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使用 tikz/pgfplots 绘制傅里叶级数展开

tag-icon • tag-icon tikz-pgf pgfplots matlab
使用 tikz/pgfplots 绘制傅里叶级数展开

这是一个 MATLAB 代码

T=0.3;
A=0.3;
t=0:0.01:4*T;
n1=length(t);
N=100;
s=0;

signal=0;
for i=1:n1
s=0;
for n=1:N
s=s+A*4/(pi*(2*n-1))*sin(2*pi*(2*n-1)/T*t(i));
end
signal(i)=s;
end
plot(t,signal);

是否可以用 tikz/pgfplots 绘制这个？

在此处输入图片描述

答案1

我使用与键gnuplot sum相结合的函数，允许用户给出将要执行的原始命令。tikzraw gnuplottikz/pgfplotsgnuplot

在此处输入图片描述

\documentclass{standalone}
\usepackage{pgfplots}
\begin{document}
\begin{tikzpicture}
\begin{axis}[
             xlabel = $t$,
             xtick = {-.5,.5},
             xticklabels = {$-\frac{T}{2}$, $\frac{T}{2}$},
             ytick = {-1,-.5,.5,1},
             yticklabels = {$-A$, $-\frac{A}{2}$, $\frac{A}{2}$, $A$},
             domain = -.75:.75,
             samples = 200,
             legend style = {%
               at = {(0.5,1.02)},
               anchor = south},
             ]
  \addplot[mark = none] gnuplot {(x - floor(x +.5)) < 0 ? -1 : 1};
  \addlegendentry{Signal}
  \foreach \i in {2,4,6,8}{%
    \addplot+[mark = none] gnuplot[raw gnuplot] {%
      set samples 200;
      fourier(k, x) = 4/((2*k+1)*pi) * cos(2*(2*k+1)*pi*x - pi/2);
      plot[-.75:.75] sum [k=0:\i] fourier(k,x)
    };
    \addlegendentryexpanded{\number\numexpr 2*\i+1\relax{} first terms}
}
\end{axis}
\end{tikzpicture}
\end{document}

答案2

在此处输入图片描述

该Asymptote解决方案使用一个函数来评估总和，可以根据您的需要进行调整f.tex：

\documentclass[a4paper]{article}
\usepackage[inline]{asymptote}

\begin{document}
\begin{figure}
\begin{asy}
size(300);
import graph;
real T,A;
T=0.3;
A=0.3;

real tmin=0;
real tmax=1.4;
real ymin=-0.4;
real ymax=0.4;

real signal(real t){
  int NN=400;
  real s=0;
  for(int n=1;n<=NN;++n){
    s=s+A*4/(pi*(2*n-1))*sin(2*pi*(2*n-1)/T*t);
  }
  return s;
}

pen linePen=red+1.2pt;
pen axPen=darkblue+0.5pt;

draw(graph(signal,tmin,tmax,n=200),linePen);

string noLabels(real x){return "";};  // format tick labels (empty)
defaultpen(fontsize(10pt));
xaxis(YEquals(ymin),tmin,tmax,axPen,LeftTicks(Step=0.2));
xaxis(YEquals(ymax),tmin,tmax,axPen,RightTicks(noLabels,Step=0.2));
yaxis(ymin,ymax,axPen,RightTicks(Step=0.1));
yaxis(XEquals(tmax),ymin,ymax,axPen,LeftTicks(noLabels,Step=0.1));

\end{asy}
\caption{Fourier Series Expansion with \texttt{Asymptote}}
\end{figure}
\end{document}

为了处理它latexmk，请创建文件latexmkrc：

sub asy {return system("asy '$_[0]'");}
add_cus_dep("asy","eps",0,"asy");
add_cus_dep("asy","pdf",0,"asy");
add_cus_dep("asy","tex",0,"asy");

然后运行latexmk -pdf f.tex。

答案3

我会考虑使用优秀的matlab2tikz，将 MATLAB 绘图转换为 TikZ 图形。这可能是杰克在他的评论中建议。

我matlab2tikz()在上面添加了你的 MATLAB 代码（复制后这三个文件从存储库复制到同一目录中，阅读说明），这会产生一些代码，我手动清理了一下。结果如下。

这当然只是数据的导出，你也可以直接用PGFPlots

结果

\documentclass{article}
\usepackage{tikz,pgfplots}
\usepackage\[active,tightpage\]{preview}
    \PreviewEnvironment{tikzpicture}
\begin{document}

\begin{tikzpicture}
    \begin{axis}
        \addplot \[color=blue,solid\]
            table\[row sep=crcr\]{
            0 0\\
            0.01 0.302387144957655\\
            0.02 0.301150753370238\\
            0.03 0.298375570984069\\
            0.04 0.300647458957776\\
            0.05 0.300548549766943\\
            0.06 0.298995957934019\\
            0.07 0.300480519514177\\
            0.08 0.300480519514176\\
            0.09 0.29899595793402\\
            0.1 0.300548549766943\\
            0.11 0.300647458957775\\
            0.12 0.298375570984069\\
            0.13 0.301150753370238\\
            0.14 0.302387144957655\\
            0.15 3.77542115127404e-15\\
            0.16 -0.302387144957655\\
            0.17 -0.301150753370238\\
            0.18 -0.298375570984069\\
            0.19 -0.300647458957775\\
            0.2 -0.300548549766942\\
            0.21 -0.298995957934019\\
            0.22 -0.300480519514176\\
            0.23 -0.300480519514176\\
            0.24 -0.29899595793402\\
            0.25 -0.300548549766943\\
            0.26 -0.300647458957776\\
            0.27 -0.298375570984068\\
            0.28 -0.301150753370237\\
            0.29 -0.302387144957655\\
            0.3 -7.55084230254808e-15\\
            0.31 0.302387144957654\\
            0.32 0.301150753370237\\
            0.33 0.29837557098407\\
            0.34 0.300647458957777\\
            0.35 0.300548549766944\\
            0.36 0.298995957934018\\
            0.37 0.300480519514177\\
            0.38 0.300480519514174\\
            0.39 0.298995957934022\\
            0.4 0.300548549766944\\
            0.41 0.300647458957777\\
            0.42 0.298375570984067\\
            0.43 0.301150753370237\\
            0.44 0.302387144957654\\
            0.45 -8.18728593532897e-15\\
            0.46 -0.302387144957655\\
            0.47 -0.301150753370238\\
            0.48 -0.298375570984068\\
            0.49 -0.300647458957778\\
            0.5 -0.300548549766943\\
            0.51 -0.298995957934016\\
            0.52 -0.300480519514178\\
            0.53 -0.300480519514179\\
            0.54 -0.29899595793402\\
            0.55 -0.300548549766945\\
            0.56 -0.300647458957773\\
            0.57 -0.298375570984064\\
            0.58 -0.301150753370239\\
            0.59 -0.302387144957652\\
            0.6 -1.51016846050962e-14\\
            0.61 0.302387144957655\\
            0.62 0.301150753370239\\
            0.63 0.298375570984065\\
            0.64 0.300647458957779\\
            0.65 0.300548549766947\\
            0.66 0.298995957934013\\
            0.67 0.300480519514179\\
            0.68 0.300480519514178\\
            0.69 0.298995957934022\\
            0.7 0.300548549766941\\
            0.71 0.300647458957774\\
            0.72 0.298375570984066\\
            0.73 0.301150753370235\\
            0.74 0.302387144957653\\
            0.75 -3.68337151806705e-15\\
            0.76 -0.302387144957655\\
            0.77 -0.301150753370235\\
            0.78 -0.298375570984065\\
            0.79 -0.300647458957776\\
            0.8 -0.30054854976694\\
            0.81 -0.298995957934016\\
            0.82 -0.300480519514178\\
            0.83 -0.300480519514175\\
            0.84 -0.298995957934021\\
            0.85 -0.300548549766944\\
            0.86 -0.300647458957778\\
            0.87 -0.298375570984064\\
            0.88 -0.301150753370239\\
            0.89 -0.302387144957646\\
            0.9 -7.08452764472111e-14\\
            0.91 0.302387144957655\\
            0.92 0.301150753370237\\
            0.93 0.298375570984071\\
            0.94 0.300647458957776\\
            0.95 0.300548549766945\\
            0.96 0.298995957934014\\
            0.97 0.300480519514176\\
            0.98 0.300480519514172\\
            0.99 0.298995957934027\\
            1 0.300548549766942\\
            1.01 0.300647458957771\\
            1.02 0.298375570984071\\
            1.03 0.301150753370237\\
            1.04 0.302387144957656\\
            1.05 -3.7046597480602e-14\\
            1.06 -0.302387144957659\\
            1.07 -0.301150753370238\\
            1.08 -0.29837557098407\\
            1.09 -0.30064745895778\\
            1.1 -0.300548549766942\\
            1.11 -0.298995957934014\\
            1.12 -0.300480519514181\\
            1.13 -0.300480519514172\\
            1.14 -0.298995957934024\\
            1.15 -0.300548549766942\\
            1.16 -0.300647458957776\\
            1.17 -0.298375570984067\\
            1.18 -0.301150753370239\\
            1.19 -0.302387144957663\\
            1.2 -3.02033692101923e-14\\
            };
    \end{axis}
\end{tikzpicture}

\end{document}

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