References : Paul Kellett
Linked file : nsdither.txt
(this linked file is included below)
Notes :
(see linked file)
Linked files
Noise shaped dither  (March 2000)

This is a simple implementation of highpass triangular-PDF dither with
2nd-order noise shaping, for use when truncating floating point audio
data to fixed point.

The noise shaping lowers the noise floor by 11dB below 5kHz (@ 44100Hz
sample rate) compared to triangular-PDF dither. The code below assumes
input data is in the range +1 to -1 and doesn't check for overloads!

To save time when generating dither for multiple channels you can do
things like this:  r3=(r1 & 0x7F)<<8; instead of calling rand() again.

  int   r1, r2;                //rectangular-PDF random numbers
  float s1, s2;                //error feedback buffers
  float s = 0.5f;              //set to 0.0f for no noise shaping
  float w = pow(2.0,bits-1);   //word length (usually bits=16)
  float wi= 1.0f/w;            
  float d = wi / RAND_MAX;     //dither amplitude (2 lsb)
  float o = wi * 0.5f;         //remove dc offset
  float in, tmp;
  int   out;

//for each sample...

  r2=r1;                               //can make HP-TRI dither by
  r1=rand();                           //subtracting previous rand()
  in += s * (s1 + s1 - s2);            //error feedback
  tmp = in + o + d * (float)(r1 - r2); //dc offset and dither 
  out = (int)(w * tmp);                //truncate downwards
  if(tmp<0.0f) out--;                  //this is faster than floor()

  s2 = s1;                            
  s1 = in - wi * (float)out;           //error