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spectre.go
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spectre.go
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package fennec
import (
"github.com/mjibson/go-dsp/fft"
"github.com/mjibson/go-dsp/window"
"math"
"math/cmplx"
"sort"
)
const (
// целевая Hz при получении PCM звука
SampleRate = 11025
// Размер окна FFT
FFTWinSize = 1 << (binBits + 1)
// Величина перекрывания окон FFT
FFTOverlap = FFTWinSize / 2
// Половина ширины окна FFT
FFTHalfWinSize = FFTWinSize / 2
// Ширина распространения пиков (см. параметр width в Gaussian.Make)
gaussianWidth = 30.0
// Максимум локальных пиков в одном фрейме, которые будут в итоге запомнены (ТОП самых "влиятельных")
maxPeaksPerFrame = 6
// Максимальное число пар пиков, которое можно образовать с каждым отдельным пиком
maxPairsPerPeak = 2
// максимальный lookahead по частотным диапазонам (bin'ы) про поиске пар (ограничен числом бит, выделяемых на дельту bin'ов в хеше)
// берем как половину от binDiffMask, т.к. старший бит уходит под знак
lookaheadBinDiffMax = binDiffMask >> 1
// минимальный lookahead по времени при поиске пар пиков
lookaheadTimeDiffMin = 3
// максимальный lookahead по времени при поиске пар пиков (ограничен числом бит, выделяемых на дельту времени в хеше)
lookaheadTimeDiffMax = timeDiffMask
// Размерности частей хешей
binBits = 10
binDiffBits = 6 // не стоит повышать
timeDiffBits = 6
binMask = (1 << binBits) - 1
binDiffMask = (1 << binDiffBits) - 1
timeDiffMask = (1 << timeDiffBits) - 1
// Минимальное число совпадений хешей при сверке двух треков, чтобы соответствующее смещение вообще бралось в рассмотрение
minAllowedCnt = 5
// Максимальное смещение во времени между треками, когда оно еще может считаться релевантным
maxTimeMsDiffForTracksCompare = 10 * 60 * 1000
)
var (
// коэффициент затухания огибающей пиков (findPeaksInSpectre)
decayingKoeff = 0.98
)
type (
Float float32
PeakSpectr struct {
Val Float
Idx uint
}
Peak struct {
Time uint // X axis
Bin uint // Y axis
}
PeakPair struct {
Time1 uint
Bin1 uint
Bin2 uint
TimeDiff uint
}
Hash struct {
Time uint32
Hash uint32
}
Gaussian struct {
gaus []float64
n int
width float64
}
)
var (
gaussian Gaussian
)
// Сколько колонок (элементов []Hash) в одной секунде трека
func HashColsInOneSec() float64 {
// Пока захардкодил единственные параметры
return float64(SampleRate) / float64(FFTWinSize/2)
}
func NewPeakPair(time1, bin1, time2, bin2 uint) PeakPair {
return PeakPair{
Time1: time1,
Bin1: bin1,
TimeDiff: time2 - time1,
Bin2: bin2,
}
}
func (pp PeakPair) ToHash() uint32 {
bin1 := pp.Bin1 & binMask
binDiff := (pp.Bin2 - pp.Bin1) & binDiffMask
timeDiff := pp.TimeDiff & timeDiffMask
hash := (((bin1 << binDiffBits) | binDiff) << timeDiffBits) | timeDiff
return uint32(hash)
}
func (pp PeakPair) Time2() uint {
return pp.Time1 + pp.TimeDiff
}
func (h Hash) ToPeakPair() PeakPair {
timeDiff := uint(h.Hash & timeDiffMask)
binDiff := uint((h.Hash >> timeDiffBits) & binDiffMask)
bin1 := uint(((h.Hash >> timeDiffBits) >> binDiffBits) & binMask)
d := int(binDiff)
if (d & ((binDiffMask + 1) >> 1)) > 0 {
d = -((binDiffMask + 1) - d)
}
bin2 := uint(d + int(bin1))
return PeakPair{
Time1: uint(h.Time),
Bin1: bin1,
Bin2: bin2,
TimeDiff: timeDiff,
}
}
func (g *Gaussian) Make(n int, width float64) []float64 {
if (g.n != n) || (g.width != width) {
g.gaus = make([]float64, 2*n+1)
for i := -n; i < n; i++ {
g.gaus[i+n] = math.Exp(-0.5 * math.Pow(float64(i)/width, 2))
}
}
g.n = n
g.width = width
return g.gaus
}
func minInt(a, b int) int {
if a < b {
return a
} else {
return b
}
}
func minUint(a, b uint) uint {
if a < b {
return a
} else {
return b
}
}
func maxFloat(a, b Float) Float {
if a > b {
return a
} else {
return b
}
}
func minFloat(a, b Float) Float {
if a < b {
return a
} else {
return b
}
}
func absInt(a int) int {
if a < 0 {
return -a
}
return a
}
func maxPerLine(lines [][]Float) (maxs []Float) {
maxs = make([]Float, len(lines))
for i, line := range lines {
max := float64(0)
for _, val := range line {
max = math.Max(max, float64(val))
}
maxs[i] = Float(max)
}
return
}
func maximumFloat(a []Float, b []Float) {
l := minInt(len(a), len(b))
for i := 0; i < l; i++ {
if a[i] < b[i] {
a[i] = b[i]
}
}
}
func fading(vec []Float, factor Float) {
for i := range vec {
vec[i] *= factor
}
}
func buildSpectre(wave []Float) (spectre [][]Float) {
waveLen := len(wave)
if waveLen == 0 {
return
}
winFunc := window.Hann(FFTWinSize + 2)[1 : FFTWinSize+1]
spectre = make([][]Float, FFTHalfWinSize+1) // rows x cols
win := make([]float64, FFTWinSize)
winZeroes := make([]float64, FFTWinSize)
stride := FFTWinSize - FFTOverlap
winCnt := (waveLen + stride - 1) / stride
for winIdx, offs := 0, 0; winIdx < winCnt; winIdx, offs = winIdx+1, offs+stride {
idx := minInt(waveLen, offs+FFTWinSize)
if idx < (offs + FFTWinSize) {
copy(win, winZeroes)
}
for i := offs; i < idx; i++ {
win[i-offs] = float64(wave[i])
}
for i, w := range winFunc {
win[i] *= w
}
line := fft.FFTReal(win)
for i := 0; i < FFTHalfWinSize+1; i++ {
win[i] = cmplx.Abs(line[i])
}
for i, mag := range win[0 : FFTHalfWinSize+1] {
spectre[i] = append(spectre[i], Float(mag))
}
}
spectreMin, spectreMax := Float(math.MaxFloat32), Float(0.0)
for _, line := range spectre {
for _, mag := range line {
spectreMax = maxFloat(spectreMax, mag)
spectreMin = minFloat(spectreMin, mag)
}
}
if spectreMax < 1e-6 {
panic(`Zero signal`)
}
minMag := spectreMax / 1e6
spectreMean, cnt := float64(0), 0
for y, line := range spectre {
for x, magRaw := range line {
if magRaw < minMag {
magRaw = minMag
}
mag := math.Log(float64(magRaw))
//mag = math.Max(0, mag) // раскомментировать, чтобы получить спектрограмму как в презентации
spectre[y][x] = Float(mag)
spectreMean += mag
cnt++
}
}
spectreMean /= float64(cnt)
for y, line := range spectre {
for x := range line {
spectre[y][x] -= Float(spectreMean)
}
}
spectre = spectre[:len(spectre)-1]
return
}
func findPeaksInSpectre(spectre [][]Float) (peakList []Peak) {
peaks := scanForPeaks(spectre, Float(decayingKoeff))
peaks = filterPeaks(spectre, peaks, Float(decayingKoeff))
srows, scols := len(spectre), len(spectre[0])
for x := 0; x < scols; x++ {
for y := 0; y < srows; y++ {
if peaks[y][x] > 0 {
peakList = append(peakList, Peak{Time: uint(x), Bin: uint(y)})
}
}
}
return
}
func findPeaks(wave []Float) (peakList []Peak, spectre [][]Float) {
spectre = buildSpectre(wave)
if len(spectre) == 0 {
return
}
return findPeaksInSpectre(spectre), spectre
}
func scanForPeaks(spectre [][]Float, shadingCoeff Float) [][]int {
numRows, numCols := len(spectre), len(spectre[0])
scolsThresh := minInt(10, numCols)
lines := make([][]Float, numRows)
for y, line := range spectre {
lines[y] = line[0:scolsThresh]
}
maximumInLines := maxPerLine(lines)
thresh := spreadPeaksInVector(maximumInLines, gaussianWidth)
peaks := make([][]int, numRows)
for y := range spectre {
peaks[y] = make([]int, numCols)
}
scol := make([]Float, numRows)
for col := 0; col < numCols; col++ {
for y := 0; y < numRows; y++ {
scol[y] = spectre[y][col]
}
var peaksPositions []int
for i, isLocMax := range locMax(scol) {
if isLocMax && (scol[i] > thresh[i]) {
peaksPositions = append(peaksPositions, i)
}
}
if len(peaksPositions) > 0 {
var valsPeaks PeakSpectrSlice
for _, idx := range peaksPositions {
valsPeaks = append(valsPeaks, PeakSpectr{Idx: uint(idx), Val: scol[idx]})
}
sort.Sort(valsPeaks)
if len(valsPeaks) > maxPeaksPerFrame {
valsPeaks = valsPeaks[0:maxPeaksPerFrame]
}
for _, valsPeak := range valsPeaks {
peakPos := valsPeak.Idx
peak := PeakSpectr{Idx: peakPos, Val: scol[peakPos]}
thresh = spreadPeaks([]PeakSpectr{peak}, 0, gaussianWidth, thresh)
peaks[peakPos][col] = 1
}
}
fading(thresh, Float(shadingCoeff))
}
return peaks
}
func filterPeaks(spectre [][]Float, peaks [][]int, shadingCoeff Float) [][]int {
numRows, numCols := len(spectre), len(spectre[0])
lastCol := make([]Float, numRows)
for y := 0; y < numRows; y++ {
lastCol[y] = spectre[y][numCols-1]
}
thresh := spreadPeaksInVector(lastCol, gaussianWidth)
for col := numCols; col > 0; col-- {
var colPeaks PeakSpectrSlice
for y := 0; y < numRows; y++ {
if peaks[y][col-1] > 0 {
colPeaks = append(colPeaks, PeakSpectr{Idx: uint(y), Val: spectre[y][col-1]})
}
}
sort.Sort(colPeaks)
for _, peak := range colPeaks {
if peak.Val > thresh[peak.Idx] {
thresh = spreadPeaks([]PeakSpectr{peak}, 0, gaussianWidth, thresh)
if col < numCols {
peaks[peak.Idx][col] = 0
}
} else {
peaks[peak.Idx][col-1] = 0
}
}
fading(thresh, shadingCoeff)
}
return peaks
}
func locMaxIndices(vec []Float) []int {
neighbours := locMax(vec)
var idxs []int
for i, isLocMax := range neighbours {
if isLocMax {
idxs = append(idxs, i)
}
}
return idxs
}
func locMax(vec []Float) []bool {
l := len(vec)
neighbours := make([]bool, l)
neighbours[0] = vec[0] >= vec[1]
neighbours[l-1] = vec[l-1] >= vec[l-2]
for i := 1; i < l-1; i++ {
neighbours[i] = (vec[i-1] <= vec[i]) && (vec[i] >= vec[i+1])
}
return neighbours
}
func spreadPeaksInVector(vector []Float, width float64) []Float {
var peaks []PeakSpectr
for _, idx := range locMaxIndices(vector) {
peaks = append(peaks, PeakSpectr{Idx: uint(idx), Val: vector[idx]})
}
return spreadPeaks(peaks, len(vector), width, nil)
}
func spreadPeaks(peaks []PeakSpectr, numPoints int, width float64, base []Float) []Float {
if base != nil {
numPoints = len(base)
}
vec := make([]Float, numPoints)
if base != nil {
copy(vec, base)
}
gaus := gaussian.Make(numPoints, width)
gausVal := make([]Float, numPoints)
for _, peak := range peaks {
for i := 0; i < numPoints; i++ {
gausVal[i] = peak.Val * Float(gaus[uint(i+numPoints)-peak.Idx])
}
maximumFloat(vec, gausVal)
}
return vec
}
func PeaksToPairs(peaks []Peak) (pairs []PeakPair) {
if len(peaks) == 0 {
return
}
timeCnt := peaks[len(peaks)-1].Time + 1
peaksAt := make([][]uint, timeCnt)
for _, peak := range peaks {
peaksAt[peak.Time] = append(peaksAt[peak.Time], peak.Bin)
}
for time1 := uint(0); time1 < timeCnt; time1++ {
pairsLoop:
for _, bin1 := range peaksAt[time1] {
pairsFromThisPeak := 0
lastTime2 := minUint(timeCnt, time1+lookaheadTimeDiffMax)
for time2 := time1 + lookaheadTimeDiffMin; time2 < lastTime2; time2++ {
for _, bin2 := range peaksAt[time2] {
if absInt(int(bin2)-int(bin1)) < lookaheadBinDiffMax {
pair := NewPeakPair(time1, bin1, time2, bin2)
pairs = append(pairs, pair)
if pairsFromThisPeak++; pairsFromThisPeak >= maxPairsPerPeak {
continue pairsLoop
}
}
}
}
}
}
return
}
func PeakPairsToHashes(pairs []PeakPair) (hashes Hashes) {
hashes = make([]Hash, len(pairs))
for i, pair := range pairs {
hashes[i] = Hash{Time: uint32(pair.Time1), Hash: pair.ToHash()}
}
return
}
func FindHashes(peaks []Peak) (hashes Hashes) {
return PeakPairsToHashes(PeaksToPairs(peaks))
}