%% task1parta
'See book'
%% task1partb
% y[0] = y(2).
c = cos(pi/6);
y(1) = 0;
y(2) = 1;
for k = 3:100
y(k) = 2*c*y(k-1) - y(k-2);
end
plot(((1:100)-1)/pi, y)
%% task1partc
'See book for derivation'
%y[0] = y(5)
%x[0] = x(5)

x = 0*(1:204);
y = 0*(1:4);

x(5) = 1 - 2*c^2;
x(4) = c;

for k = 4:204
y(k) = x(k) + 2*c*y(k-1) - y(k-2);
end
plot((1:200)-1, y(5:204))

%% task2parta
r = 0.9;
p1 = 0.45*pi;
p2 = 0.6*pi;
p3 = 0.85*pi;

p = poly([r*exp(i*p1) r*exp(i*p2) r*exp(i*p3) r*exp(-i*p1) r*exp(-i*p2) r*exp(-i*p3)]);
impz(p)

%% task2partb

fr(r,r,r,p1,p2,p3);


%% task2partc1
fr(r,r,1/r,p1,p2,p3);
%% task2partc2
fr(r,1/r,r,p1,p2,p3);
%% task2partc3
fr(r,1/r,1/r,p1,p2,p3);
%% task2partc4
fr(1/r,r,r,p1,p2,p3);
%% task2partc5
fr(1/r,r,1/r,p1,p2,p3);
%% task2partc6
fr(1/r,1/r,r,p1,p2,p3);
%% task2partc7
fr(1/r,1/r,1/r,p1,p2,p3);

%% task2partd1
ir(r,r,r,p1,p2,p3);
%% task2partd2
ir(r,r,1/r,p1,p2,p3);
%% task2partd3
ir(r,1/r,r,p1,p2,p3);
%% task2partd4
ir(r,1/r,1/r,p1,p2,p3);
%% task2partd5
ir(1/r,r,r,p1,p2,p3);
%% task2partd6
ir(1/r,r,1/r,p1,p2,p3);
%% task2partd7
ir(1/r,1/r,r,p1,p2,p3);
%% task2partd8
ir(1/r,1/r,1/r,p1,p2,p3);

%% task2parte
frr(r,r,r,p1,p2,p3, 1);