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Diffstat (limited to 'utils/bsincgen.c')
| -rw-r--r-- | utils/bsincgen.c | 374 |
1 files changed, 374 insertions, 0 deletions
diff --git a/utils/bsincgen.c b/utils/bsincgen.c new file mode 100644 index 00000000..d53b3cb5 --- /dev/null +++ b/utils/bsincgen.c @@ -0,0 +1,374 @@ +/*
+ * Sinc interpolator coefficient and delta generator for the OpenAL Soft
+ * cross platform audio library.
+ *
+ * Copyright (C) 2015 by Christopher Fitzgerald.
+ *
+ * This library is free software; you can redistribute it and/or
+ * modify it under the terms of the GNU Library General Public
+ * License as published by the Free Software Foundation; either
+ * version 2 of the License, or (at your option) any later version.
+ *
+ * This library is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ * Library General Public License for more details.
+ *
+ * You should have received a copy of the GNU Library General Public
+ * License along with this library; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston,
+ * MA 02110-1301 USA
+ *
+ * Or visit: http://www.gnu.org/licenses/old-licenses/lgpl-2.0.html
+ *
+ * --------------------------------------------------------------------------
+ *
+ * This is a modified version of the bandlimited windowed sinc interpolator
+ * algorithm presented here:
+ *
+ * Smith, J.O. "Windowed Sinc Interpolation", in
+ * Physical Audio Signal Processing,
+ * https://ccrma.stanford.edu/~jos/pasp/Windowed_Sinc_Interpolation.html,
+ * online book,
+ * accessed October 2012.
+ */
+
+#include <stdio.h>
+#include <math.h>
+#include <string.h>
+
+#ifndef M_PI
+#define M_PI (3.14159265358979323846)
+#endif
+
+// The number of distinct scale and phase intervals within the filter table.
+#define BSINC_SCALE_COUNT (16)
+#define BSINC_PHASE_COUNT (16)
+
+#define BSINC_REJECTION (60.0)
+#define BSINC_POINTS_MIN (12)
+
+static double MinDouble(double a, double b)
+{ return (a <= b) ? a : b; }
+
+static double MaxDouble(double a, double b)
+{ return (a >= b) ? a : b; }
+
+/* NOTE: This is the normalized (instead of just sin(x)/x) cardinal sine
+ * function.
+ * 2 f_t sinc(2 f_t x)
+ * f_t -- normalized transition frequency (0.5 is nyquist)
+ * x -- sample index (-N to N)
+ */
+static double Sinc(const double x)
+{
+ if(fabs(x) < 1e-15)
+ return 1.0;
+ return sin(M_PI * x) / (M_PI * x);
+}
+
+static double BesselI_0(const double x)
+{
+ double term, sum, last_sum, x2, y;
+ int i;
+
+ term = 1.0;
+ sum = 1.0;
+ x2 = x / 2.0;
+ i = 1;
+
+ do {
+ y = x2 / i;
+ i++;
+ last_sum = sum;
+ term *= y * y;
+ sum += term;
+ } while(sum != last_sum);
+
+ return sum;
+}
+
+/* NOTE: k is assumed normalized (-1 to 1)
+ * beta is equivalent to 2 alpha
+ */
+static double Kaiser(const double b, const double k)
+{
+ double k2;
+
+ if((k < -1.0) || (k > 1.0))
+ return 0.0;
+
+ k2 = MaxDouble(1.0 - (k * k), 0.0);
+
+ return BesselI_0(b * sqrt(k2)) / BesselI_0(b);
+}
+
+/* NOTE: Calculates the transition width of the Kaiser window. Rejection is
+ * in dB.
+ */
+static double CalcKaiserWidth(const double rejection, const int order)
+{
+ double w_t = 2.0 * M_PI;
+
+ if(rejection > 21.0)
+ return (rejection - 7.95) / (order * 2.285 * w_t);
+
+ return 5.79 / (order * w_t);
+}
+
+static double CalcKaiserBeta(const double rejection)
+{
+ if(rejection > 50.0)
+ return 0.1102 * (rejection - 8.7);
+ else if(rejection >= 21.0)
+ return (0.5842 * pow(rejection - 21.0, 0.4)) +
+ (0.07886 * (rejection - 21.0));
+ return 0.0;
+}
+
+/* Generates the coefficient, delta, and index tables required by the bsinc resampler */
+static void BsiGenerateTables()
+{
+ static double filter[BSINC_SCALE_COUNT][BSINC_PHASE_COUNT + 1][2 * BSINC_POINTS_MIN];
+ static double scDeltas[BSINC_SCALE_COUNT - 1][BSINC_PHASE_COUNT][2 * BSINC_POINTS_MIN];
+ static double phDeltas[BSINC_SCALE_COUNT][BSINC_PHASE_COUNT + 1][2 * BSINC_POINTS_MIN];
+ static double spDeltas[BSINC_SCALE_COUNT - 1][BSINC_PHASE_COUNT][2 * BSINC_POINTS_MIN];
+ static int mt[BSINC_SCALE_COUNT];
+ static double at[BSINC_SCALE_COUNT];
+ double width, beta, scaleBase, scaleRange;
+ int si, pi, i;
+
+ memset(filter, 0, sizeof(filter));
+ memset(scDeltas, 0, sizeof(scDeltas));
+ memset(phDeltas, 0, sizeof(phDeltas));
+ memset(spDeltas, 0, sizeof(spDeltas));
+
+ /* Calculate windowing parameters. The width describes the transition
+ band, but it may vary due to the linear interpolation between scales
+ of the filter.
+ */
+ width = CalcKaiserWidth(BSINC_REJECTION, BSINC_POINTS_MIN);
+ beta = CalcKaiserBeta(BSINC_REJECTION);
+ scaleBase = width / 2.0;
+ scaleRange = 1.0 - scaleBase;
+
+ // Determine filter scaling.
+ for(si = 0; si < BSINC_SCALE_COUNT; si++)
+ {
+ const double scale = scaleBase + (scaleRange * si / (BSINC_SCALE_COUNT - 1));
+ const double a = MinDouble(BSINC_POINTS_MIN, BSINC_POINTS_MIN / (2.0 * scale));
+ int m = 2 * (int)floor(a);
+
+ // Make sure the number of points is a multiple of 4 (for SSE).
+ m += ~(m - 1) & 3;
+
+ mt[si] = m;
+ at[si] = a;
+ }
+
+ /* Calculate the Kaiser-windowed Sinc filter coefficients for each scale
+ and phase.
+ */
+ for(si = 0; si < BSINC_SCALE_COUNT; si++)
+ {
+ const int m = mt[si];
+ const int o = BSINC_POINTS_MIN - (m / 2);
+ const int l = (m / 2) - 1;
+ const double a = at[si];
+ const double scale = scaleBase + (scaleRange * si / (BSINC_SCALE_COUNT - 1));
+ const double cutoff = (0.5 * scale) - (scaleBase * MaxDouble(0.5, scale));
+
+ for(pi = 0; pi <= BSINC_PHASE_COUNT; pi++)
+ {
+ const double phase = l + ((double)pi / BSINC_PHASE_COUNT);
+
+ for(i = 0; i < m; i++)
+ {
+ const double x = i - phase;
+ filter[si][pi][o + i] = Kaiser(beta, x / a) * 2.0 * cutoff * Sinc(2.0 * cutoff * x);
+ }
+ }
+ }
+
+ /* Linear interpolation between scales is simplified by pre-calculating
+ the delta (b - a) in: x = a + f (b - a)
+
+ Given a difference in points between scales, the destination points
+ will be 0, thus: x = a + f (-a)
+ */
+ for(si = 0; si < (BSINC_SCALE_COUNT - 1); si++)
+ {
+ const int m = mt[si];
+ const int o = BSINC_POINTS_MIN - (m / 2);
+
+ for(pi = 0; pi < BSINC_PHASE_COUNT; pi++)
+ {
+ for(i = 0; i < m; i++)
+ scDeltas[si][pi][o + i] = filter[si + 1][pi][o + i] - filter[si][pi][o + i];
+ }
+ }
+
+ // Linear interpolation between phases is also simplified.
+ for(si = 0; si < BSINC_SCALE_COUNT; si++)
+ {
+ const int m = mt[si];
+ const int o = BSINC_POINTS_MIN - (m / 2);
+
+ for(pi = 0; pi < BSINC_PHASE_COUNT; pi++)
+ {
+ for(i = 0; i < m; i++)
+ phDeltas[si][pi][o + i] = filter[si][pi + 1][o + i] - filter[si][pi][o + i];
+ }
+ }
+
+ /* This last simplification is done to complete the bilinear equation for
+ the combination of scale and phase.
+ */
+ for(si = 0; si < (BSINC_SCALE_COUNT - 1); si++)
+ {
+ const int m = mt[si];
+ const int o = BSINC_POINTS_MIN - (m / 2);
+
+ for(pi = 0; pi < BSINC_PHASE_COUNT; pi++)
+ {
+ for(i = 0; i < m; i++)
+ spDeltas[si][pi][o + i] = phDeltas[si + 1][pi][o + i] - phDeltas[si][pi][o + i];
+ }
+ }
+
+ // Calculate the table size.
+ i = mt[0];
+ for(si = 1; si < BSINC_SCALE_COUNT; si++)
+ i += BSINC_PHASE_COUNT * mt[si];
+ for(si = 0; si < (BSINC_SCALE_COUNT - 1); si++)
+ i += 2 * BSINC_PHASE_COUNT * mt[si];
+ for(si = 1; si < BSINC_SCALE_COUNT; si++)
+ i += BSINC_PHASE_COUNT * mt[si];
+
+ fprintf(stdout, "static const float bsincTab[%d] =\n{\n", i);
+
+ /* Only output enough coefficients for the first (cut) scale as needed to
+ perform interpolation without extra branching.
+ */
+ fprintf(stdout, " /* %2d,%2d */", mt[0], 0);
+ for(i = 0; i < mt[0]; i++)
+ fprintf(stdout, " %+14.9ef,", filter[0][0][i]);
+ fprintf(stdout, "\n\n");
+
+ for(si = 1; si < BSINC_SCALE_COUNT; si++)
+ {
+ const int m = mt[si];
+ const int o = BSINC_POINTS_MIN - (m / 2);
+
+ for(pi = 0; pi < BSINC_PHASE_COUNT; pi++)
+ {
+ fprintf(stdout, " /* %2d,%2d */", m, pi);
+ for(i = 0; i < m; i++)
+ fprintf(stdout, " %+14.9ef,", filter[si][pi][o + i]);
+ fprintf(stdout, "\n");
+ }
+ }
+ fprintf(stdout, "\n");
+
+ // There are N-1 scale deltas for N scales.
+ for(si = 0; si < (BSINC_SCALE_COUNT - 1); si++)
+ {
+ const int m = mt[si];
+ const int o = BSINC_POINTS_MIN - (m / 2);
+
+ for(pi = 0; pi < BSINC_PHASE_COUNT; pi++)
+ {
+ fprintf(stdout, " /* %2d,%2d */", m, pi);
+ for(i = 0; i < m; i++)
+ fprintf(stdout, " %+14.9ef,", scDeltas[si][pi][o + i]);
+ fprintf(stdout, "\n");
+ }
+ }
+ fprintf(stdout, "\n");
+
+ // Exclude phases for the first (cut) scale.
+ for(si = 1; si < BSINC_SCALE_COUNT; si++)
+ {
+ const int m = mt[si];
+ const int o = BSINC_POINTS_MIN - (m / 2);
+
+ for(pi = 0; pi < BSINC_PHASE_COUNT; pi++)
+ {
+ fprintf(stdout, " /* %2d,%2d */", m, pi);
+ for(i = 0; i < m; i++)
+ fprintf(stdout, " %+14.9ef,", phDeltas[si][pi][o + i]);
+ fprintf(stdout, "\n");
+ }
+ }
+ fprintf(stdout, "\n");
+
+ for(si = 0; si < (BSINC_SCALE_COUNT - 1); si++)
+ {
+ const int m = mt[si];
+ const int o = BSINC_POINTS_MIN - (m / 2);
+
+ for(pi = 0; pi < BSINC_PHASE_COUNT; pi++)
+ {
+ fprintf(stdout, " /* %2d,%2d */", m, pi);
+ for(i = 0; i < m; i++)
+ fprintf(stdout, " %+14.9ef,", spDeltas[si][pi][o + i]);
+ fprintf(stdout, "\n");
+ }
+ }
+ fprintf(stdout, "};\n\n");
+
+ /* The scaleBase is calculated from the Kaiser window transition width.
+ It represents the absolute limit to the filter before it fully cuts
+ the signal. The limit in octaves can be calculated by taking the
+ base-2 logarithm of its inverse: log_2(1 / scaleBase)
+ */
+ fprintf(stdout, " static const ALfloat scaleBase = %.9ef, scaleRange = %.9ef;\n", scaleBase, 1.0 / scaleRange);
+ fprintf(stdout, " static const ALuint m[BSINC_SCALE_COUNT] = {");
+
+ fprintf(stdout, " %d", mt[0]);
+ for(si = 1; si < BSINC_SCALE_COUNT; si++)
+ fprintf(stdout, ", %d", mt[si]);
+
+ fprintf(stdout, " };\n");
+ fprintf(stdout, " static const ALuint to[4][BSINC_SCALE_COUNT] =\n {\n { 0");
+
+ i = mt[0];
+ for(si = 1; si < BSINC_SCALE_COUNT; si++)
+ {
+ fprintf(stdout, ", %d", i);
+ i += BSINC_PHASE_COUNT * mt[si];
+ }
+ fprintf(stdout, " },\n {");
+ for(si = 0; si < (BSINC_SCALE_COUNT - 1); si++)
+ {
+ fprintf(stdout, " %d,", i);
+ i += BSINC_PHASE_COUNT * mt[si];
+ }
+ fprintf(stdout, " 0 },\n { 0");
+ for(si = 1; si < BSINC_SCALE_COUNT; si++)
+ {
+ fprintf(stdout, ", %d", i);
+ i += BSINC_PHASE_COUNT * mt[si];
+ }
+ fprintf (stdout, " },\n {");
+ for(si = 0; si < (BSINC_SCALE_COUNT - 1); si++)
+ {
+ fprintf(stdout, " %d,", i);
+ i += BSINC_PHASE_COUNT * mt[si];
+ }
+ fprintf(stdout, " 0 }\n };\n");
+
+ fprintf(stdout, " static const ALuint tm[2][BSINC_SCALE_COUNT] = \n {\n { 0");
+ for(si = 1; si < BSINC_SCALE_COUNT; si++)
+ fprintf(stdout, ", %d", mt[si]);
+ fprintf(stdout, " },\n {");
+ for(si = 0; si < (BSINC_SCALE_COUNT - 1); si++)
+ fprintf(stdout, " %d,", mt[si]);
+ fprintf(stdout, " 0 }\n };\n");
+}
+
+int main(void)
+{
+ BsiGenerateTables();
+ return 0;
+}
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