约翰·埃勒斯（John Ehlers）利用数字信号处理方面的专业，探讨了价格与成交量之间的关联性，并尝试通过这些关系来预测市场动向。该滤波器基于航天模拟滤波器，旨在降低价格数据中的噪声。Ehlers 高通滤波器可消除周期长于特定值的波分量。

埃勒斯运用高通滤波对价格和成交量数据进行处理，以提取出关键的数据波长。他认为，通过这种方法得到的埃勒斯Ehlers循环，能够根据价格成交量图中的曲线运动——包括其曲率和旋转方向——来预测市场未来的看涨或看跌趋势。

我们日常使用的EMA函数或者MA函数均属于一阶数字低通滤波器，详细算法详见下图所示：

那么，在一个高通滤波器中，对离散信号的处理将明显优于低通滤波。

根据高通滤波的算法，我们可以对市场走势进行Highpass Filter。在广发金融工程此前发明的LLT算法就属于高通滤波算法的其中一种。

如果想要在通达信中使用该函数，就要利用C#语言创建通达信dll，以下是通达信高通滤波算法的源代码：

namespace NinjaTrader.NinjaScript.Indicators.AUN_Indi.Ehlers{  public class EhlersHighPassLowPassRoofingFilter : Indicator  {    private Series<double> hb;    private int MINBAR = 5;    private double a1, a2, c1, c2, c3;    protected override void OnStateChange()    {      if (State == State.SetDefaults)      {        Description                  = @"The HighPass-LowPass Roofing Filter: John Ehlers, Cycle Analytics For Traders, pg.78";        Name                    = "EhlersHighPassLowPassRoofingFilter";        Calculate                  = Calculate.OnBarClose;        IsOverlay                  = false;        DisplayInDataBox              = true;        DrawOnPricePanel              = true;        DrawHorizontalGridLines            = true;        DrawVerticalGridLines            = true;        PaintPriceMarkers              = true;        ScaleJustification              = NinjaTrader.Gui.Chart.ScaleJustification.Right;        //Disable this property if your indicator requires custom values that cumulate with each new market data event.         //See Help Guide for additional information.        IsSuspendedWhileInactive          = true;        HPLength          = 48;        SSFLength          = 10;        ColorD          = Brushes.Red;        ColorU          = Brushes.LimeGreen;                AddPlot(Brushes.ForestGreen, "Rb");      }      else if (State == State.Configure)      {         double twoPiPrd = 2 * Math.PI / HPLength;         double alpha1   = (Math.Cos(twoPiPrd) + Math.Sin(twoPiPrd) - 1) / Math.Cos(twoPiPrd);         double alpha2   = Math.Exp(-Math.Sqrt(2) * Math.PI / SSFLength);            double beta     = 2 * alpha2 * Math.Cos(Math.Sqrt(2) * Math.PI / SSFLength);             c2       = beta;             c3       = -Math.Pow(alpha2, 2);             c1       = 1 - c2 - c3;             a1       = 1 - alpha1 / 2;               a2       = 1 - alpha1;              }      else if (State == State.DataLoaded)      {                hb = new Series<double>(this);      }    }    protected override void OnBarUpdate()    {      if (CurrentBar <= MINBAR) return;              hb[0] = a1 * (Close[0] - Close[1]) + a2 * hb[1];         Rb[0] = c1 * (hb[0] + hb[1]) / 2 + c2 * Rb[1] + c3 * Rb[2];                     if (Rb[0] < 0) PlotBrushes[0][0] = ColorD;         else            if (Rb[0] > 0) PlotBrushes[0][0] = ColorU;             }    #region Properties    [NinjaScriptProperty]    [Range(1, int.MaxValue)]    [Display(Name="HPLength", Order=1, GroupName="Parameters")]    public int HPLength    { get; set; }    [NinjaScriptProperty]    [Range(1, int.MaxValue)]    [Display(Name="SSFLength", Order=2, GroupName="Parameters")]    public int SSFLength    { get; set; }    [Browsable(false)]    [XmlIgnore]    public Series<double> Rb    {      get { return Values[0]; }    }            [NinjaScriptProperty]    [XmlIgnore]    [Display(Name="ColorD", Description="Color for bear", Order=2, GroupName="Parameters")]    public Brush ColorD    { get; set; }    [Browsable(false)]    public string ColorDSerializable    {      get { return Serialize.BrushToString(ColorD); }      set { ColorD = Serialize.StringToBrush(value); }    }          [NinjaScriptProperty]    [XmlIgnore]    [Display(Name="ColorU", Description="Color for bool", Order=3, GroupName="Parameters")]    public Brush ColorU    { get; set; }    [Browsable(false)]    public string ColorUSerializable    {      get { return Serialize.BrushToString(ColorU); }      set { ColorU = Serialize.StringToBrush(value); }    }              #endregion  }}

本文所采用的正是巴特沃斯滤波器

源代码：

var UltimateSmoother (var *Data, int Length){  var f = (1.414*PI) / Length;  var a1 = exp(-f);  var c2 = 2*a1*cos(f);  var c3 = -a1*a1;  var c1 = (1+c2-c3)/4;  vars US = series(*Data,4);  return US[0] = (1-c1)*Data[0] + (2*c1-c2)*Data[1] - (c1+c3)*Data[2]+ c2*US[1] + c3*US[2];}

最后是通达信成果：