%-------------Begin Lab #5---

%**********************
%  Colin D. Joye      *
%  Lab #5             *
%  ECE 3220 - 001     *
%  Due Tue. 11/28/00  *
%**********************
   
% Objective and Conclusions:
%  The purpose of this practicum was to design 
%  various filters and see the relation of the 
%  pole / zero positions and how they affect the 
%  filters.
clear;   
% 2.a)
N  = 6; % N is the order of the filter.
w0 = 120*pi; % w0 is the cutoff frequency (rad/sec)
[z,p,k]=cheb2ap(N, 40); 
%   z: vector of zeros.
%   p: vector of poles.
%   k: gain constant.
num = k*poly(z);
den = poly(p);

[num,den] = lp2lp(num,den,w0);
z = roots(num);
p = roots(den);

pang = -angle(p);
pamp = abs(p);

zang = -angle(z);
zamp = abs(z);

figure(1)
  polar(zang, zamp, 'b*');
  hold on;
  polar(pang, pamp, 'rd');
  hold off;
  text(1,2,'2, Colin D. Joye');
  title('Chebychev LP: Plot of poles (diamond) and zeros (*)');
  
[res,pol,dr]=residue(num',den');

wdel   = 10;
w      = [10:wdel:100000];
hfreq1 = freqs(num,den,w);
mag1   = abs(hfreq1);
phase1 = angle(hfreq1)*180/pi;

figure(2)
  subplot(211);
  semilogx(w,phase1);
  grid;
  text(1000,150,'2, Colin D. Joye');
  xlabel('log w');
  ylabel('angle(H(jw))');
  title('Chebychev LP: Plot of phase response vs. frequency');

figure(2)
  subplot(212);
  semilogx(w,20*log10(mag1));
  grid;
  text(1000,-15,'2, Colin D. Joye');
  xlabel('log w');
  ylabel('|H(jw)|');
  title('Chebychev LP: Plot of magnitude vs. frequency');

%See attached sheet for impulse response.
abs(res)
angle(res)

% 3)
%  The location of the first zero (at ~390 hz) on the plot of the
%  poles and zeros in the s-plane is very close to the break 
%  point for the Chebychev filter of 120pi= ~377 hz.  The second
%  zero (533 hz) in the pole-zero plot, is the second dip in the
%  magnitude vs frequency plot.  The third zero at 1456 hz coresponds
%  to the third (and largest) dip in the magnitude plot.  The zeros 
%  also corespond to the abrupt phase shifts in the phase response
%  plot.  The poles in the pole-zero plot corespond to peaks in the 
%  magnitude plot.

%-------------End Lab #5---