下面是ZSCORE算法的PHP实现:

<?php
$y = array(1,7,1.1,1,0.9,1,1,1.1,1,0.9,1,1.1,1,1,0.9,1,1,1.1,1,1,1,1,1.1,0.9,1,1.1,1,1,0.9,
       1,1.1,1,1,1.1,1,0.8,0.9,1,1.2,0.9,1,1,1.1,1.2,1,1.5,10,3,2,5,3,2,1,1,1,0.9,1,1,3,
       2.6,4,3,3.2,2,1,1,0.8,4,4,2,2.5,1,1,1);

function mean($data, $start, $len) {
    $avg = 0;
    for ($i = $start; $i < $start+ $len; $i ++)
        $avg += $data[$i];
    return $avg / $len;
}
    
function stddev($data, $start,$len) {
    $mean = mean($data,$start,$len);
    $dev = 0;
    for ($i = $start; $i < $start+$len; $i++) 
        $dev += (($data[$i] - $mean) * ($data[$i] - $mean));
    return sqrt($dev / $len);
}

function zscore($data, $len, $lag= 20, $threshold = 1, $influence = 1) {

    $signals = array();
    $avgFilter = array();
    $stdFilter = array();
    $filteredY = array();
    $avgFilter[$lag - 1] = mean($data, 0, $lag);
    $stdFilter[$lag - 1] = stddev($data, 0, $lag);
    
    for ($i = 0; $i < $len; $i++) {
        $filteredY[$i] = $data[$i];
        $signals[$i] = 0;
    }


    for ($i=$lag; $i < $len; $i++) {
        if (abs($data[$i] - $avgFilter[$i-1]) > $threshold * $stdFilter[$lag - 1]) {
            if ($data[$i] > $avgFilter[$i-1]) {
                $signals[$i] = 1;
            }
            else {
                $signals[$i] = -1;
            }
            $filteredY[$i] = $influence * $data[$i] + (1 - $influence) * $filteredY[$i-1];
        } 
        else {
            $signals[$i] = 0;
            $filteredY[$i] = $data[$i];
        }
        
        $avgFilter[$i] = mean($filteredY, $i - $lag, $lag);
        $stdFilter[$i] = stddev($filteredY, $i - $lag, $lag);
    }
    return $signals;
}

$sig = zscore($y, count($y));

print_r($y); echo "<br><br>";
print_r($sig); echo "<br><br>";

for ($i = 0; $i < count($y); $i++) echo $i. " " . $y[$i]. " ". $sig[$i]."<br>";

下面是我尝试为“Smoothed z-score算法”创建一个Ruby解决方案:

module ThresholdingAlgoMixin
  def mean(array)
    array.reduce(&:+) / array.size.to_f
  end

  def stddev(array)
    array_mean = mean(array)
    Math.sqrt(array.reduce(0.0) { |a, b| a.to_f + ((b.to_f - array_mean) ** 2) } / array.size.to_f)
  end

  def thresholding_algo(lag: 5, threshold: 3.5, influence: 0.5)
    return nil if size < lag * 2
    Array.new(size, 0).tap do |signals|
      filtered = Array.new(self)

      initial_slice = take(lag)
      avg_filter = Array.new(lag - 1, 0.0) + [mean(initial_slice)]
      std_filter = Array.new(lag - 1, 0.0) + [stddev(initial_slice)]
      (lag..size-1).each do |idx|
        prev = idx - 1
        if (fetch(idx) - avg_filter[prev]).abs > threshold * std_filter[prev]
          signals[idx] = fetch(idx) > avg_filter[prev] ? 1 : -1
          filtered[idx] = (influence * fetch(idx)) + ((1-influence) * filtered[prev])
        end

        filtered_slice = filtered[idx-lag..prev]
        avg_filter[idx] = mean(filtered_slice)
        std_filter[idx] = stddev(filtered_slice)
      end
    end
  end
end

以及示例用法:

test_data = [
  1, 1, 1.1, 1, 0.9, 1, 1, 1.1, 1, 0.9, 1, 1.1, 1, 1, 0.9, 1,
  1, 1.1, 1, 1, 1, 1, 1.1, 0.9, 1, 1.1, 1, 1, 0.9, 1, 1.1, 1,
  1, 1.1, 1, 0.8, 0.9, 1, 1.2, 0.9, 1, 1, 1.1, 1.2, 1, 1.5,
  1, 3, 2, 5, 3, 2, 1, 1, 1, 0.9, 1, 1, 3, 2.6, 4, 3, 3.2, 2,
  1, 1, 0.8, 4, 4, 2, 2.5, 1, 1, 1
].extend(ThresholdingAlgoMixin)

puts test_data.thresholding_algo.inspect

# Output: [
#   0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
#   0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0,
#   0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1,
#   1, 1, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0
# ]

在信号处理中，峰值检测通常采用小波变换。基本上就是对时间序列数据进行离散小波变换。返回的细节系数中的过零将对应于时间序列信号中的峰值。你会在不同的细节系数水平上检测到不同的峰值振幅，这给了你多层次的分辨率。

我为Jean-Paul最受欢迎的答案写了一个Go包。它假设y值的类型为float64。

github.com/MicahParks/peakdetect

下面的示例使用了这个包，并基于上面提到的流行答案中的R示例。它在编译时没有任何依赖关系，试图保持较低的内存占用，并且在有新数据点进入时不重新处理过去的点。该项目有100%的测试覆盖率，主要来自上述R示例的输入和输出。但是，如果有人发现任何错误，请打开一个GitHub问题。

编辑:我对v0.0.5进行了性能改进，似乎快了10倍!它使用Welford的方法进行初始化，并使用类似的方法计算滞后期(滑动窗口)的平均值和总体标准偏差。特别感谢另一个帖子的回答:https://stackoverflow.com/a/14638138/14797322

下面是基于R例子的Golang例子:

package main

import (
    "fmt"
    "log"

    "github.com/MicahParks/peakdetect"
)

// This example is the equivalent of the R example from the algorithm's author.
// https://stackoverflow.com/a/54507329/14797322
func main() {
    data := []float64{1, 1, 1.1, 1, 0.9, 1, 1, 1.1, 1, 0.9, 1, 1.1, 1, 1, 0.9, 1, 1, 1.1, 1, 1, 1, 1, 1.1, 0.9, 1, 1.1, 1, 1, 0.9, 1, 1.1, 1, 1, 1.1, 1, 0.8, 0.9, 1, 1.2, 0.9, 1, 1, 1.1, 1.2, 1, 1.5, 1, 3, 2, 5, 3, 2, 1, 1, 1, 0.9, 1, 1, 3, 2.6, 4, 3, 3.2, 2, 1, 1, 0.8, 4, 4, 2, 2.5, 1, 1, 1}

    // Algorithm configuration from example.
    const (
        lag       = 30
        threshold = 5
        influence = 0
    )

    // Create then initialize the peak detector.
    detector := peakdetect.NewPeakDetector()
    err := detector.Initialize(influence, threshold, data[:lag]) // The length of the initial values is the lag.
    if err != nil {
        log.Fatalf("Failed to initialize peak detector.\nError: %s", err)
    }

    // Start processing new data points and determine what signal, if any they produce.
    //
    // This method, .Next(), is best for when data is being processed in a stream, but this simply iterates over a slice.
    nextDataPoints := data[lag:]
    for i, newPoint := range nextDataPoints {
        signal := detector.Next(newPoint)
        var signalType string
        switch signal {
        case peakdetect.SignalNegative:
            signalType = "negative"
        case peakdetect.SignalNeutral:
            signalType = "neutral"
        case peakdetect.SignalPositive:
            signalType = "positive"
        }

        println(fmt.Sprintf("Data point at index %d has the signal: %s", i+lag, signalType))
    }

    // This method, .NextBatch(), is a helper function for processing many data points at once. It's returned slice
    // should produce the same signal outputs as the loop above.
    signals := detector.NextBatch(nextDataPoints)
    println(fmt.Sprintf("1:1 ratio of batch inputs to signal outputs: %t", len(signals) == len(nextDataPoints)))
}

下面是在Golang中实现的Smoothed z-score算法(上图)。它假设一个[]int16 (PCM 16bit样本)的切片。你可以在这里找到要点。

/*
Settings (the ones below are examples: choose what is best for your data)
set lag to 5;          # lag 5 for the smoothing functions
set threshold to 3.5;  # 3.5 standard deviations for signal
set influence to 0.5;  # between 0 and 1, where 1 is normal influence, 0.5 is half
*/

// ZScore on 16bit WAV samples
func ZScore(samples []int16, lag int, threshold float64, influence float64) (signals []int16) {
    //lag := 20
    //threshold := 3.5
    //influence := 0.5

    signals = make([]int16, len(samples))
    filteredY := make([]int16, len(samples))
    for i, sample := range samples[0:lag] {
        filteredY[i] = sample
    }
    avgFilter := make([]int16, len(samples))
    stdFilter := make([]int16, len(samples))

    avgFilter[lag] = Average(samples[0:lag])
    stdFilter[lag] = Std(samples[0:lag])

    for i := lag + 1; i < len(samples); i++ {

        f := float64(samples[i])

        if float64(Abs(samples[i]-avgFilter[i-1])) > threshold*float64(stdFilter[i-1]) {
            if samples[i] > avgFilter[i-1] {
                signals[i] = 1
            } else {
                signals[i] = -1
            }
            filteredY[i] = int16(influence*f + (1-influence)*float64(filteredY[i-1]))
            avgFilter[i] = Average(filteredY[(i - lag):i])
            stdFilter[i] = Std(filteredY[(i - lag):i])
        } else {
            signals[i] = 0
            filteredY[i] = samples[i]
            avgFilter[i] = Average(filteredY[(i - lag):i])
            stdFilter[i] = Std(filteredY[(i - lag):i])
        }
    }

    return
}

// Average a chunk of values
func Average(chunk []int16) (avg int16) {
    var sum int64
    for _, sample := range chunk {
        if sample < 0 {
            sample *= -1
        }
        sum += int64(sample)
    }
    return int16(sum / int64(len(chunk)))
}

一种方法是根据以下观察来检测峰:

时间t是一个峰值(y (t) > y (t - 1)) & & ((t) > y (t + 1))

它通过等待上升趋势结束来避免误报。它并不完全是“实时”的，因为它会比峰值差一个dt。灵敏度可以通过要求比较的裕度来控制。在噪声检测和时延检测之间存在一种折衷。 您可以通过添加更多参数来丰富模型:

峰如果y (y (t) - (t-dt) > m) && (y (t) - y (t + dt) > m)

dt和m是控制灵敏度和延时的参数

这是你用上述算法得到的结果:

下面是在python中重现图的代码:

import numpy as np
import matplotlib.pyplot as plt
input = np.array([ 1. ,  1. ,  1. ,  1. ,  1. ,  1. ,  1. ,  1.1,  1. ,  0.8,  0.9,
    1. ,  1.2,  0.9,  1. ,  1. ,  1.1,  1.2,  1. ,  1.5,  1. ,  3. ,
    2. ,  5. ,  3. ,  2. ,  1. ,  1. ,  1. ,  0.9,  1. ,  1. ,  3. ,
    2.6,  4. ,  3. ,  3.2,  2. ,  1. ,  1. ,  1. ,  1. ,  1. ])
signal = (input > np.roll(input,1)) & (input > np.roll(input,-1))
plt.plot(input)
plt.plot(signal.nonzero()[0], input[signal], 'ro')
plt.show()

通过设置m = 0.5，你可以得到一个更清晰的信号，只有一个假阳性: