无法完成Wolfram-mathmetica中的傅立叶分析？

问题描述

首先： 我是一个完全菜鸟，因此为糟糕的格式表示歉意。

我正在追踪this tutorial，以获取图像的傅立叶级数。在本教程的中期，我一直在这段代码中遇到错误：

(* Fourier coefficients of a single curve *)
    fourierComponentData[pointList_,nMax_,op_] := 
     Module[{\[CurlyEpsilon] = 10^-3,\[Mu] = 2^14,M = 10000,s,scale,\[CapitalDelta],L,nds,sMax,if,\[ScriptX]\[ScriptY]Function,X,Y,XFT,YFT,type},(* prepare curve *)
      scale = 
       1. Mean[Table[ 
          Max[ fl /@ pointList] - 
           Min[fl /@ pointList],{fl,{First,Last}}]];
       \[CapitalDelta] = 
       EuclideanDistance[First[pointList],Last[pointList]];
       L = Which[op === "Closed",type = "Closed";
                                                                
        If[First[pointList] === Last[pointList],pointList,Append[pointList,First[pointList]]],op === "Open",type = "Open"; pointList,\[CapitalDelta] == 0.,type = "Closed";  
        pointList,\[CapitalDelta]/scale < op,type = "Closed"; 
        Append[pointList,First[pointList]],True,type = "Open"; 
        Join[pointList,Rest[Reverse[pointList]]]];
      (* re-parametrize curve by arclength *)
      \[ScriptX]\[ScriptY]Function = BSplineFunction[L,SplineDegree -> 4];
      nds = NDSolve[{s'[t] == 
          Sqrt[\[ScriptX]\[ScriptY]Function'[
             t].\[ScriptX]\[ScriptY]Function'[t]],s[0] == 0},{t,1},MaxSteps -> 10^5,PrecisionGoal -> 4];
      (* total curve length *)
           sMax = s[1] /. nds[[1]];
           if = 
       Interpolation[
        Table[{s[\[Sigma]] /. nds[[1]],\[Sigma]},{\[Sigma],1,1/M}]];
      X[t_Real] :=  
       BSplineFunction[L][Max[Min[1,if[(t + Pi)/(2 Pi) sMax]],0]][[1]];
      Y[t_Real] :=  
       BSplineFunction[L][Max[Min[1,0]][[2]]; 
      (* extract Fourier coefficients *)
      {XFT,YFT} = 
       Fourier[Table[#[N @ t],-Pi + \[CurlyEpsilon],Pi - \[CurlyEpsilon],(2 Pi - 
               2 \[CurlyEpsilon])/\[Mu]}]] & /@ {X,Y};   
      {type,2 Pi/Sqrt[\[Mu]] *
        ((Transpose[
             Table[{Re[#],Im[#]} &[Exp[I k Pi]  #[[k + 1]]],{k,nMax}]] & /@ {XFT,YFT}))}  ]
    
        Options[fourierComponents] = {"MaxOrder" -> 180,"OpenClose" -> 0.025};
    
    fourierComponents[pointLists_,OptionsPattern[]] := 
     Monitor[Table[
        fourierComponentData[pointLists[[k]],\
         If[Head[#] === List,#[[k]],#] &[ OptionValue["MaxOrder"]],#] &[ OptionValue["OpenClose"]]],Length[pointLists]}],Grid[{{Text[
           Style["progress calculating Fourier coefficients",Darker[Green,0.66]]],ProgressIndicator[k/Length[pointLists]]} },Alignment -> Left,Dividers -> Center]] /; 
      Depth[pointLists] === 4
    
        fCs = fourierComponents[hLines,"OpenClose" -> Table["Closed",{Length[hLines]}]];

堆栈跟踪为：

非常感谢您的帮助。

解决方法

我检查了您的代码，它与本教程中的代码完全相同。

请检查发布到Wolfram云的代码：

https://www.wolframcloud.com/obj/dg356172/Published/Fourier%20Transform%20Image.nb

对我有用。

在定义hLines时，您可能会遇到一些问题。