# Speech Synthesis

TODO

## Example

This is a simple C program (using 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;
}
```