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/*
* Copyright 2009 Phil Burk, Mobileer Inc
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package com.jsyn.engine;
/*
* Multiple tables of sawtooth data.
* organized by octaves below the Nyquist Rate.
* used to generate band-limited Sawtooth, Impulse, Pulse, Square and Triangle BL waveforms
*
<pre>
Analysis of octave requirements for tables.
OctavesIndex Frequency Partials
0 N/2 11025 1
1 N/4 5512 2
2 N/8 2756 4
3 N/16 1378 8
4 N/32 689 16
5 N/64 344 32
6 N/128 172 64
7 N/256 86 128
</pre>
*
* @author Phil Burk (C) 2009 Mobileer Inc
*/
public class MultiTable {
public final static int NUM_TABLES = 8;
public final static int CYCLE_SIZE = (1 << 10);
private static MultiTable instance = new MultiTable(NUM_TABLES, CYCLE_SIZE);
private double phaseScalar;
private float[][] tables; // array of array of tables
/**************************************************************************
* Initialize sawtooth wavetables. Table[0] should contain a pure sine wave. Succeeding tables
* should have increasing numbers of partials.
*/
public MultiTable(int numTables, int cycleSize) {
int tableSize = cycleSize + 1;
// Allocate array of arrays.
tables = new float[numTables][tableSize];
float[] sineTable = tables[0];
phaseScalar = (float) (cycleSize * 0.5);
/* Fill initial sine table with values for -PI to PI. */
for (int j = 0; j < tableSize; j++) {
sineTable[j] = (float) Math.sin(((((double) j) / (double) cycleSize) * Math.PI * 2.0)
- Math.PI);
}
/*
* Build each table from scratch and scale partials by raised cosine* to eliminate Gibbs
* effect.
*/
for (int i = 1; i < numTables; i++) {
int numPartials;
double kGibbs;
float[] table = tables[i];
/* Add together partials for this table. */
numPartials = 1 << i;
kGibbs = Math.PI / (2 * numPartials);
for (int k = 0; k < numPartials; k++) {
double ampl, cGibbs;
int sineIndex = 0;
int partial = k + 1;
cGibbs = Math.cos(k * kGibbs);
/* Calculate amplitude for Nth partial */
ampl = cGibbs * cGibbs / partial;
for (int j = 0; j < tableSize; j++) {
table[j] += (float) ampl * sineTable[sineIndex];
sineIndex += partial;
/* Wrap index at end of table.. */
if (sineIndex >= cycleSize) {
sineIndex -= cycleSize;
}
}
}
}
/* Normalize after */
for (int i = 1; i < numTables; i++) {
normalizeArray(tables[i]);
}
}
/**************************************************************************/
public static float normalizeArray(float[] fdata) {
float max, val, gain;
int i;
// determine maximum value.
max = 0.0f;
for (i = 0; i < fdata.length; i++) {
val = Math.abs(fdata[i]);
if (val > max)
max = val;
}
if (max < 0.0000001f)
max = 0.0000001f;
// scale array
gain = 1.0f / max;
for (i = 0; i < fdata.length; i++)
fdata[i] *= gain;
return gain;
}
/*****************************************************************************
* When the phaseInc maps to the highest level table, then we start interpolating between the
* highest table and the raw sawtooth value (phase). When phaseInc points to highest table:
* flevel = NUM_TABLES - 1 = -1 - log2(pInc); log2(pInc) = - NUM_TABLES pInc = 2**(-NUM_TABLES)
*/
private final static double LOWEST_PHASE_INC_INV = (1 << NUM_TABLES);
/**************************************************************************/
/* Phase ranges from -1.0 to +1.0 */
public double calculateSawtooth(double currentPhase, double positivePhaseIncrement,
double flevel) {
float[] tableBase;
double val;
double hiSam; /* Use when verticalFraction is 1.0 */
double loSam; /* Use when verticalFraction is 0.0 */
double sam1, sam2;
/* Use Phase to determine sampleIndex into table. */
double findex = ((phaseScalar * currentPhase) + phaseScalar);
// findex is > 0 so we do not need to call floor().
int sampleIndex = (int) findex;
double horizontalFraction = findex - sampleIndex;
int tableIndex = (int) flevel;
if (tableIndex > (NUM_TABLES - 2)) {
/*
* Just use top table and mix with arithmetic sawtooth if below lowest frequency.
* Generate new fraction for interpolating between 0.0 and lowest table frequency.
*/
double fraction = positivePhaseIncrement * LOWEST_PHASE_INC_INV;
tableBase = tables[(NUM_TABLES - 1)];
/* Get adjacent samples. Assume guard point present. */
sam1 = tableBase[sampleIndex];
sam2 = tableBase[sampleIndex + 1];
/* Interpolate between adjacent samples. */
loSam = sam1 + (horizontalFraction * (sam2 - sam1));
/* Use arithmetic version for low frequencies. */
/* fraction is 0.0 at 0 Hz */
val = currentPhase + (fraction * (loSam - currentPhase));
} else {
double verticalFraction = flevel - tableIndex;
if (tableIndex < 0) {
if (tableIndex < -1) // above Nyquist!
{
val = 0.0;
} else {
/*
* At top of supported range, interpolate between 0.0 and first partial.
*/
tableBase = tables[0]; /* Sine wave table. */
/* Get adjacent samples. Assume guard point present. */
sam1 = tableBase[sampleIndex];
sam2 = tableBase[sampleIndex + 1];
/* Interpolate between adjacent samples. */
hiSam = sam1 + (horizontalFraction * (sam2 - sam1));
/* loSam = 0.0 */
// verticalFraction is 0.0 at Nyquist
val = verticalFraction * hiSam;
}
} else {
/*
* Interpolate between adjacent levels to prevent harmonics from popping.
*/
tableBase = tables[tableIndex + 1];
/* Get adjacent samples. Assume guard point present. */
sam1 = tableBase[sampleIndex];
sam2 = tableBase[sampleIndex + 1];
/* Interpolate between adjacent samples. */
hiSam = sam1 + (horizontalFraction * (sam2 - sam1));
/* Get adjacent samples. Assume guard point present. */
tableBase = tables[tableIndex];
sam1 = tableBase[sampleIndex];
sam2 = tableBase[sampleIndex + 1];
/* Interpolate between adjacent samples. */
loSam = sam1 + (horizontalFraction * (sam2 - sam1));
val = loSam + (verticalFraction * (hiSam - loSam));
}
}
return val;
}
public double convertPhaseIncrementToLevel(double positivePhaseIncrement) {
if (positivePhaseIncrement < 1.0e-30) {
positivePhaseIncrement = 1.0e-30;
}
return -1.0 - (Math.log(positivePhaseIncrement) / Math.log(2.0));
}
public static MultiTable getInstance() {
return instance;
}
}
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