Add anti-aliasing/bandlimit for looped wav sample (NOT Fourier transform) - audio

Question

How to build antialiasing interpolation using c++ code? I have a simple 4096 or 1024 buffer. Of course when I play this at high frequencies I get aliasing issues. to avoid this, the signal must be limited by the bandwidth at high frequencies. Roughly speaking, the 'sawtooth' wave at high frequencies should looks like a regular sine. And that is what I want to get so that my sound didn't sound dirty like you moving knobs in your old FM/AM radio in your car.
I know how to build bandlimited square,triangle,sawtoth with Fourier transform. So my question is only about wavetable

Answer 1

Found solution in the AudioKit sources. One buffer will be split into 10 buffers/octaves. So when you play a sound, you don't play your original wave, but play a sample that was prepared for a specific octave.
Import to your project WaveStack.hpp
namespace AudioKitCore
{
// WaveStack represents a series of progressively lower-resolution sampled versions of a
// waveform. Client code supplies the initial waveform, at a resolution of 1024 samples,
// equivalent to 43.6 Hz at 44.1K samples/sec (about 23.44 cents below F1, midi note 29),
// and then calls initStack() to create the filtered higher-octave versions.
// This provides a basis for anti-aliased oscillators; see class WaveStackOscillator.
struct WaveStack
{
// Highest-resolution rep uses 2^maxBits samples
static constexpr int maxBits = 10; // 1024
// maxBits also defines the number of octave levels; highest level has just 2 samples
float *pData[maxBits];
WaveStack();
~WaveStack();
// Fill pWaveData with 1024 samples, then call this
void initStack(float *pWaveData, int maxHarmonic=512);
void init();
void deinit();
float interp(int octave, float phase);
};
}
WaveStack.cpp
#include "WaveStack.hpp"
#include "kiss_fftr.h"
namespace AudioKitCore
{
WaveStack::WaveStack()
{
int length = 1 << maxBits; // length of level-0 data
pData[0] = new float[2 * length]; // 2x is enough for all levels
for (int i=1; i<maxBits; i++)
{
pData[i] = pData[i - 1] + length;
length >>= 1;
}
}
WaveStack::~WaveStack()
{
delete[] pData[0];
}
void WaveStack::initStack(float *pWaveData, int maxHarmonic)
{
// setup
int fftLength = 1 << maxBits;
float *buf = new float[fftLength];
kiss_fftr_cfg fwd = kiss_fftr_alloc(fftLength, 0, 0, 0);
kiss_fftr_cfg inv = kiss_fftr_alloc(fftLength, 1, 0, 0);
// copy supplied wave data for octave 0
for (int i=0; i < fftLength; i++) pData[0][i] = pWaveData[i];
// perform initial forward FFT to get spectrum
kiss_fft_cpx spectrum[fftLength / 2 + 1];
kiss_fftr(fwd, pData[0], spectrum);
float scaleFactor = 1.0f / (fftLength / 2);
for (int octave = (maxHarmonic==512) ? 1 : 0; octave < maxBits; octave++)
{
// zero all harmonic coefficients above new Nyquist limit
int maxHarm = 1 << (maxBits - octave - 1);
if (maxHarm > maxHarmonic) maxHarm = maxHarmonic;
for (int h=maxHarm; h <= fftLength/2; h++)
{
spectrum[h].r = 0.0f;
spectrum[h].i = 0.0f;
}
// perform inverse FFT to get filtered waveform
kiss_fftri(inv, spectrum, buf);
// resample filtered waveform
int skip = 1 << octave;
float *pOut = pData[octave];
for (int i=0; i < fftLength; i += skip) *pOut++ = scaleFactor * buf[i];
}
// teardown
kiss_fftr_free(inv);
kiss_fftr_free(fwd);
delete[] buf;
}
void WaveStack::init()
{
}
void WaveStack::deinit()
{
}
float WaveStack::interp(int octave, float phase)
{
while (phase < 0) phase += 1.0;
while (phase >= 1.0) phase -= 1.0f;
int nTableSize = 1 << (maxBits - octave);
float readIndex = phase * nTableSize;
int ri = int(readIndex);
float f = readIndex - ri;
int rj = ri + 1; if (rj >= nTableSize) rj -= nTableSize;
float *pWaveTable = pData[octave];
float si = pWaveTable[ri];
float sj = pWaveTable[rj];
return (float)((1.0 - f) * si + f * sj);
}
}
Then use it in this way:
//wave and outputWave should be float[1024];
void getSample(int octave, float* wave, float* outputWave){
uint_fast32_t impulseCount = 1024;
if (octave == 0){
impulseCount = 737;
}else if (octave == 1){
impulseCount = 369;
}
else if (octave == 2){
impulseCount = 185;
}
else if (octave == 3){
impulseCount = 93;
}
else if (octave == 4){
impulseCount = 47;
}
else if (octave == 5){
impulseCount = 24;
}
else if (octave == 6){
impulseCount = 12;
}
else if (octave == 7){
impulseCount = 6;
}
else if (octave == 8){
impulseCount = 3;
}
else if (octave == 9){
impulseCount = 2;
}
//Get sample for octave
stack->initStack(wave, impulseCount);
for (int i = 0; i < 1024;i++){
float phase = (1.0/float(1024))*i;
//get interpolated wave and apply volume compensation
outputWave[i] = stack->interp(0, phase) / 2.0;
}
}
Then... when 10 buffers is ready. You can use them when playing a sound. Using this code you can get index of buffer/octave depending to your frequency
uint_fast8_t getBufferIndex(const float& frequency){
if (frequency >= 0 && frequency < 40){
return 0;
}
else if (frequency >= 40 && frequency < 80){
return 1;
}else if (frequency >= 80 && frequency < 160){
return 2;
}else if (frequency >= 160 && frequency < 320){
return 3;
}else if (frequency >= 320 && frequency < 640){
return 4;
}else if (frequency >= 640 && frequency < 1280){
return 5;
}else if (frequency >= 1280 && frequency < 2560){
return 6;
}else if (frequency >= 2560 && frequency < 5120){
return 7;
}else if (frequency >= 5120 && frequency < 10240){
return 8;
}else if (frequency >= 10240){
return 9;
}
return 0;
}
So if I know that my note frequency 440hz. Then for this note I'm getting wave in this way:
float notInterpolatedSound[1024];
float interpolatedSound[1024];
uint_fast8_t octaveIndex = getBufferIndex(440.0);
getSample(octaveIndex, notInterpolatedSound, interpolatedSound);
//tada!
ps. the code above is a low pass filter. I also tried to do sinc interpolation. But sinc worked for me very expensive and not exactly. Although maybe I did it wrong.