%**************************************************************************
% Comparison of "standard" and a bit more "advanced" window functions
%**************************************************************************

%**************************************************************************
% Basis parameters
%**************************************************************************
N_win =   64;
N_dft = 1024*16;

%**************************************************************************
% Basic windows - rectangle window
%**************************************************************************
h_rec     = ones(N_win,1);
h_rec     = h_rec / sum(h_rec);

H_rec     = fft(h_rec,N_dft);
H_rec     = H_rec(1:N_dft/2+1);
H_rec_log = 20*log10(abs(H_rec)+eps);

%**************************************************************************
% Basic windows - Hann window
%**************************************************************************
h_han     = hann(N_win);
h_han     = h_han / sum(h_han);

H_han     = fft(h_han,N_dft);
H_han     = H_han(1:N_dft/2+1);
H_han_log = 20*log10(abs(H_han)+eps);

%**************************************************************************
% Basic windows - Hamming window
%**************************************************************************
h_ham     = hamming(N_win);
h_ham     = h_ham / sum(h_ham);

H_ham     = fft(h_ham,N_dft);
H_ham     = H_ham(1:N_dft/2+1);
H_ham_log = 20*log10(abs(H_ham)+eps);

%**************************************************************************
% Advanced windows - "Chebyshev" window
%**************************************************************************
h_che     = chebwin(N_win,10);
h_che     = h_che / sum(h_che);

H_che     = fft(h_che,N_dft);
H_che     = H_che(1:N_dft/2+1);
H_che_log = 20*log10(abs(H_che)+eps);

%**************************************************************************
% Advanced windows - "Prolate" window
%**************************************************************************
h_pro     = dpss(N_win,1.18);
h_pro     = h_pro / sum(h_pro);

H_pro     = fft(h_pro,N_dft);
H_pro     = H_pro(1:N_dft/2+1);
H_pro_log = 20*log10(abs(H_pro)+eps);

%**************************************************************************
% Show results
%**************************************************************************
fig = figure(1);
f = (0:N_dft/2)/N_dft*2;

plot(f,H_rec_log,'b', ...
     f,H_han_log,'r', ...
     f,H_ham_log,'k', ...
     f,H_che_log,'m', ...
     f,H_pro_log,'c', ...
     'LineWidth',2);
legend('Rectangle window', ...
       'Hann window', ...
       'Hamming window', ...
       'Chebyshev window', ...
       'Prolate spheroidal window')
grid on;
xlabel('Normalized frequency \(\Omega/\pi\)','interpreter','latex');
ylabel('dB')
ylim([-90 10])

%**************************************************************************
% Design parameters
%**************************************************************************
N   =  8;     % Filter order
f_c =  0.1;   % Normalized cut-off frequency (0 ... 1)
R_p =  0.5;   % Ripple in dB in passband
R_s = 80;     % Stopband attenuation in dB

%**************************************************************************
% Design of an elliptic lowpass filter
%**************************************************************************
[b,a] = ellip(N, R_p, R_s, f_c);

%**************************************************************************
% Show frequency response
%**************************************************************************
fig = figure(1);
set(fig,'Units','Normalized');
set(fig,'Position',[0.1 0.1 0.8 0.8]);
[H,Omega] = freqz(b,a,2048*4,'whole',2);
plot(Omega,20*log10(abs(H)+eps),'b','LineWidth',2);
grid on
axis([0 2 (-R_s -20) 20])
xlabel('Normalized frequency \Omega/\pi')
ylabel('dB')


%**************************************************************************
% Quantization
%**************************************************************************
B = 32; % Number of bits

a_max = max(abs(a));
b_max = max(abs(b));

a_q = round(a / a_max * 2^B) / 2^B * a_max;
b_q = round(b / b_max * 2^B) / 2^B * b_max;

%**************************************************************************
% Show frequency response of quantized filter
%**************************************************************************
[H_q,Omega] = freqz(b_q,a_q,2048*4,'whole',2);
hold on;
plot(Omega,20*log10(abs(H_q)+eps),'r','LineWidth',2);
hold off;
legend('Non-quantized',['Quantized with ',num2str(B),' bits'])

%**************************************************************************
% Show coefficients
%**************************************************************************
format long;
a
a_q
b
b_q

%**************************************************************************
% Transform to cascade of biquad filters
%**************************************************************************
[sos,g] = tf2sos(b,a);

[L,L_tmp] = size(sos);

sos_q = round(sos / max(max(abs(sos))) * 2^B) / 2^B * max(max(abs(sos)));
g_q   = round(g^(1/L) * 2^B) / 2^B;

H_bq_q = freqz(g_q*sos_q(1,1:3),sos_q(1,4:6),2048*4,'whole',2);
for k = 2:L
    H_bq_q = H_bq_q .* freqz(g_q*sos_q(k,1:3),sos_q(k,4:6),2048*4,'whole',2);
end;

%**************************************************************************
% Show frequency response of quantized biquad filters
%**************************************************************************
[H_q,Omega] = freqz(b_q,a_q,2048*4,'whole',2);
hold on;
plot(Omega,20*log10(abs(H_bq_q)+eps),'k','LineWidth',2);
hold off;
legend('Non-quantized',['Quantized with ',num2str(B),' bits'],...
       'Biquad structure (also qunatized)');