matlab验证时域采样定理2

1、 1 12 23 54 MATLAB 55 85.1 85.2 85.3 96 12 131. 1 (DFT)DFT(FFT)FFTDFT60 MATLABMATLABMATLABMATLAB2. MATLAB MATLAB MATLABMATLABMATLAB,MATLABC,FORTRAN.C,FORTRAN,c+ ,JAVA.,MATLAB 2 (1) 12maxFmax2FFsmax2FFs (2) (3) af(t) )(tfa)()(ttsST=)(tfs)(jH)(0tf3. )()()(tstftfaa= 1)(tfa)(tfas(t)?=?=nnTtts)()( 2 )(tf

2、a)(?jFa?=?=?msaamjFTjF)(1)( 3)(?jFa)(?jFas?=2/T(3)(tfa)(?jFa)(?jFa(2)(1)nTjnatjnatjnaaenTfdtenTttfdtenTttfjF?=?=?=?=?=?)()()()()()( 4af(nT)f(n)f(n)=af (nT)f(n) ?=?=nnjjenfeF)()( 5(5)(4) TjaeFjF?=?)()( 6T4. F(je)02MNf(n)?=?=10)()(NnnjjkkemfeF 71,.,1,0,2?=MkkMkM)(kjeF (4) )(tf)(tfs)(tfs)(tf)(*)()(tfth

3、tfs=(8) ?=?=?=?=nssnssnTtnTfnTttftf)()()()()()()()(1tSaTjHFthccs=?)(th)(tfs8 ?=?=nscscsccssnTtSanTfTtSaTtftf)()()(*)()( (9)9)(snTf)(tfMATLAB)(tSac)(tf)(snTf)(tf 5. 3 1 f(x)= sin(2*pi*60*t)+cos(2*pi*25*t)+cos(2*pi*30*t)2 80Hz120 Hz150 Hz3435 4MATLAB %function fz=caiyang(fy,fs)%fy%fs0=10000; tp=0.1;t=

4、-tp:1/fs0:tp;k1=0:999; k2=-999:-1;m1=length(k1); m2=length(k2);f=fs0*k2/m2,fs0*k1/m1; %w=-2*pi*k2/m2,2*pi*k1/m1;fx1=eval(fy);FX1=fx1*exp(-j*1:length(fx1)*w);%figure 6. % subplot(2,1,1),plot(t,fx1,r)title(), xlabel(t (s)axis(min(t),max(t),min(fx1),max(fx1) % subplot(2,1,2),plot(f,abs(FX1),r)title() ,

5、 xlabel(f (Hz)axis(-100,100,0,max(abs(FX1)+5) % Ts=1/fs; %t1=-tp:Ts:tp; %f1=fs*k2/m2,fs*k1/m1; %t=t1; %fz=eval(fy); %FZ=fz*exp(-j*1:length(fz)*w);%figure% subplot(2,1,1),stem(t,fz,.),title() , xlabel(t (s)line(min(t),max(t),0,0)% subplot(2,1,2),plot(f1,abs(FZ),m)title() , xlabel(f (Hz)%function fh=h

6、uifu(fz,fs)%T=1/fs; dt=T/10; tp=0.1; 7. t=-tp:dt:tp; n=-tp/T:tp/T;TMN=ones(length(n),1)*t-n*T*ones(1,length(t);fh=fz*sinc(fs*TMN); % k1=0:999; k2=-999:-1;m1=length(k1); m2=length(k2);w=-2*pi*k2/m2,2*pi*k1/m1;FH=fh*exp(-j*1:length(fh)*w);% figure% subplot(2,1,1),plot(t,fh,g),st1=sprintf(fs=%d,fs);st2

7、=;st=st1,st2; title(st) , xlabel(t (s)axis(min(t),max(t),min(fh),max(fh)line(min(t),max(t),0,0) % f=10*fs*k2/m2,10*fs*k1/m1; %subplot(2,1,2),plot(f,abs(FH),g)title() , xlabel(f (Hz)axis(-100,100,0,max(abs(FH)+2);%f1=sin(2*pi*60*t)+cos(2*pi*25*t)+cos(2*pi*30*t);%fs0=caiyang(f1,80); %maxs2ff fr2=huifu

8、(fs2,150); 8. 5 1 TMN=ones(length(n),1)*t-n*T*ones(1,length(t);fh=fz*sinc(fs*TMN); %plot(t,f) %fxstem(t,f) %()subpolt(,) %f=10*fs*k2/m2,10*fs*k1/m1; %abs(x) %xones %1 2 -0.1- 0.08-0.06-0.04-0.0200.020.040.060.080.1- 2- 1012t (s)- 100-80-60-40-20020406080100050100f (Hz) 1 9 3 (1)sfmax2f67 -0.1- 0.08-0.06-0.04-0.0200.020.040.060.080.1- 4- 202t (s)- 150-100-5005010015005101520f (Hz) 6 sf=150Hz -0.1-0.08-0.06-0.04-0.0200.020.040.060.080.1- 2- 1012fs=150t (s