function lpeq_view(T,fo)
%
% USAGE: lpeq_view(T,fo);
% 
% Inputs: T = pause time between plots
%                 If T is "inf" then you have to hit a key to move to the next plot
%         fo = frequency in cycle/sample of a linear phase component 
%                 Must have -0.5 <= fo <= 0.5.
%                 Use fo = 0 for the case of having no explicit linear phase term
%                 Use fo not equal to zero to model the case
%                 where you want to explicitly include a linear phase component in the signal model...
%                 ... this can be useful when you want to see the effect of a mismatch of 
%                 carrier frequency synchronization in communication signals)
%
% Outputs: Only plots, no matlab variables
%
% Description: Generates a lowpass eq. signal that has a triangular phase and some wiggly sort of 
%      envelope and then displays its motion around the complex plane.  
% 
%      Also plots the vectors showing the in-phase x_i(n) and the quadrature x_q(n) signals
%             The magenta vector = lp eq signal
%             The red vector = in-phase signal
%             The blue vector = quadrature signal
% 
%      Also plots the signal's 
%      envelope and phase functions.  As time progresses you see the vector showing the complex signal 
%      rotating around the complex plane.  You also see the red version of the envelope and phase plots
%      progressing along the time axis - the blue plots show the whole signal, the red plots show the 
%      signal's progression up to the current time.
%
%  HAVE FUN!!!


%% The steps below create an example of a lowpass equivalent signal

%%% First I create a triangularly varying phase theta(t):
up_down=(pi/4)*[0:10 9:-1:1]/10;  
	% creates a single triangle going up to pi/4 and down again in 20 samples
temp=(ones(5,1)*up_down).';  % replicates this triangle 5 times (now total of 100 samples)
theta= temp(:).';  % strings the replicas into 100 samples in a row vector
%% Now I have a triangular theta

%% next I create an envelope - I want something that wiggles around a bit and that never goes negative:
%%  ... so I first add together some sine waves to get a wiggle and then take the absolute value to get
%%  a valid envelope.  This is just some Fourier Series trickery using sine waves to build something that wiggles
env=abs(cos(2*pi*0.01*(0:99))+0.5*sin(2*pi*0.05*(0:99))+0.2*sin(2*pi*0.1*(0:99))+0.05*sin(2*pi*0.2*(0:99)));

%% Now I use these two made-up quantities to create a made-up lowpass eq. signal by using the
%%  the polar format:
x=env.*exp(j*(2*pi*fo*(0:99) + theta) );   
		% note: if fo=0 you have a "true" lpeq signal, if not you have something that still MIGHT be thought of as lpeq
      
      
%% Now we have a signal... so let's look at it.
      
% First plot all the vectors in x on the complex plane and then
% delete them, and "hold" the axes....  This just gives me a fixed 
% set of polar axes that will be big enough to show the largest vector,
% and the "hold" keeps them there without allowing matlab to adjust their
%  size each time I plot to them
subplot(4,2,2)
stem(0:99,env);xlabel('Sample Index');ylabel('Env(n)')
hold on
subplot(4,2,4)
stem(0:99,theta);xlabel('Sample Index');ylabel('\theta(n)')
hold on

subplot(4,2,6)
stem(0:99,real(x));xlabel('Sample Index');ylabel('x_i(n)')
hold on
subplot(4,2,8)
stem(0:99,imag(x));xlabel('Sample Index');ylabel('x_q(n)')
hold on

subplot(2,2,3)
h=compass(x);delete(h);hold on
% compass(x) plots each complex number in x as a vector on the plane
title('magenta = lp eq Signal; red = x_i(n); blue = x_q(n)')

% Now, loop through each element in the lowpass eq. signal x and plot its vector
%  on the complex plane using 
for n=1:100
   subplot(2,2,3)
   h1=compass(x(n),'m');set(h1,'linewidth',2);   % plot the LP Eq signal vector for sample n
   	% The "set" command just makes the width of the drawn 
      %  vector bigger so you can see it better 
   h2=compass(real(x(n)),'r');set(h2,'linewidth',2);
   h3=compass(j*imag(x(n)),'b');set(h3,'linewidth',2);
      
      
   subplot(4,2,2)
	stem(n-1,env(n),'r')
	subplot(4,2,4)
	stem(n-1,theta(n),'r')
   
   subplot(4,2,6)
	stem(n-1,real(x(n)),'r')
	subplot(4,2,8)
	stem(n-1,imag(x(n)),'r')

      
   if isinf(T)
      pause      % if T is "inf" then pause until user hits key
   else
      pause(T)   % if T is not "inf" use its value to pause for that many seconds
   end
   delete(h1);    % Now delete the plotted vectors so you get an empty set of axes for the next loop
   delete(h2);  
   delete(h3);  
end
subplot(4,2,2);hold off
subplot(4,2,4);hold off
subplot(4,2,6);hold off
subplot(4,2,8);hold off
subplot(2,2,3);hold off