-15696747,-23835745,18813071,6077793,6241733,12287884,-11144430,-5104533,-1602054,-5912941,6950698,5461255,-2939985,-1072542,80690};形成M-filefunctionHd=firbandstop%firbandstopReturnsadiscrete-timefilterobjectFs=2000;%SamplingFrequencyFstop1=200;%FirstStopbandFrequencyFpass1=300;%FirstPassbandFrequencyFpass2=700;%SecondPassbandFrequencyFstop2=800;%SecondStopbandFrequencyDstop1=0.000177827941;%FirstStopbandAttenuationDpass=0.0057563991496;%Passban