%Program 11.1 Audio codec
%input: vector x of input signal
%output: vector out of output signal
%Example usage: out=simplecodec(cos((1:2^(12))*2*pi*256/2^(13)));
%               example signal is 1/2 sec. pure tone of frequency f = 256
function out=simplecodec2(x,f)
len=length(x);
n = 32                                      % length of window
nw=floor(len/n);                      % number of length n windows in x
x=x(1:n*nw);                          % cut x to integer number of n windows
Fs = 2^13;                            % Fs=sampling rate
b=4; L=0.3;                           % b = quantization bits, [-L,L] amplitude range
q=2*L/(2^b-1);                        % q used for b bits on interval [-L, L]
for i=1:n                             % form the MDCT matrix
  for j=1:2*n
    M(i,j)= cos((i-1+1/2)*(j-1+1/2+n/2)*pi/n);
  end
end
M=sqrt(2/n)*M;
N=M';                                 % inverse MDCT
x=0.3*x/max(abs(x));                  % normalize signal to max amplitude = 0.3
%sound(x,Fs)                           % Matlab's sound command
out=[];

j = (1:2*n);
hj = sqrt(2)*sin( ( j - 0.5)*(pi/(2*n)) )';%windowing function

for k=1:nw-1                          % loop over l ength 2n windows
  x0=x((1+(k-1)*n):(2*n+(k-1)*n))'.*hj;
  y0=M*x0;
  y1=round(y0/q);                     % transform components quantized
  
  % Storage/transmission of file occurs here  
  y2=y1*q;                            % transform components dequantized
  w(:,k)=(N*y2).*hj;                        % invert the MDCT
  if(k>1)
      w2=w(n+1:2*n,k-1);
      w3=w(1:n,k);
      out=[out;(w2+w3)/2];          % collect the reconstructed signal
  end                                 % (of length 2n less than length of x)
end
pause(1)
sound(out,Fs)                         % play the reconstructed tone


