FourierAnalysis.tex

% Schematic Fourier Analysis
% Author: Tobit Flatscher (https://github.com/2b-t)
%
% Disclaimer
% The following code is based on a previous version of popular community member 
% Jake but I tried to make it more visually appealing. Some noise is added to the 
% curves in order to make them look more realistic.
%
% Description
% This code creates a schematic representation of an FFT analysis. A signal 
% over time is decomposed into its harmonic oscillations with a corresponding 
% frequency using a Fourier series. The amplitude of the frequency components 
% is plotted.


\documentclass[border=10pt]{standalone}

\usepackage{pgfplots}
\pgfplotsset{compat=1.8}
\usepgfplotslibrary{fillbetween} %for fill under curve

\begin{document}
    
    %define colors
    \definecolor{lightgray}{rgb}{0.8, 0.8, 0.8} %grid of coordinate system, axes
    \definecolor{midgray}{rgb}{0.6, 0.6, 0.6} %layer of border
    \definecolor{darkgray}{rgb}{0.4, 0.4, 0.4} %curves, fill under curve
    
    \begin{tikzpicture} %create tikz picture
    \begin{axis}[ %create 3d plot within tikz
        set layers=standard, %use predefined layers
        view={50}{30}, %perspective adjustment
        domain=0:10, %plot limit in time direction
        samples y=1, %samples for frequency direction
        unit vector ratio*=1 2 1, %rescale unit vectors
        hide axis, %do not plot axes
        xtick=\empty, ytick=\empty, ztick=\empty, %no ticks on coordinate axes
        clip=false %let me plot outside the coordinate system
    ]
        %limit variables
        \def\xmax{100} %limits for curves and layers
        \def\xmin{0}
        \def\ymax{35}
        \def\ymin{5}
        \def\zmax{25}
        \def\zmin{-5}
        \def\xlayer{110} %frequency layer
        \def\sumcurve{0} %sum curve of time signal
        
        %frequency curves
        \pgfplotsinvokeforeach{1,2,3}{ %for each frequency component
            \draw [on layer=background, lightgray] (axis cs:0,#1,0) -- (axis cs:10,#1,0); %axes
            \addplot3 [on layer=main, darkgray, smooth, samples=200] (x,#1,{1.3*sin(2*#1*x*(157))/(#1*2)}); %plot curves (curves are somewhat arbitrary)
        
            \xdef\sumcurve{\sumcurve + sin(#1*x*(157))/(#1*2)} %add current curve to sumcurve
        }
    
        %transparent layers
        \fill[white,opacity=0.7] (\xmin,0,\zmin) -- (\xmin,0,\zmax) -- (\xmax,0,\zmax) -- (\xmax,0,\zmin) -- cycle; %transparent layer in time space
        \fill[white,opacity=0.7] (\xlayer,\ymin,\zmin) -- (\xlayer,\ymin,\zmax) -- (\xlayer,\ymax,\zmax) -- (\xlayer,\ymax,\zmin) -- cycle; % transparent layer for frequency space
        
        %grid lines
        \pgfplotsinvokeforeach{\xmin,\xmin+5,...,\xmax}{ %create horizontal grid lines (time layer)
            \draw[lightgray,opacity=0.6] (#1,0,\zmin) -- (#1,0,\zmax);
        }
        \pgfplotsinvokeforeach{\ymin,\ymin+2.5,...,\ymax}{ %create horizontal grid lines (frequency layer)
            \draw[lightgray,opacity=0.6] (\xlayer,#1,\zmin) -- (\xlayer,#1,\zmax);
        }
        \pgfplotsinvokeforeach{\zmin,\zmin+5,...,\zmax}{ %create vertical grid lines (both layers)
            \draw[lightgray,opacity=0.6] (\xmin,0,#1) -- (\xmax,0,#1);
            \draw[lightgray,opacity=0.6] (\xlayer,\ymin,#1) -- (\xlayer,\ymax,#1);
        }
    
        %borders layer
        \draw[midgray] (\xmin,0,\zmin) -- (\xmin,0,\zmax) -- (\xmax,0,\zmax) -- (\xmax,0,\zmin) -- cycle; %time space layer border line
        \draw[midgray] (\xlayer,\ymin,\zmin) -- (\xlayer,\ymin,\zmax) -- (\xlayer,\ymax,\zmax) -- (\xlayer,\ymax,\zmin) -- cycle; %frequency space layer border line
    
        %sum curve
        \addplot3 [samples=200] (x,0,{\sumcurve+rand/7+0.2*sin(x*400)}); %sum curve time space with added random noise
        
        % frequency curve
        \addplot3 [name path=f,samples=200,domain=0.5:3.5] (11,x,{rand/30+2*sin((x-0.7)*180)^200*e^(-x/2)-0.3}); %experimentally modified curve with noise
        
        %create fill under curve
        \addplot3 [name path=ax,draw=none,samples=2,domain=0.5:3.5] (11,x,-0.5); %create fill axis
        \addplot3 [darkgray] fill between [of=f and ax]; %create fill between curve and axis
        
        %create coordinate axis
        \draw[-{stealth}] (\xmin,0,\zmin-7) -- (\xmax/5.3,0,\zmin-7); %time axis
        \draw[-{stealth}] (\xlayer,\ymin,\zmin-7) -- (\xlayer,\ymin+\ymax/4,\zmin-7); %frequency axis
        
        %axis labels
        \node[scale=0.7] at (0,0,-21) {Time}; %axis time space
        \node[scale=0.7] at (100,22,-32) {Frequency}; %axis frequency space
        
    \end{axis}
    \end{tikzpicture}
    
\end{document}