void convolve_wave(const long int sequence_len, 
                   const double *f,
                   const double *g, 
                   double *y)
{
    auto unsigned long int x,
                           n;
    for (n = 0; n < sequence_len; n++)
    {
        y[n] = 0.0;
        for (x = 0; x < n; x++)
        {
            y[n] += f[x] * g[n - x];
        }
    }
    return;
}







