%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Creative Commons
% Attribution-Noncommercial 2.5 India
% You are free:
% to Share — to copy, distribute and transmit the work
% to Remix — to adapt the work
% Under the following conditions:
% Attribution. You must attribute the work in the manner 
% specified by the author or licensor (but not in any way 
% that suggests that they endorse you or your use of the work). 
% Noncommercial. You may not use this work for commercial purposes. 
% For any reuse or distribution, you must make clear to others the 
% license terms of this work. The best way to do this is with a 
% link to this web page.
% Any of the above conditions can be waived if you get permission 
% from the copyright holder.
% Nothing in this license impairs or restricts the author's moral rights.
% http://creativecommons.org/licenses/by-nc/2.5/in/

% Checked for proper operation with Octave Version 3.0.0
% Author	: Krishna
% Email		: krishna@dsplog.com
% Version	: 1.0
% Date		: 14 April 2008
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Script for simulating transmit filtering via a rectangular filtering
% sinc fitlering. Both shows that there is no inter-symbol-interference.
% However, spectrum of sinc shaped filter is much shorter

clear 
N  = 10^4; % number of symbols
am = 2*(rand(1,N)>0.5)-1 + j*(2*(rand(1,N)>0.5)-1); % generating random binary sequence
fs = 10; % sampling frequency in Hz

% recatangular filter
gt1 = ones(1,fs); 

% sinc filter
gt2 = sin(pi*[-fs:1/fs:fs])./(pi*[-fs:1/fs:fs]);
gt2(fs*fs+1) = 1;

% upsampling the transmit sequence 
amUpSampled = [am;zeros(fs-1,length(am))];
amU = amUpSampled(:).';

% filtered seqeunce
st1 = conv(amU,gt1);
st2 = conv(amU,gt2);

% checking for the difference on the output of the filter to the input sequence
errRect = st1(fs:fs:end)-am;
errRectSum = errRect*errRect'/N  % no difference
errSinc = st2(101:10:end-101)-am;
errSincSum = errSinc*errSinc'/N  % no difference

close all
[Pxx1,W] = pwelch(st1,[],[],4096,fs);    
[Pxx2,W] = pwelch(st2,[],[],4096,fs);    
plot([-2048:2047]*fs/4096,10*log10(fftshift(Pxx1)),'b','LineWidth',2);
hold on
plot([-2048:2047]*fs/4096,10*log10(fftshift(Pxx2)),'m','LineWidth',2);
xlabel('frequency, Hz')
ylabel('power spectral density')
title('Transmit spectrum');
legend('recatangular', 'sinc');
axis([-2 2 -50 10])
grid on