% Program 11_8
% Sigma-Delta D/A Converter Operation
%
clf;
% Generate the input sinusoidal sequence
N = input('Type in length of the input sequence = ');
A = input('Type in amplitude of the input = ');;
w0 = 2*pi*0.02;
n = 1:N;
m = n-1;
x = A*cos(w0*m);
axis([0 N -1 1]);
stem(m,x);
xlabel('Time index'); ylabel('Amplitude');
title ('Input digital signal');
pause
% Generation of quantized output
x = (x)/(A);
y = zeros(1,N+1);
a = zeros(1,N+1);
e = 0;
for k = 2:N+1
   a(k) = x(k-1) - e;
   if a(k) >= 0,
      y(k) = 1;
   else
      y(k) = -1;
   end
   e = y(k) - a(k);
end
yn = y(2:N+1);
axis([0 N -1.2 1.2]);
stem(m, yn); % Plot the quantized output
xlabel('Time'); ylabel('Amplitude');
title ('Digital output of sigma-delta quantizer');
pause
Y = fft(yn);
H = [1 1 0.5 zeros(1,N-5) 0.5 1];% Lowpass filter
YF = Y.*H; % Filtering in the DFT domain
out = ifft(YF);
plot(m,out);
xlabel('Time'); ylabel('Amplitude');
title ('Lowpass filtered analog output');