Speech Synthesis

   TODO

Example

   This is a simple [1]C program (using [2]float for simplicity of
   demonstration) that creates basic vowel sounds using formant synthesis
   (run e.g. as gcc -lm program.c && ./a.out | aplay, 8000 Hz 8 bit audio is
   supposed):

 #include <stdio.h>
 #include <math.h>

 double vowelParams[] = { // vocal tract shapes, can be found in literature
   // formant1  formant2  width1  width2  amplitude1 amplitude2
      850,      1650,     500,    500,    1,         0.2, // a
      390,      2300,     500,    450,    1,         0.9, // e
      240,      2500,     300,    500,    1,         0.5, // i
      250,      600,      500,    400,    1,         0.9, // o
      300,      400,      400,    400,    1,         1.0  // u
   };

 double tone(double t, double f) // tone of given frequency
 {
   return sin(f * t * 2 * M_PI);
 }

 /* simple linear ("triangle") function for modelling spectral shape
    of one formant with given frequency location, width and amplitude */
 double formant(double freq, double f, double w, double a)
 {
   double r = ((freq - f + w / 2) * 2 * a) / w;

   if (freq > f)
     r = -1 * (r - a) + a;

   return r > 1 ? 1 : (r < 0 ? 0 : r);
 }

 /* gives one sample of speech, takes two formants as input, fundamental
    frequency and possible offset of both formants (can model "bigger/smaller
    head") */
 double speech(double t, double fundamental, double offset,
   double f1, double f2,
   double w1, double w2,
   double a1, double a2)
 {
   int harmonic = 1; // number of harmonic frequency

   double r = 0;

   /* now generate harmonics (multiples of fundamental frequency) as the source,
      and multiply them by the envelope given by formants (no need to deal with
      multiplication of spectra; as we're constructing the result from basic
      frequencies, we can simply multiply each one directly): */
   while (1)
   {
     double f = harmonic * fundamental;
     double formant1 = formant(f,f1 + offset,w1,a1);
     double formant2 = formant(f,f2 + offset,w2,a2);

     // envelope = max(formant1,formant2)
     r += (formant1 > formant2 ? formant1 : formant2) * 0.1 * tone(t,f);

     if (f > 10000) // stop generating harmonics above 10000 Hz
       break;

     harmonic++;
   }

   return r > 1.0 ? 1.0 : (r < 0 ? 0 : r); // clamp between 0 and 1
 }

 int main(void)
 {
   for (int i = 0; i < 50000; ++i)
   {
     double t = ((double) i) / 8000.0;
     double *vowel = vowelParams + ((i / 4000) % 5) * 6; // change vowels

     putchar(128 + 127 *
       speech(t,150,-100,vowel[0],vowel[1],vowel[2],vowel[3],vowel[4],vowel[5]));
   }

   return 0;
 }

Links:
1. c.md
2. float.md