%%Figure 4 simulated apparent frequency
t=0:1e-6:1-1e-6;
y1=sin(2*pi*100*t');
y2 = 2*sin(2*pi*120*t');
y3=y1+y2;
fso=exp(-1j*2*pi*110*(0:1e6-1)'/1e6);
yc1=gfilter(y1.*fso,1e6,0,50);
yc2=gfilter(y2.*fso,1e6,0,50);
yc3=gfilter(y3.*fso,1e6,0,50);
afy1=((real(yc1).*[diff(imag(yc1));1])-(imag(yc1).*[diff(real(yc1));1]))./(2*pi*0.000001*(abs(yc1).^2));
afy2=((real(yc2).*[diff(imag(yc2));1])-(imag(yc2).*[diff(real(yc2));1]))./(2*pi*0.000001*(abs(yc2).^2));
afy3=((real(yc3).*[diff(imag(yc3));1])-(imag(yc3).*[diff(real(yc3));1]))./(2*pi*0.000001*(abs(yc3).^2));
% h=figure;
% plot(1:1e6-1,afy1(1:end-1)+110,'linewidth',1.5,'color','y');hold on
% plot(1:1e6-1,afy2(1:end-1)+110,'linewidth',1.5,'color','k');grid on
% set(gca,'xtick',[]);xlabel(' [t]=\mus','FontSize', 20)
% 
% [ax,h1,h2]=plotyy(1:1e6-1,afy3(1:end-1)+110,1:1e6-1,abs(yc3(1:1e6-1)),'plot');
% set(ax,'fontsize',16)
% 
% set(get(ax(1), 'Ylabel'), 'String', '[af]=Hz','FontSize', 20);ylim([95 145])
% set(get(ax(2), 'Ylabel'), 'String','[A]','FontSize', 20);
% set(h1,'linewidth',2)
% set(h2,'linewidth',2) 
% set(get(ax(2), 'Ylabel'), 'String','[A]','FontSize', 20);
yyaxis left
plot(1/1000:1/1000:(1e6-1)/1000,afy3(1:end-1)+110,'b','linewidth',1.5)
hold on
plot(1/1000:1/1000:(1e6-1)/1000,100*ones(1e6-1,1),'k','linewidth',1.5)

plot(1/1000:1/1000:(1e6-1)/1000,120*ones(1e6-1,1),'k','linewidth',1.5)

xlabel('[t] = ms','FontSize', 20)
set(gca,'fontsize',16)
ylabel('[fi] = Hz','FontSize', 20)
xlim([1/1000 1.5e2])
ylim([95 145])

yyaxis right
plot(1/1000:1/1000:(1e6-1)/1000,abs(yc3(1:1e6-1)),'r','linewidth',1.5)
xlabel('[t] = ms','FontSize', 20)
set(gca,'fontsize',16)
ylabel('[|y|] = 1','FontSize', 20)
xlim([1/1000 1.5e2])


print fig4.tif -dtiff