% simulates a either a square wave or random bit stream
% through a low pass channel. Choose by commenting out w=....
% Nb,Nft, and Hbw are parameters to control the simulation
% H can be either an ideal LP or a passive 4th order,
% choose by commenting out the appropriate H=...
Nb=128; % number of bit values
Nft=16; % samples per bit
%Hbw=3*Nb/4; % filter bandwidth
%Hbw=4*Nb; % filter bandwidth
w=rand(1,Nb); % generate random sequence
w=pulsetrain(0:1:(Nb-1),2); % pulse train representing alternating bit values
b=2*binarize(w)-1; % binarize and make into bipolar signal
bft=flattop1(b,Nft); % flat top to simulate continuous time
Ebb=(bft*bft')/(Nb*Nft); % inner product of row vector times column vector
Bft=fft(bft); % get spectra of bit stream
% if bits were alternating, like a square wave, there would be
% Nb/2 cycles per the window size of Nb*Nft. Thus the fundamental
% harmonic should be at k=Nb/2
H=irect(1,Hbw+1,1,(Nb*Nft)); % use ideal Low Pass Filter
%H=lp_t1_o1_dft(Hbw/2,(Nb*Nft)/2,(Nb*Nft)); H=H.*H.*H.*H; % make 1st order Low Pass then cascade for 4th order cutoff
br=real(ifft(fft(bft).*H)); % received signal
be=2*binarize(br)-1; %reconstructed binary signal
zoom1(1:(Nb*Nft)/4)=bft(1:(Nb*Nft)/4); % look at a section closer
zoom2(1:(Nb*Nft)/4)=br(1:(Nb*Nft)/4); % look at a section closer
zoom3(1:(Nb*Nft)/4)=be(1:(Nb*Nft)/4); % look at a section closer
zoom4(1:(Nb*Nft)/4)=abs(Bft(1:(Nb*Nft)/4)); % look at a section of the fft
zoom5(1:(Nb*Nft)/4)=abs(H(1:(Nb*Nft)/4)); % look at a section of the fft
Ebbre=[(bft*br')/(Nb*Nft),(bft*be')/(Nb*Nft)] % average cross correlation energy
figure(1);
plot(zoom1);
axis([1,(Nft*Nb)/4,-2,2]);
figure(2);
plot(zoom2);
axis([1,(Nft*Nb)/4,-2,2]);
figure(3);
plot(zoom3);
axis([1,(Nft*Nb)/4,-2,2]);
figure(4);
plot(zoom4);
axis([1,(Nft*Nb)/4,min(min(zoom4)),max(max(zoom4))]);
figure(5);
plot(zoom5);
axis([1,(Nft*Nb)/4,-2,2]);