int=.001;
npts=512;
noise=.5;
here=(npts-1)/1000;
t=0:int:here;
freq=120;
[xx,n]=size(t);
x=sin(2*pi*freq*t);
y=x+noise*randn(size(t));

figure(1)
subplot(1,2,1)
plot(t(1:50),x(1:50),'b')
ylim([-2 2])
title('Clean Data')
subplot(1,2,2)
plot(t(1:50),y(1:50),'g')
title('Noisy Data')
ylim([-2 2])
pause

Y=fft(y);
Pyy=Y.*conj(Y);
f=(1/int)/512*(0:255);
f2=[-(f(255)-f) f];

figure(2)
subplot(2,2,1)
plot(t(1:50),y(1:50),'r')
title('Noisy Data')
subplot(2,2,2)
plot(f2,real(fftshift(Y)),'g')
title('Real Terms')
subplot(2,2,3)
plot(f,Pyy(1:npts/2),'b')
title('Power Spectrum')
subplot(2,2,4)
plot(f2,imag(fftshift(Y)),'c')
title('Imag Terms')
pause

%create a "step" function

b1=1:1:30;
b2=1:1:50;
b3=1:1:340;
b4=1:1:50;
b5=1:1:42;
b=[zeros(size(b1)) ones(size(b2)) zeros(size(b3)) ones(size(b4)) zeros(size(b5))];
x2=linspace(0, 1, 512)

figure(3)
plot(x2,b,'k')
ylim([0 2])
title('Filter Function')
axis tight
pause

FRY=real(Y).*b;
FIY=imag(Y).*b;
i=sqrt(-1);
FY=FRY+FIY*i;
IFY=ifft(FY);

figure(4)
subplot(2,2,1)
scale=max(real(Y));
plot(f2,real(Y),'r',f2,scale*b,'r')
title('Real Terms & Filter')
subplot(2,2,2)
scale=max(imag(Y));
plot(f2,imag(Y),'b',f2,scale*b,'g')
title('Imag Terms & Filter')
subplot(2,2,3)
plot(FRY,'b')
title('Filtered Real Terms')
subplot(2,2,4)
plot(FIY,'c')
title('Filtered Imag Terms')
pause

figure(5)
subplot(1,2,1)
plot(t(1:50),y(1:50),'r')
title('Noisy Data')
ylim([-2 2])
subplot(1,2,2)
plot(t(1:50),real(IFY(1:50)),'k')
title('Filtered Data')
ylim([-2 2])