% Question #12

N = 1024;
n = [0:N-1]'; 
k = n;  

b = [0.16217 0 -0.16217];
a = [1 0 0.67566];

hf = zeros(N,1);
[hf1,W] = freqz(b,a,N/2+1);
hf(1:N/2+1)= hf1;
hf (N/2+2:N) = conj(flipud(hf1(2:N/2)));

En = ones(N,1)*exp(-j*2*pi*n/N)';  
K = k*ones(1,N);  	
Ekn = 1/N*En.^K;  	

hk = real(Ekn*hf);  	

figure
stem(hk(1:25),'b')
AXIS([1 25 -.3 .3])
grid
title('Impulse Response')
ylabel('h[n]')
xlabel('n')

figure
plot(hk(1:25),'b')
AXIS([1 25 -.3 .3])
title('Impulse Response')
ylabel('h[n]')
xlabel('n')