Band limited Sawtooth wavetable C++ generator for "Arbitrary Waveform" (and its use)

[silveiraGo]

Band limited Sawtooth wavetable C++ generator for "Arbitrary Waveform" (and its use)

Hi, Teensy has this amazing audio lib, which we all love, but the fact of not having band limited waveforms was not allowing me to put the board in a real project. So, I've been trying to get around this limitation writing my own band limited wave forms. I got the first one, sawtooth, but I'll need some help to get the other ones, but I'll do another post just for that. So, here is how I did it and how you can do it. And please, correct me in anything that might be wrong and make any improvement that you want and share it back.

First we need to generate a wavetable that works with the Arbitrary Wave form. For that, the wavetable must be an array of "int16_t" values, which will give us values from -32767 to 32767. This array, must have 257 values, being the last the same as the first. So, this array should be like:

 const int16_t sawtoothWavetable[257] = {};

For generating one wavetable I created this c++ code. Where you can choose the table size, its resolution and how many harmonics there will be. It will generate a .h file, which you should put in your Arduino sketch folder.

//
//  main.cpp
//  Sawtooh wavetable
//
//  Created by Gustavo Silveira on 1/26/17.
//  Copyright © 2017 Gustavo Silveira. All rights reserved.
//  Sawtooth wavetable generator


#include <fstream>
#include <sstream>
#include <iostream>
#include <string>
#include <math.h>

using namespace std;

float scaleBetween(float unscaledNum, float minAllowed, float maxAllowed, float min, float max) { //scaling function
    return (maxAllowed - minAllowed) * (unscaledNum - min) / (max - min) + minAllowed;
}

const int tableSize = 256; // the size of your wavetable
const float PI = 3.141592653589793238462643;
float angularFreq = (2* PI)/tableSize;
float table[tableSize] = {0};
float output;
int16_t scaledOutput;

float maxAmp = 1;
float numberOfHarmonics = 27; //choose how many harmonics your tabke will have

float minValue = 0; //those will be used for normalizing the wavetable
float maxValue = 0;

int16_t resolution = 32767; //how big the biggest value will be. Use "32767" for teensy

int main(int argc, const char * argv[]) {
    
    //open file
    ofstream myFile;
    
    //This is the file the wavetable is going to show up in.
    myFile.open("sawtoothWave257_16bit200h.h");
    
    myFile << "const int16_t sawtoothWaveTable16bit[257] = {";
    
    for (int n=0; n<tableSize; n++) { //creates a Sawtooth wavetable
        
        for(int m=0; m<numberOfHarmonics; m++) {

            table[n] = (table[n] + ( (maxAmp/(m+1) * sin((angularFreq*(m+1))*n)))); //sawtooth formula
        }
        
        if (table[n] > maxValue) { //checks highest value
            maxValue = table[n];
        }
        if (table[n] < minValue) { //checks lowest value
            minValue = table[n];
        }

    }
    
    cout <<"maxValue = ";
    cout << maxValue;
    cout <<" | minValue = ";
    cout << minValue;
    
    
    for (int i=0; i<tableSize; i++) { // normalize the table
        
        output = table[i];
        output = scaleBetween(output, resolution*(-1), resolution, minValue, maxValue);
        output = round(output);
        myFile << output; // writes each scaled value in the table
        myFile << ",";
    }
    
    myFile << "0};"; // the table needs this last value
    //close connection to text file
    
    myFile.close();
    
    return 0;
    
}

Which should look like this:

const int16_t sawtoothWaveTable16bit[257] = {0, 11872, 21985, 29041, 32523, 32767, 30792, 27938, 25440, 24097, 24105, 25114, 26456, 27444, 27637, 26973, 25741, 24425, 23485, 23178, 23474, 24097, 24663, 24843, 24501, 23725, 22783, 21987, 21570, 21587, 21907, 22278, 22445, 22252, 21705, 20962, 20253, 19783, 19645, 19785, 20034, 20183, 20076, 19674, 19064, 18419, 17923, 17684, 17700, 17856, 17984, 17933, 17632, 17123, 16535, 16026, 15717, 15638, 15718, 15821, 15804, 15581, 15155, 14619, 14110, 13749, 13592, 13605, 13680, 13685, 13522, 13168, 12681, 12179, 11781, 11561, 11512, 11555, 11571, 11457, 11165, 10727, 10239, 9815, 9540, 9434, 9442, 9462, 9385, 9149, 8760, 8291, 7849, 7529, 7369, 7340, 7355, 7307, 7121, 6780, 6336, 5886, 5527, 5317, 5248, 5250, 5224, 5082, 4789, 4375, 3923, 3532, 3275, 3164, 3149, 3137, 3034, 2788, 2408, 1961, 1546, 1244, 1089, 1050, 1045, 977, 777, 434, -0, -434, -777, -977, -1045, -1050, -1089, -1244, -1546, -1961, -2408, -2788, -3034, -3137, -3149, -3164, -3275, -3532, -3923, -4375, -4789, -5082, -5224, -5250, -5248, -5317, -5527, -5886, -6336, -6780, -7121, -7307, -7355, -7340, -7369, -7529, -7849, -8291, -8760, -9149, -9385, -9462, -9442, -9434, -9540, -9815, -10239, -10727, -11165, -11457, -11571, -11555, -11512, -11561, -11781, -12179, -12681, -13168, -13522, -13685, -13680, -13605, -13592, -13749, -14110, -14619, -15155, -15581, -15804, -15821, -15718, -15638, -15717, -16026, -16535, -17123, -17632, -17933, -17984, -17856, -17700, -17684, -17923, -18419, -19064, -19674, -20076, -20183, -20034, -19785, -19645, -19783, -20252, -20962, -21705, -22252, -22445, -22278, -21907, -21587, -21570, -21987, -22783, -23725, -24501, -24843, -24663, -24097, -23474, -23178, -23485, -24425, -25741, -26973, -27637, -27444, -26456, -25114, -24105, -24097, -25440, -27938, -30793, -32767, -32523, -29041, -21985, -11872, 0};

An you can use this table with the arbitrary waveform. But, this is only one table, which will not be enough, you will have aliasing when its harmonics overthrow the nyquist. So, you need several wavetables. So, for that, I created this other c++ code. This will generate a two dimensional array. In this case an array that will contain 45 tables, like:

const int16_t sawtoothWavetable[45][257] = {{},{}};

Every 3 three notes get a new table. And every new table will calculate the number of harmonics, up to the nyquist, necessary to fulfill the table. To make this code work, you will need to put this "midiFrequencies.h" file with your main.cpp code. So, this is the code:

//
//  main.cpp
//  Sawtooth wavetable
//
//  Created by Gustavo Silveira on 1/26/17.
//  Copyright © 2017 Gustavo Silveira. All rights reserved.
//  Sawtooth wavetables generator


#include <fstream>
#include <sstream>
#include <iostream>
#include <string>
#include <math.h>

#include "midiFrequencies.h"

using namespace std;

float scaleBetween(float unscaledNum, float minAllowed, float maxAllowed, float min, float max) { //scaling function
    return (maxAllowed - minAllowed) * (unscaledNum - min) / (max - min) + minAllowed;
}

//const int16_t sampleRate = 44100;
const int16_t nyquist = 21000;

const int tableSize = 256; // the size of your wavetable
const int numberOfTables = 45;
//const int notesInTables = nyquist/numberOfTables;
const float PI = 3.141592653589793238462643;
//float phase = PI; //Uncoment this if you want to flip the wave phase
float phase = 0;
float angularFreq = (2* PI)/tableSize;
float table[numberOfTables][tableSize] = {{0},{0}};

float output;
int16_t scaledOutput;

float maxAmp = 1;
int numberOfHarmonics; //those will be calculated in the loop

float minValue = 0; //those will be used for normalizing the scale
float maxValue = 0;

int16_t resolution = 32767; //how big the biggest value will be


int z = 0;

int main(int argc, const char * argv[]) {
    
    
    //open file
    ofstream myFile;
    
    //This is the file the wavetable is going to show up in.
    myFile.open("sawtoothWave[45][257].h");
    
    myFile << "const int16_t sawtoothWavetable[45][257] = {";
    
    for (int t=0; t<numberOfTables; t++) {
        
        numberOfHarmonics = round(nyquist/midiFrequencies[z]); //skips every three notes
        
        for (int n=0; n<tableSize; n++) { //creates a Sawtooth wavetable
            
            for(int m=0; m<numberOfHarmonics; m++) {
                
                table[t][n] = (table[t][n] + ( (maxAmp/(m+1) * sin((angularFreq*(m+1))*n + (phase))))); //sawtooth formula
            }
            
            if (table[t][n] > maxValue) { //checks highest value
                maxValue = table[t][n];
            }
            if (table[t][n] < minValue) { //checks lowest value
                minValue = table[t][n];
            }
            
        }
        z = z+3;
    }
    
    // numberOfHarmonics = nyquist/midiFrequencies[z]; //skips every three notes
    cout <<"maxValue = ";
    cout << maxValue;
    cout <<" | minValue = ";
    cout << minValue;
    
    for (int t=0; t<numberOfTables; t++) {
        myFile << "{";
        
        for (int i=0; i<tableSize; i++) { // normalize the table
            
            output = table[t][i];
            output = scaleBetween(output, resolution*(-1), resolution, minValue, maxValue);
            output = round(output);
            myFile << output; // writes each scaled value in the table
            myFile << ",";
        }
        
        myFile << "0}, \n"; // the table needs this last value
        //close connection to text file
    }
    myFile << "};";
    
    myFile.close();
    
    return 0;
    
}

Which will generate a file like this:

const int16_t sawtoothWavetable[45][257] = {{-0,28053,27402,27407,27049,26921,26644,26460,26226,26008,25800,25562,25370,25120,24936,24681,24499,24245,24060,23810,23620,23377,23178,22945,22736,22512,22294,22080,21853,21646,21413,21211,20975,20774,20537,20337,20101,19898,19666,19459,19231,19019,18797,18579,18363,18139,17928,17700,17492,17262,17056,16824,16618,16388,16180,15952,15741,15516,15302,15081,14863,14646,14424,14211,13985,13775,13547,13338,13110,12901,12673,12463,12237,12025,11801,11586,11365,11147,10930,10709,10494,10270,10058,9832,9622,9395,9184,8958,8747,8521,8309,8086,7870,7650,7432,7214,6993,6778,6555,6342,6117,5905,5679,5468,5242,5031,4806,4593,4370,4154,3934,3716,3498,3277,3062,2839,2626,2401,2189,1964,1752,1526,1315,1090,877,654,439,218,0,-218,-439,-654,-877,-1090,-1315,-1526,-1752,-1964,-2189,-2401,-2626,-2839,-3062,-3277,-3498,-3716,-3934,-4154,-4370,-4593,-4806,-5031,-5242,-5468,-5679,-5905,-6117,-6342,-6555,-6778,-6993,-7214,-7432,-7650,-7870,-8085,-8309,-8521,-8747,-8958,-9184,-9395,-9622,-9832,-10058,-10270,-10494,-10709,-10930,-11147,-11365,-11586,-11801,-12025,-12237,-12463,-12673,-12901,-13110,-13338,-13547,-13775,-13986,-14211,-14424,-14646,-14863,-15081,-15302,-15516,-15741,-15952,-16180,-16388,-16618,-16824,-17056,-17262,-17492,-17700,-17928,-18139,-18363,-18579,-18797,-19019,-19231,-19459,-19666,-19898,-20101,-20337,-20538,-20774,-20975,-21211,-21413,-21646,-21853,-22080,-22294,-22512,-22736,-22945,-23178,-23377,-23620,-23810,-24061,-24245,-24500,-24681,-24936,-25120,-25370,-25562,-25801,-26008,-26226,-26460,-26645,-26922,-27049,-27407,-27402,-28053,0}, 
{-0,27413,27379,27227,27045,26850,26648,26443,26234,26023,25810,25595,25379,25162,24943,24723,24503,24282,24060,23838,23616,23394,23172,22950,22728,22507,22286,22066,21846,21627,21409,21191,20973,20756,20539,20322,20106,19889,19673,19456,19239,19022,18805,18587,18369,18151,17932,17712,17493,17273,17053,16833,16613,16393,16173,15953,15733,15514,15295,15076,14857,14639,14420,14203,13985,13767,13550,13332,13115,12898,12680,12463,12245,12027,11809,11590,11372,11153,10933,10714,10495,10275,10056,9836,9616,9397,9177,8958,8739,8520,8301,8083,7864,7646,7428,7210,6993,6775,6558,6340,6122,5904,5687,5468,5250,5032,4813,4594,4375,4156,3937,3718,3498,3279,3059,2840,2620,2401,2182,1963,1744,1526,1307,1089,871,653,435,218,0,-218,-435,-653,-871,-1089,-1307,-1526,-1744,-1963,-2182,-2401,-2620,-2840,-3059,-3279,-3498,-3718,-3937,-4156,-4376,-4595,-4813,-5032,-5250,-5469,-5687,-5904,-6122,-6340,-6558,-6775,-6993,-7211,-7428,-7646,-7864,-8083,-8301,-8520,-8739,-8958,-9177,-9397,-9616,-9836,-10056,-10275,-10495,-10714,-10934,-11153,-11372,-11590,-11809,-12027,-12245,-12463,-12680,-12898,-13115,-13332,-13550,-13767,-13985,-14203,-14420,-14639,-14857,-15076,-15295,-15514,-15733,-15953,-16173,-16393,-16613,-16833,-17054,-17273,-17493,-17713,-17932,-18151,-18369,-18588,-18805,-19022,-19239,-19456,-19673,-19890,-20106,-20323,-20539,-20756,-20973,-21191,-21409,-21627,-21846,-22066,-22286,-22507,-22728,-22950,-23171,-23394,-23616,-23838,-24060,-24282,-24503,-24723,-24943,-25162,-25379,-25595,-25810,-26023,-26234,-26443,-26648,-26850,-27045,-27227,-27379,-27413,0}, 
{-0,27907,27706,27204,27079,26970,26638,26404,26276,26018,25751,25593,25379,25107,24916,24727,24466,24247,24066,23825,23587,23401,23180,22933,22734,22529,22284,22069,21873,21637,21408,21213,20989,20752,20550,20338,20100,19887,19684,19450,19227,19026,18800,18569,18365,18149,17915,17704,17496,17263,17043,16839,16613,16385,16180,15961,15730,15520,15308,15077,14859,14652,14425,14201,13994,13774,13545,13335,13121,12891,12675,12466,12239,12017,11809,11587,11360,11150,10934,10705,10491,10279,10052,9832,9623,9400,9174,8965,8747,8519,8306,8093,7865,7647,7437,7213,6989,6780,6560,6333,6121,5907,5679,5462,5251,5026,4804,4594,4373,4148,3936,3720,3493,3277,3065,2840,2619,2409,2187,1962,1751,1534,1307,1092,879,653,434,224,0,-224,-434,-653,-879,-1092,-1307,-1534,-1751,-1962,-2187,-2409,-2619,-2839,-3065,-3277,-3493,-3720,-3936,-4148,-4373,-4594,-4804,-5026,-5251,-5462,-5679,-5907,-6121,-6333,-6560,-6780,-6989,-7213,-7437,-7647,-7865,-8093,-8306,-8519,-8747,-8965,-9174,-9400,-9623,-9832,-10052,-10279,-10491,-10705,-10934,-11150,-11360,-11587,-11809,-12016,-12239,-12466,-12675,-12891,-13121,-13335,-13545,-13774,-13994,-14201,-14425,-14652,-14860,-15077,-15308,-15520,-15730,-15961,-16180,-16385,-16613,-16839,-17044,-17263,-17496,-17704,-17915,-18149,-18365,-18570,-18800,-19026,-19227,-19450,-19684,-19887,-20100,-20338,-20550,-20752,-20989,-21213,-21408,-21637,-21873,-22069,-22284,-22529,-22734,-22933,-23180,-23401,-23587,-23825,-24067,-24247,-24466,-24727,-24916,-25107,-25379,-25593,-25751,-26019,-26277,-26404,-26638,-26970,-27079,-27204,-27706,-27907,0}, 
{-0,28103,27568,27185,27226,26839,26637,26516,26174,26024,25821,25528,25387,25137,24891,24733,24463,24255,24069,23801,23615,23400,23147,22969,22730,22500,22315,22064,21855,21654,21404,21210,20990,20750,20560,20325,20101,19905,19662,19453,19245,19004,18805,18583,18350,18153,17920,17699,17497,17259,17050,16838,16602,16400,16177,15948,15747,15515,15297,15091,14856,14647,14432,14199,13995,13771,13545,13342,13111,12894,12685,12452,12243,12026,11796,11591,11366,11142,10937,10706,10490,10280,10048,9839,9621,9392,9186,8961,8739,8532,8301,8087,7874,7644,7435,7215,6988,6782,6556,6335,6127,5897,5683,5469,5240,5031,4810,4585,4378,4151,3932,3722,3492,3280,3064,2835,2627,2405,2181,1973,1746,1528,1317,1087,876,659,431,223,-0,-223,-431,-659,-876,-1087,-1317,-1528,-1746,-1973,-2181,-2405,-2627,-2835,-3064,-3280,-3492,-3722,-3932,-4151,-4378,-4585,-4810,-5031,-5240,-5469,-5683,-5897,-6127,-6335,-6556,-6782,-6988,-7215,-7435,-7644,-7874,-8087,-8301,-8532,-8739,-8961,-9186,-9392,-9621,-9839,-10048,-10280,-10490,-10706,-10937,-11142,-11366,-11591,-11796,-12026,-12243,-12452,-12685,-12894,-13111,-13342,-13545,-13771,-13995,-14199,-14432,-14647,-14856,-15091,-15297,-15515,-15747,-15948,-16177,-16400,-16602,-16838,-17050,-17259,-17497,-17699,-17920,-18153,-18350,-18583,-18805,-19004,-19245,-19453,-19662,-19905,-20101,-20325,-20560,-20750,-20990,-21210,-21404,-21654,-21855,-22064,-22315,-22500,-22730,-22969,-23147,-23400,-23615,-23800,-24069,-24255,-24463,-24733,-24891,-25137,-25387,-25528,-25822,-26025,-26174,-26516,-26637,-26838,-27226,-27185,-27568,-28103,0}, 
{-0,27831,27835,27270,26963,26936,26753,26399,26172,26058,25832,25530,25330,25178,24934,24661,24474,24298,24045,23794,23611,23416,23161,22927,22744,22534,22281,22060,21874,21652,21404,21193,21001,20771,20529,20326,20127,19890,19656,19457,19250,19011,18785,18587,18372,18133,17914,17716,17494,17256,17044,16843,16615,16382,16174,15968,15737,15508,15304,15092,14859,14636,14432,14216,13982,13764,13560,13338,13106,12893,12687,12461,12231,12022,11813,11583,11357,11151,10937,10706,10485,10279,10061,9830,9612,9406,9184,8954,8741,8533,8307,8079,7869,7658,7430,7206,6998,6783,6553,6333,6125,5907,5677,5460,5253,5030,4802,4588,4379,4154,3927,3717,3505,3277,3053,2845,2629,2400,2180,1972,1753,1524,1308,1100,877,649,436,226,-0,-226,-436,-649,-877,-1100,-1308,-1524,-1753,-1972,-2180,-2400,-2629,-2845,-3053,-3277,-3505,-3717,-3927,-4153,-4379,-4589,-4802,-5030,-5253,-5460,-5677,-5907,-6125,-6333,-6553,-6783,-6998,-7206,-7430,-7658,-7869,-8079,-8307,-8533,-8741,-8954,-9184,-9406,-9613,-9830,-10061,-10279,-10485,-10706,-10937,-11151,-11357,-11583,-11813,-12022,-12231,-12461,-12687,-12893,-13106,-13338,-13560,-13764,-13982,-14216,-14432,-14636,-14859,-15092,-15304,-15508,-15737,-15968,-16174,-16382,-16615,-16843,-17044,-17256,-17494,-17716,-17914,-18133,-18372,-18587,-18785,-19011,-19250,-19457,-19656,-19890,-20127,-20326,-20529,-20771,-21001,-21193,-21404,-21652,-21874,-22060,-22281,-22534,-22744,-22927,-23161,-23416,-23611,-23793,-24045,-24298,-24474,-24661,-24934,-25178,-25330,-25530,-25832,-26058,-26172,-26399,-26753,-26936,-26963,-27270,-27835,-27831,0}, 
{-0,27058,27196,27099,26944,26765,26574,26376,26173,25968,25761,25552,25341,25130,24917,24704,24490,24275,24060,23844,23628,23411,23194,22977,22759,22541,22322,22103,21884,21665,21445,21225,21005,20785,20564,20344,20123,19902,19682,19461,19240,19020,18799,18579,18358,18138,17918,17698,17478,17258,17038,16819,16600,16380,16161,15943,15724,15506,15287,15069,14851,14633,14416,14198,13980,13763,13546,13328,13111,12894,12676,12459,12242,12024,11807,11589,11372,11154,10936,10719,10501,10283,10064,9846,9628,9409,9190,8972,8753,8534,8315,8095,7876,7657,7437,7218,6998,6779,6559,6339,6120,5900,5681,5461,5242,5022,4803,4584,4364,4145,3926,3707,3489,3270,3051,2833,2614,2396,2178,1960,1742,1524,1306,1088,871,653,435,218,-0,-218,-435,-653,-871,-1088,-1306,-1524,-1742,-1960,-2178,-2396,-2614,-2833,-3051,-3270,-3489,-3707,-3926,-4145,-4364,-4584,-4803,-5022,-5242,-5461,-5681,-5900,-6120,-6339,-6559,-6779,-6998,-7218,-7437,-7657,-7876,-8095,-8314,-8534,-8753,-8972,-9190,-9409,-9628,-9846,-10064,-10283,-10501,-10719,-10936,-11154,-11372,-11589,-11807,-12024,-12242,-12459,-12676,-12894,-13111,-13328,-13546,-13763,-13980,-14198,-14416,-14633,-14851,-15069,-15287,-15506,-15724,-15943,-16162,-16380,-16600,-16819,-17038,-17258,-17478,-17698,-17918,-18138,-18358,-18579,-18799,-19020,-19240,-19461,-19682,-19902,-20123,-20344,-20564,-20785,-21005,-21225,-21445,-21664,-21884,-22103,-22322,-22541,-22759,-22977,-23194,-23412,-23628,-23844,-24060,-24275,-24490,-24704,-24917,-25130,-25341,-25552,-25761,-25969,-26174,-26376,-26574,-26765,-26944,-27099,-27196,-27058,0}, 
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};

 

[silveiraGo]

Now we need to find a way to use it with Teensy. The way you use the Arbitrary Waveform is calling the right array. To do that I created a function that would convert frequency into an index, then this index would be used to call the right array. So, the way to do that is using like this:

waveform.arbitraryWaveform(sawtoothWavetable[oscFreqIndex(frequency)], maxFreq);

Being "oscFreqIndex: the function that will do the conversion. And forget "maxFreq, it's not being used by the library.

In the end I came up with a code like that:

#include <Audio.h>
#include <Wire.h>
#include <SPI.h>
#include <SD.h>
#include <SerialFlash.h>

// GUItool: begin automatically generated code
AudioSynthWaveform       waveform;      //xy=2631.2500381469727,2188.7500324249268
AudioMixer4              mixer;         //xy=2810,2223.75
AudioOutputI2S           i2s;           //xy=2973,2226
AudioConnection          patchCord1(waveform, 0, mixer, 0);
AudioConnection          patchCord2(mixer, 0, i2s, 0);
AudioConnection          patchCord3(mixer, 0, i2s, 1);
AudioControlSGTL5000     sgtl5000_1;     //xy=2841,2312
// GUItool: end automatically generated code



/* include some wavetables: the files need to contain arrays [256] of type const short int wt1[] = { ... } */


//#include "SineWave.h"
#include "sineWave257_16bit.h"
#include "sawtoohWave257_16bit.h"
#include "sawtoothWavetable.h"


// OSC 1
int osc1 = WAVEFORM_ARBITRARY;
float osc1freq = 440;
float osc1level = 0.5;
int osc1FreqIndex = (osc1freq / 3) + 1;

// OSC 2
int osc2 = WAVEFORM_SAWTOOTH;
int osc2freq = 150;
float osc2level = 0.5;

// mixers
float mixer1Gain0 = 0.5; // osc 1
float mixer1Gain1 = 0.5; // osc 2

int maxFreq = 20000;

void setup() {
  Serial.begin(9600);

  AudioMemory(12);
  Serial.begin(115200);
  sgtl5000_1.enable();
  sgtl5000_1.volume(0.45);

  waveform.begin(osc1level, osc1freq, osc1);

  waveform.arbitraryWaveform(sawtoothWavetable[oscFreqIndex(osc1freq)], maxFreq);

  mixer.gain(0, mixer1Gain0);


  waveform.frequency(osc1freq);

}

void loop() {


  waveform.begin(WAVEFORM_ARBITRARY);
  for (int i = 1; i < 110; i++) {
    waveform.arbitraryWaveform(sawtoothWavetable[oscFreqIndex(midiToFreq(i))], maxFreq);
    waveform.frequency(midiToFreq(i));
    delay(200);
  }

  delay(1000);
  waveform.begin(WAVEFORM_SAWTOOTH);
  for (int i = 1; i < 110; i++) {
    waveform.frequency(midiToFreq(i));
    delay(200);
  }

}

int oscFreqIndex(float freq)
{
  int freqIndex = (freqToMidi(freq) / 3) + 1;
  return freqIndex;
}

float midiToFreq(float midival)
{
  float f = 0.0;
  if (midival) f = 8.1757989156 * pow(2.0, midival / 12.0);
  return f;
}

float freqToMidi(float f)
{
  int midival = log(f / 440.0) / log(2) * 12 + 69;
  return midival;
}

This code compare the built in Sawtooth and my sawtooth, so you can compare the aliasing. Don't forget to put the wavetable ".h" file in the same folder as the arduino sketch.

So, people, what do you think?

 

[silveiraGo]

Here are the repository of the files: https://github.com/silveirago/Band-limited-Sawtooth-wave-form-C-generator

 

[jeppius]

Cool! I will take a look at it, I guess in terms of efficiency it is just comparable to an AudioSynthWaveform (plus some extra checking to select the appropiate table)? I am intrigued why AudioSynthWaveform is slower than AudioSynthWaveformSine by the way..