% show high pass and low pass filter pairs and their action on a 1d signal

% define signal, sample rate, sample domain
N = 256;
T = (0:1:(N-1))/N;
X = 2*cos(5*2*pi*T)+0.5*sin(60*2*pi*T)+ 0.25*sin(100*2*pi*T)+0.5*(2*rand(size(T))-1);
%X = cos(5*2*pi*t);
%X = sin(30*2*pi*t);

SD = 0:(N-1);
FD = SD-N/2;

% define low and high pass masks
lo = [1 1];  lo = lo/sum(lo);
hi = [1,-1]; hi = hi/sum(abs(hi));
Xl = circconv(X,lo);
Xh = circconv(X,hi);
elo = [lo,zeros(1,N-length(lo))];
ehi = [hi,zeros(1,N-length(hi))];
M = max(abs(X));


figure(1);
subplot(3,1,1)
plot(SD,X)
axis([0,N,-M,M]);
title('original')
subplot(3,1,2)
plot(SD,Xl)
axis([0,N,-M,M]);
title('low pass')
subplot(3,1,3)
plot(SD,Xh)
axis([0,N,-M,M]);
title('high pass')



figure(2);
subplot(3,1,1)
plot(FD,fftshift(abs(fft(X))))
axis tight
title('|dft(X)|')
subplot(3,1,2)
plot(FD,fftshift(abs(fft(elo))))
axis tight
title('|dft(lo)|')
subplot(3,1,3)
plot(FD,fftshift(abs(fft(ehi))))
axis tight
title('|dft(hi)|')