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# 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
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;
}
``````

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