Baseline Algorithm for Morse CW Decoding from Sound

[JG1VPP]

音声からモールス信号を解読するサンプル

アルゴリズム

1. モールス信号の音声波形を用意する
2. FFTでビート周波数を算出し、移動平均LPFのカットオフ周波数を決める
3. 音声波形の2乗を時間領域で計算し、パワー時系列として扱う
4. 多段階の移動平均LPFでパワー時系列を平滑化する
5. 1階微分を計算する
6. 1回微分のピークtoピーク値を計算する
7. 1回微分が正負のピーク付近に達した瞬間をエッジとして抽出する
8. エッジの間隔からモールス信号の短点の時間を推定する
9. エッジを利用して、モールス信号の短点と長点と空白を取り出す

注意

今回は、短点もしくは短点1個に相当する空白が必ず含まれる想定で短点の時間を推定した。常にそれで推定できるとは限らないので、厳密には最尤推定を行うべき。

実装

/*
MIT License

Copyright (c) 2022 JA1ZLO

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
*/

package main

import (
    "fmt"
    "github.com/mjibson/go-dsp/spectral"
    "github.com/mjibson/go-dsp/wav"
    "gonum.org/v1/plot"
    "gonum.org/v1/plot/plotter"
    "gonum.org/v1/plot/plotutil"
    "gonum.org/v1/plot/vg"
    "log"
    "math"
    "os"
)

type XYs []XY

type XY struct {
    X, Y float64
}

func Decode(signal []float64, interval float64) {
    prev_up := 0
    prev_dn := 0

    for i, val := range signal {
        if val == 1.0 {
            prev_up = i
            span := int(math.Round(float64(i-prev_dn) / interval))
            if span == 3 {
                fmt.Print(" ")
            } else if span > 3 {
                fmt.Println()
            }
        } else if val == -1.0 {
            prev_dn = i
            span := int(math.Round(float64(i-prev_up) / interval))
            if span == 1 {
                fmt.Print(".")
            } else if span >= 2 {
                fmt.Print("-")
            }
        }
    }

    fmt.Println()
}

func PeakValue(source []float64) float64 {
    peak := 0.0

    for _, val := range source {
        if val > peak {
            peak = val
        } else if val < -peak {
            peak = -val
        }
    }

    return peak
}

func DetectEdges(threshold float64, source []float64) (result []float64, interval int) {
    peak_value := PeakValue(source)
    threshold = peak_value * threshold

    hold := 0
    count_start := 0
    interval = len(source)
    result = make([]float64, len(source))

    for i, val := range source {
        if val > threshold && hold == 0 {
            result[i] = 1.0
            hold = 1
            if i-count_start < interval {
                interval = i - count_start
            }
            count_start = i
        } else if val < -threshold && hold == 0 {
            result[i] = -1.0
            hold = -1
            if i-count_start < interval {
                interval = i - count_start
            }
            count_start = i
        } else if -threshold < val && val < threshold {
            hold = 0
        }
    }

    return
}

func OneStepDiff(source []float64) (result []float64) {
    result = make([]float64, len(source))

    for i, val := range source[1:] {
        result[i] = val - source[i]
    }

    return
}

func LPF(source []float64, n int) (result []float64) {
    result = make([]float64, len(source)-n)
    ave := float64(0.0)

    for i := 0; i < n; i++ {
        ave += source[i] / float64(n)
    }

    result[0] = ave

    for i := 1; i < len(result); i++ {
        neg := source[i+0] / float64(n)
        pos := source[i+n] / float64(n)
        ave = ave - neg + pos
        result[i] = ave
    }

    return
}

func PeakFreq(signal []float64, sampling_freq uint32) float64 {
    var opt spectral.PwelchOptions

    opt.NFFT = 4096
    opt.Noverlap = 1024
    opt.Window = nil
    opt.Pad = 4096
    opt.Scale_off = false

    Power, Freq := spectral.Pwelch(signal, float64(sampling_freq), &opt)

    peakFreq := 0.0
    peakPower := 0.0
    for i, val := range Freq {
        if val > 10 && val < 3000 {
            if Power[i] > peakPower {
                peakPower = Power[i]
                peakFreq = val
            }
        }
    }

    return peakFreq
}

func main() {
    file, err := os.Open("JA1ZLO.wav")
    if err != nil {
        log.Fatal(err)
    }

    w, werr := wav.New(file)
    if werr != nil {
        log.Fatal(werr)
    }

    len_sound := w.Samples
    rate_sound := w.SampleRate
    SoundData, werr := w.ReadFloats(len_sound)
    if werr != nil {
        log.Fatal(werr)
    }

    Signal64 := make([]float64, len_sound)
    SquaredSignal64 := make([]float64, len_sound)
    for i, val := range SoundData {
        Signal64[i] = float64(val)
        SquaredSignal64[i] = float64(val) * float64(val)
    }

    ave_num := 6 * int(float64(rate_sound)/PeakFreq(Signal64, rate_sound))
    cut_freq := 0.443 * float64(rate_sound) / math.Sqrt(float64(ave_num)*float64(ave_num)-1)
    fmt.Println("cut_off", cut_freq)

    smoothed := LPF(LPF(LPF(LPF(SquaredSignal64, ave_num), ave_num), ave_num), ave_num)
    diff := OneStepDiff(smoothed)
    edge, interval := DetectEdges(0.9, diff)

    pts := make(plotter.XYs, len(smoothed))
    pts_diff := make(plotter.XYs, len(diff))

    for i, val := range smoothed {
        pts[i].X = float64(i) / float64(rate_sound)
        pts[i].Y = val
    }

    for i, val := range diff {
        pts_diff[i].X = float64(i) / float64(rate_sound)
        pts_diff[i].Y = val
    }

    p := plot.New()

    p.Title.Text = "signal power"
    p.X.Label.Text = "t"
    p.Y.Label.Text = "power"

    plotutil.AddLines(p, pts)
    p.Save(10*vg.Inch, 3*vg.Inch, "smoothed.png")

    p = plot.New()

    p.Title.Text = "signal power diff"
    p.X.Label.Text = "t"
    p.Y.Label.Text = "power diff"

    plotutil.AddLines(p, pts_diff)
    p.Save(10*vg.Inch, 3*vg.Inch, "diff.png")

    Decode(edge, float64(interval))
}

信号処理の結果

[JG1VPP]

実行方法

JA1ZLOのコールサインが解読できた。別途、英数字への復号処理が必要。

$ go run fft.go 
cut_off 45.22485535942758
 .--- .- .---- --.. .-.. ---