static double kaiser(params *p, double x)
{
double a = p->params[0];
double epsilon = 1e-12;
double i0a = 1 / bessel_i0(epsilon, a);
return bessel_i0(epsilon, a * sqrt(1 - x * x)) * i0a;
}
static double kaiser(kernel *k, double x)
{
double a = k->params[0];
double b = k->params[1];
double epsilon = 1e-12;
double i0a = 1 / bessel_i0(epsilon, b);
return bessel_i0(epsilon, a * sqrt(1 - x * x)) * i0a;
}
/*
* Returns the value of the Kaiser window at point n with shape alpha and
* length M+1.
*/
double
kaiser(double alpha, double M, double n)
{
if (n < 0 || n > M)
return 0;
return bessel_i0(alpha * sqrt(1.0 - pow(2.0 * n / M - 1.0, 2))) /
bessel_i0(alpha);
}
static double kaiser(double beta, int M, int n)
{
if (M == 1)
return 1.;
if (fabs((double)n / (double)M - 0.5) >= 0.5)
return 0.;
return bessel_i0(beta * sqrt(1. - pow(2. * (double)n / (double)M - 1., 2.)))
/ bessel_i0(beta);
}
static void
lfr_filter_calculate_s16(short *data, int nsamp, int nfilt,
double offset, double cutoff, double beta)
{
double x, x0, t, y, z, xscale, yscale, err;
int i, j;
double *a, sum, fac, scale;
a = malloc(nsamp * sizeof(double));
if (!a)
abort(); /* FIXME: report an error */
if (nsamp <= 8)
scale = 31500;
else
scale = 32767;
yscale = 2.0 * cutoff / bessel_i0(beta);
xscale = (8.0 * atan(1.0)) * cutoff;
for (i = 0; i < nfilt; ++i) {
x0 = (nsamp - 1) / 2 + offset * i;
sum = 0.0;
for (j = 0; j < nsamp; ++j) {
x = j - x0;
t = x * (2.0 / (nsamp - 2));
if (t <= -1.0 || t >= 1.0) {
y = 0.0;
} else {
y = yscale *
bessel_i0(beta * sqrt(1.0 - t * t)) *
sinc(xscale * x);
}
a[j] = y;
sum += y;
}
fac = scale / sum;
err = 0.0;
for (j = 0; j < nsamp; ++j) {
y = a[j] * fac + err;
z = floor(y + 0.5);
err = z - y;
data[i * nsamp + j] = (short) z;
}
}
}
/*
* modified bessel function
*/
double bessel_i0(double x)
{
if (x < 0.)
return bessel_i0(-x);
if (x < 8.)
return exp(x) * chebeval(x / 4. - 1., ARRAY_SIZE(coeff_0to8), coeff_0to8);
return exp(x) * chebeval(16. / x - 1., ARRAY_SIZE(coeff_8toinf), coeff_8toinf) / sqrt(x);
}
static void
lfr_filter_calculate_f32(float *data, int nsamp, int nfilt,
double offset, double cutoff, double beta)
{
double x, x0, t, y, xscale, yscale;
int i, j;
yscale = 2.0 * cutoff / bessel_i0(beta);
xscale = (8.0 * atan(1.0)) * cutoff;
for (i = 0; i < nfilt; ++i) {
x0 = (nsamp - 1) / 2 + offset * i;
for (j = 0; j < nsamp; ++j) {
x = j - x0;
t = x * (2.0 / (nsamp - 2));
if (t <= -1.0 || t >= 1.0) {
y = 0.0;
} else {
y = yscale *
bessel_i0(beta * sqrt(1.0 - t * t)) *
sinc(xscale * x);
}
data[i * nsamp + j] = (float) y;
}
}
}
