ЛАБ 3 1
Clf
X1=[5 4 2 1];
X2=[6 5 4]
c1=length(X1); c2=length(X2);
c=c1+c2-1; X11=X1; X21=X2;
X11(c)=0; X21(c)=0;
f11=fft(X11); f21=fft(X21);
f1=f11.*f21;
f3=conv(X1,X2)
qq=round(real(ifft(f1)))
plot(f3); hold
plot(qq,'pr'); grid
2
clear
N=256;
T=0.01;
tm=N*T/2;
t=-tm:T:(tm-T);
f=exp(-100*t.^2);
f(N/2+1)=1;
ff=fft(f);
k=0:N-1;
fi=ifft(ff);
clf;
subplot(221),plot(f);xlabel('k');ylabel('real(X(k)),imag(X(k))');
subplot(223),plot(k,real(ff),k,imag(ff));xlabel('k');
ylabel('real(X(k)),imag(X(k))');
pause
subplot(222),plot(real(fi));xlabel('k');ylabel('real(X(k)),imag(X(k))');
pause;
%`````````````````````````````````````````
clf;
k1=0:N/2-1;
k2=-N/2+1:0;
k=[k1 k2];
F=k/(N*T);
subplot(221),plot(k,real(ff),k,imag(ff));xlabel('k');
ylabel('real(X(k)),imag(X(k))');
pause;
subplot(223),plot(F,real(ff),'r',F,imag(ff),'b');xlabel('v');
ylabel('real(X(v)),imag(X(v))');
pause;
%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
for k=1:N
ff(k)=ff(k)*exp(i*pi*(k-1));
end;
subplot(222),plot(F,real(ff),'r',F,imag(ff),'b');xlabel('v');
ylabel('real(X(v))=red,imag(X(v))=blue');
f1=30 49 52 32 13 4
qq=30 49 52 32 13 4
3
clear
clf
N=256;
T=0.02; tm=N*T/2;
t=-tm:T:(tm-T);
f=(sin(2*pi*10*t)./(2*pi*10*t)).^2;
f(N/2+1)=1;
ff=fft(f);
k=0:N-1;
subplot(311),plot(f);xlabel('k');ylabel('real(X(k)),imag(X(k))');
pause;
subplot(312),plot(k,real(ff),'r',k,imag(ff),'b');xlabel('k');
ylabel('real(X(k)),imag(X(k))');
pause;
k1=0:N/2-1;
k2=-N/2+1:0;
k3=[k1 k2];
for k4=1:N
r=128;
ff(k4)=ff(k4)*exp(i*2*pi*r*(k4-1)/256);
end;
subplot(313),plot(k3,real(ff),'r',k3,imag(ff),'b');
xlabel('k');
ylabel('real(X(v))=red,imag(X(v))=blue');
pause;
end
4
clear
N=256;
T=0.01;
tm=N*T/2;
t=-64*T+0.000001:T:191*T+0.000001;
f=(sin(2*pi*10*t)./(2*pi*10*t)).^2;
ff=fft(f);
subplot(311),plot(t,f);
%`````````````````````````````````````````
k1=1:N/2-1;
k2=-N/2:0;
k=[k2 k1];
subplot(312),plot(k,real(ff),'r',k,imag(ff),'b');
%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
for kk=1:N;
r=64;
ff(kk)=ff(kk)*exp(i*2*pi*r*(kk-1)/N);
end;
subplot(313),plot(k,real(ff),'r',k,imag(ff),'b');