soundfield.sty

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% MIT License
%
% Copyright (c) 2017 Fiete Winter
%
% Permission is hereby granted, free of charge, to any person obtaining a copy
% of this software and associated documentation files (the "Software"), to deal
% in the Software without restriction, including without limitation the rights
% to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
% copies of the Software, and to permit persons to whom the Software is
% furnished to do so, subject to the following conditions:
%
% The above copyright notice and this permission notice shall be included in all
% copies or substantial portions of the Software.
%
% THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
% IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
% FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
% AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
% LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
% OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
% SOFTWARE.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\NeedsTeXFormat{LaTeX2e}[1994/06/01]
\ProvidesPackage{soundfield}

\RequirePackage{amsmath}
\RequirePackage{amssymb}
\RequirePackage{amsfonts}
\RequirePackage{accents}
\RequirePackage{pgf, pgffor}
\RequirePackage[T3,T1]{fontenc}

\pgfkeys{/sf/.is family}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% FUNCTIONS  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% helper function to create a key representing a variable length list including brackets and delimiter
% parameters:
%   optional parameters (keyvalue pairs): left bracket, right bracket, delimiter, modifier
%   keyname: name of key
%
% Examples:
% afterwards elements can be added via: \pgfkeys{sf, <keyname>={arg1,arg2,arg3}}
%
% all non-empty lists will be printed by calling: \pgfkeys{sf, print}
% all lists will be reset by calling: \pgfkeys{sf, reset}
\newcommand\sfnewlistkey[2][]{  %
  \pgfkeys{  %
    sf,  %
    #2/.style={ #2/enum/.list={##1} },  %  interprete 'argument = {1,2,3}' as list
    % initialize enum of valid elements
    #2/enum/.is choice,
    % 
    #2/current/.initial=\empty,  %
    #2/current/.code = {  %
      \edef\currentvalue{##1}
      \edef\listvalue{\pgfkeysvalueof{/sf/#2/current}}
      \ifx\currentvalue\empty\else
        \ifx\listvalue\empty\else
          \pgfkeys{sf, #2/current/.append=\pgfkeysvalueof{/sf/#2/delimiter} }
        \fi
        \pgfkeys{sf, #2/current/.append={##1}}
      \fi
    },
    #2/print/.code={  %
      \edef\listvalue{\pgfkeysvalueof{/sf/#2/current}}
      \ifx\listvalue\empty\else
        \pgfkeysvalueof{/sf/#2/modifier}
        {  %
        \pgfkeysvalueof{/sf/#2/brackets/left}
        \pgfkeysvalueof{/sf/#2/current}
        \pgfkeysvalueof{/sf/#2/brackets/right}
        }
      \fi
    },
    % add list to print
    print/.append style={ #2/print },  %
    % reset list
    #2/reset/.style = { #2/current/.initial=\empty },  %
    % replace current content of list
    #2/rep/.style = { #2/reset, #2=##1 },  %
    % append reset function to overall reset function
    reset/.append style={ #2/reset }  %
  }
  
  \pgfkeys{sf,  %
    list/.cd, %
    left bracket/.style = {/sf/#2/brackets/left/.initial={##1}},  %
    right bracket/.style = {/sf/#2/brackets/right/.initial={##1}},  %
    delimiter/.style = {/sf/#2/delimiter/.initial={##1}},  %
    modifier/.style = {/sf/#2/modifier/.initial={##1}},   %
    % default values
    left bracket=,  %
    right bracket=,  %
    delimiter= {,},  %
    modifier=,  %
    % optional input
    #1  %
  }
}
% Define a possible choice for key
% \sfnewkeychoice{<keyname>}{<choicename>}{<value>}
\newcommand\sfnewkeychoice[3]{  %
  \pgfkeys{sf, #1/enum/#2/.style={#1/current=#3}}  %
}
% Link a choice for key to symbol
% \sflinkkeychoice{<keyname>}{<choicename>}{<symbol>}
\newcommand\sflinkkeychoice[3]{%
  \pgfkeys{sf,#1/enum/#2/.style={% 
    #1/current=\pgfkeysvalueof{/sf/symbol/enum/#3}%
  }}%
}

% Define a new symbol
% \sfnewsymbol[list of <key-value-pairs>]{<symbolname>}{<value>}
\newcommand\sfnewsymbol[3][]{  %
  \pgfkeys{sf, symbol/new={#2}{#3}{#1} } %
}
% Redefine a new symbol
% \sfrenewsymbol[list of <key-value-pairs>]{<symbolname>}{<value>}
\newcommand\sfrenewsymbol[3][]{  %
  \pgfkeys{sf, symbol/renew={#2}{#3}{#1} } %
}
% Extend existing symbols by additional parameters speficied by key-value-pairs
% \sfextendsymbol[list of <key-value-pairs>]{list of <symbol>}{<symbolsuffix>}
%
% Afterwards for each <symbol> specfied the following command is available:
% \sf<symbolname><symbolsuffix>
\newcommand\sfextendsymbol[3][]{  %
  \pgfkeys{sf,  %
    tmp/symbolname/.style={  %
      tmp/symbolsuffix/.style={symbol/extend={##1}{####1}{#1}},  %
      tmp/symbolsuffix/.list={#3}  %
    },  %
    tmp/symbolname/.list={#2}  %
  }  %
}

\newcommand{\sfprint}[1][]{  %
  \pgfkeys{sf, reset, #1, print, reset}
}

\newcommand\sfnewprefix[2]{  %
  \sfnewkeychoice{prefix}{#1}{#2}
}

\newcommand\sfcustom[2][]{
  \sfprint[symbol/current=#2, #1] 
}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% INITIALISATION %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%% Prefix
\pgfkeys{
  sf,  %
  prefix/.style = { prefix/enum=#1 },
  prefix/enum/.is choice,  %
  prefix/current/.initial=\empty
}

%% Reset and Print
\pgfkeys{  %
  sf,  %
  reset/.style={  %
    symbol/current/.initial=\empty,  %
    prefix/current/.initial=\empty,  %
  },  %
  print/.style={  %
    symbol/current/print  %
  },  %
}

%% Symbols
\pgfkeys{
  sf,  %
  symbol/.style = {symbol/enum=#1},
  symbol/enum/.is choice,  %
  symbol/new/.style n args={3}{  %
    symbol/newcommand={#1},  %
    symbol/enum/#1/.initial=#2,  %
    symbol/enum/#1/.style={symbol/current=\pgfkeysvalueof{/sf/symbol/enum/#1}, #3}  %
  },  %
  symbol/renew/.style n args={3}{  %
    symbol/enum/#1/.initial=#2,  %
    symbol/enum/#1/.style={symbol/current=\pgfkeysvalueof{/sf/symbol/enum/#1}, 
    #3}  %
  },  %
  symbol/extend/.style n args={3}{  %
    symbol/newcommand={#1#2},  %
    symbol/enum/#1#2/.style={symbol/enum/#1, #3}
  }, %
  symbol/newcommand/.code= {  %
    \expandafter\newcommand\csname sf#1\endcsname[1][]{%
      \sfprint[symbol=#1, ##1]  %
    }  %
  },  %
  % current symbol for printing
  symbol/current/.initial=\empty,  %
  symbol/current/print/.code={  %
    \pgfkeysvalueof{/sf/prefix/current}  %
    {\pgfkeysvalueof{/sf/symbol/current}}
  }
}

%% Helper Commands %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\newcommand{\pdiff}[2][]{\frac{\partial^{#1}}{\partial #2^{#1}}}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% SYMBOLS, SUBSCRIPTS, SUPERSCRIPTS, MODIFIERS  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% List of Modifiers %%%%
\sfnewlistkey[modifier={_}]{subscript}  % subscript
\sfnewlistkey[modifier={^}]{superscript}  % superscript

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% List of Elementary Symbols %%%%
%%% Coordinates %%%

%% Cartesian Coordiantes %%
\sfnewsymbol{x}{x}
\sfnewsymbol{y}{y}
\sfnewsymbol{z}{z}
%% Cylindrical Coordinates %%
\sfnewsymbol{cylr}{\rho}
\sfnewsymbol{cylphi}{\phi}
\sfnewsymbol{cylz}{z}
%% Spherical Coordinates %%
\sfnewsymbol{sphr}{r}
\sfnewsymbol{sphphi}{\phi}
\sfnewsymbol{sphtheta}{\vartheta}

%%% Vectors %%%

\sfnewprefix{vec}{\mathbf}
\sfnewsymbol[prefix=vec]{pos}{x}  % position vector
\sfnewsymbol[prefix=vec]{normal}{n}  % normal vector
\sfnewsymbol[prefix=vec]{tangent}{t}  % tangent vector
\sfnewsymbol[prefix=vec]{origin}{0}  % coordinate's origin
\sfnewsymbol[prefix=vec]{unit}{u}  % unit vector

%%% Frequency Domain %%%

%% Spatio-Frequency Domain in Cartesian Coordinates %%
\sfnewsymbol{k}{k}
\sfnewsymbol{kappa}{\kappa}
\sfnewsymbol{kappaprime}{\kappa'}
\sfnewsymbol{kvecnorm}{\hat{\mathbf{k}}}
%\sfnewsymbol{kappa}{\sqrt{\left(\frac \omega c\right)^2 - k_x^2 - k_y^2}}
%\sfnewsymbol{kappaprime}{\sqrt{k_x^2 + k_y^2 - \left(\frac \omega c\right)^2}}
%% Spatio-Frequency Domain in Polar Coordinates %%
\sfnewsymbol{cylm}{m}
\sfnewsymbol{cylmu}{\mu}
%% Spatio-Frequency Domain in Spherical Coordinates %%
\sfnewsymbol{sphn}{n}
\sfnewsymbol{sphm}{m}
\sfnewsymbol{sphnu}{\nu}
\sfnewsymbol{sphmu}{\mu}
%% Time-Frequency Domain %%
\sfnewsymbol{omega}{\omega}  % angular frequency
\sfnewsymbol{f}{f}  % temporal frequency

%% Misc.
\sfnewsymbol{wc}{k}  % wavenumber
\sfnewsymbol{wl}{\lambda}  % wavelength
\sfnewsymbol{t}{t}  % time
\sfnewsymbol{n}{n}  % discrete time
\sfnewsymbol{T}{T}  % constant time

%%% Set Theory, Areas and Boundaries %%%

\sfnewsymbol{set}{\Omega}
\sfnewsymbol{boundary}{\partial \Omega}
\sfnewsymbol{volume}{V}
\sfnewsymbol{area}{A}

\sfnewsymbol{region}{\mathcal S}
\sfnewsymbol{contour}{\partial {\mathcal S}}
\sfnewsymbol{circle}{\mathcal{C}}  % circular area
\sfnewsymbol{R}{R}  % radius of circular area
\sfnewsymbol{line}{l}

%% Sets of numbers
\sfnewsymbol{complex}{\mathbb C}
\sfnewsymbol{real}{\mathbb R}
\sfnewsymbol{int}{\mathbb Z}
\sfnewsymbol{natural}{\mathbb N}

%%% Special Functions %%%

%% spherical Basis function
\sfnewsymbol[subscript=sphn, superscript=sphm]{sphharmonics}{\Psi}
\sfnewsymbol[subscript=sphn]{sphbessel}{j}
\sfnewsymbol[subscript=sphn]{sphneumann}{y}
\sfnewsymbol[subscript=sphn,superscript=secondkind]{sphhankel}{h}
\sfnewsymbol[superscript=sphm,subscript=sphn]{sphreg}{I}% int. sph. basis func.
\sfnewsymbol[superscript=sphm,subscript=sphn]{sphsin}{E}% ext. sph. basis func. 
\sfnewsymbol[superscript={sphm,sphmu},subscript={sphn,sphnu}]{sphrr}{(I|I)}
\sfnewsymbol[superscript={sphm,sphmu},subscript={sphn,sphnu}]{sphss}{(E|E)}
\sfnewsymbol[superscript={sphm,sphmu},subscript={sphn,sphnu}]{sphrs}{(I|E)}
\sfnewsymbol[superscript={sphm,sphmu},subscript={sphn,sphnu}]{sphsr}{(E|I)}
%% cylindrical Basis function
\sfnewsymbol[subscript=cylm]{cylbessel}{J}
\sfnewsymbol[subscript=cylm]{cylneumann}{Y}
\sfnewsymbol[subscript=cylm,superscript=secondkind]{cylhankel}{H}
\sfnewsymbol[subscript=cylm]{cylreg}{I}% int. cyl. basis func.
\sfnewsymbol[subscript=cylm]{cylsin}{E}% ext. cyl. basis func.
\sfnewsymbol[subscript={cylm,cylmu}]{cylrr}{(I|I)}
\sfnewsymbol[subscript={cylm,cylmu}]{cylss}{(E|E)}
\sfnewsymbol[subscript={cylm,cylmu}]{cylrs}{(I|E)}
\sfnewsymbol[subscript={cylm,cylmu}]{cylsr}{(E|I)}
%% differential Operators
\sfnewsymbol{laplace}{\nabla^2} % scalar Laplace operator
\sfnewsymbol{grad}{\mathbf{grad}} % gradient of a scalar field
\sfnewprefix{differential}{\,\mathrm d}
\sfnewprefix{partial}{\partial}
\sfnewprefix{pdiff}{\pdiff}
\sfnewprefix{pdifftwo}{\pdiff[2]}
%% other %%
\sfnewsymbol{dirac}{\delta}
\sfnewsymbol{legendre}{L}
\sfnewsymbol{heaviside}{\Theta}
\sfnewsymbol{signum}{\mathrm{sgn}}
% Sha Symbol
\DeclareFontFamily{U}{wncy}{}
\DeclareFontShape{U}{wncy}{m}{n}{<->wncyr10}{}
\DeclareSymbolFont{mcy}{U}{wncy}{m}{n}
\DeclareMathSymbol{\Sha}{\mathord}{mcy}{"58}
\sfnewsymbol{comb}{\Sha}

%%% Sound Field Synthesis %%%
%% time-frequency dependent %%
\sfnewsymbol{pressure}{P}  % sound pressure
\sfnewsymbol{virtualsource}{S}  % virtual sound field
\sfnewsymbol{driving}{D}  % driving function
\sfnewsymbol{greens}{G}  % Green's function
\sfnewsymbol{hrtf}{H}  % head-related transfer function
\sfnewsymbol{brtf}{B}  % binaural room transfer function
\sfnewsymbol{filter}{H}  % head-related transfer function
\sfnewsymbol{density}{Q}  % density function
\sfnewsymbol{function}{F}  % function
\sfnewsymbol{kernel}{K}  % kernel
\sfnewsymbol{phase}{\Phi}  % kernel
\sfnewsymbol{amp}{A}  % kernel
%% time-frequency independent %%
\sfnewsymbol{select}{a}  % selection function
\sfnewsymbol{window}{w}  % windows function
\sfnewsymbol[subscript=twohalfD]{correct}{c}  % correction factor
\sfnewsymbol{dist}{\Delta}  % selection function
%%% Transforms %%%

\sfnewprefix{transform}{\mathcal}
\sfnewsymbol[prefix=transform]{fourier}{F}  % general fourier transform
\sfnewsymbol[prefix=transform]{inh}{I}  % inhomogeneous part of a sound field
\sfnewsymbol[prefix=transform]{hom}{H}  % homogeneous part of a sound field
\sfnewsymbol[prefix=transform]{sht}{S}  % spherical harmonics transform
\sfnewsymbol[prefix=transform]{cht}{C}  % circular harmonics transform

%%% Utilities %%%

%% Numbers %%
\sfnewsymbol{N}{N}
\sfnewsymbol{M}{M}
%% Constants %%
\sfnewprefix{const}{\mathrm}
\sfnewsymbol[prefix=const]{euler}{e}  % Euler number
\sfnewsymbol[prefix=const]{im}{j}  % imaginary unit
\sfnewsymbol[prefix=const]{speedofsound}{c}  % speed of sound
\sfnewsymbol[prefix=const]{c}{c}  % speed of sound
%% Misc. %%
\sfnewsymbol{dot}{\,.}
\sfnewsymbol{comma}{\,{,}}
\sfnewsymbol{err}{\epsilon}  % general error of something
\sfnewsymbol{delta}{\Delta}  % sampling distance
\sfnewsymbol{cost}{c}  % cost functions
\sfnewsymbol{eta}{\eta}
\sfnewsymbol{zeta}{\zeta}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% List of elementary Prefixes %%%%

%%% Normalisation %%%
\sfnewprefix{norm}{\hat}

%%% Transforms %%%
%% Temporal %%
\sfnewprefix{time}{\MakeLowercase}
\sfnewprefix{ft}{\tilde}
%% Cartesian Coordinates %%
\sfnewprefix{pwd}{\tilde}  % general plane wave decompostion 
\sfnewprefix{ppwd}{\bar}  % signature function
%% Cylindrical Coordinates %%
\sfnewprefix{cht}{\accentset{\diamond}}  % cylindrical harmonics transform
\sfnewprefix{rcb}{\check}  % regular cylindrical basis transform
\sfnewprefix{scb}{\hat}  % singular cylindrical basis transform
%% Spherical Coordinates %%
\sfnewprefix{sht}{\accentset{\circ}} % spherical harmonics transform
\sfnewprefix{rsb}{\breve} % regular spherical basis expansion
\DeclareSymbolFont{tipa}{T3}{cmr}{m}{n}
\DeclareMathAccent{\invbreve}{\mathalpha}{tipa}{16}
\sfnewprefix{ssb}{\invbreve} % regular spherical basis expansion 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% List of elementary Subscripts %%%%

%%% Sound Field Synthesis %%%

%% Dimensions %%
\sfnewkeychoice{subscript}{twoD}{\mathrm{2D}}
\sfnewkeychoice{subscript}{twohalfD}{\mathrm{2.5D}}
\sfnewkeychoice{subscript}{threeD}{\mathrm{3D}}
%% Boundary Conditions %%
\sfnewkeychoice{subscript}{neumann}{\mathrm{N}}  % Neumann/sound hard
\sfnewkeychoice{subscript}{dirichlet}{\mathrm{D}}  % Dirichlet/sound soft
\sfnewkeychoice{subscript}{robin}{\mathrm{R}}  % Robin
%% Source Types %%
\sfnewkeychoice{subscript}{s}{\mathrm{s}}  % virtual source
\sfnewkeychoice{subscript}{pw}{\mathrm{pw}}  % plane wave
\sfnewkeychoice{subscript}{ps}{\mathrm{ps}}  % point source
\sfnewkeychoice{subscript}{dps}{\mathrm{dps}}  % dipole point source
\sfnewkeychoice{subscript}{fs}{\mathrm{fs}}  % focused source
\sfnewkeychoice{subscript}{ls}{\mathrm{ls}}  % line source
%% Domains %%
\sfnewkeychoice{subscript}{local}{\mathrm{l}}  % local domain
\sfnewkeychoice{subscript}{sec}{0}  % loudspeaker domain
\sfnewkeychoice{subscript}{wc}{\{\mathrm{0},l\}}  % wildcard for both
\sfnewkeychoice{subscript}{interior}{\mathrm i}  % interior domain
\sfnewkeychoice{subscript}{exterior}{\mathrm e}  % exterior domain
\sfnewkeychoice{subscript}{h}{\mathrm{h}}  % head domain
%% Coordinates Subscript
\sfnewkeychoice{subscript}{pos}{{\mathbf{x}}}
\sfnewkeychoice{subscript}{possec}{{\mathbf{x}_0}}
\sfnewkeychoice{subscript}{poss}{{\mathbf{x}_{\mathrm{s}}}}
%% HRTF %%
\sfnewkeychoice{subscript}{left}{\mathrm{L}}
\sfnewkeychoice{subscript}{right}{\mathrm{R}}
\sfnewkeychoice{subscript}{leftright}{{\{\mathrm{L},\mathrm{R}\}}}
%% others %%
\sfnewkeychoice{subscript}{c}{\mathrm{c}}  % "center"
\sfnewkeychoice{subscript}{ref}{\mathrm{ref}}  % reference
\sfnewkeychoice{subscript}{incoming}{\mathrm{in}}  % incoming
\sfnewkeychoice{subscript}{scatter}{\mathrm{sc}}  % scattered
\sfnewkeychoice{subscript}{pre}{\mathrm{pre}}  % pre
\sfnewkeychoice{subscript}{samp}{\mathrm{s}}  % sampling
\sfnewkeychoice{subscript}{spa}{\mathrm{SPA}}  % stationary phase approximation

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% List of Subscript derived from Elementary Symbols %%%%

%% Cartesian Coordinates Subscript
\sflinkkeychoice{subscript}{x}{x}
\sflinkkeychoice{subscript}{y}{y}
\sflinkkeychoice{subscript}{z}{z}
%% Cylindrical Coordinates Subscript
\sflinkkeychoice{subscript}{cylr}{cylr}
\sflinkkeychoice{subscript}{cylphi}{cylphi}
%% Spherical Coordinates Subscript
\sflinkkeychoice{subscript}{sphr}{sphr}
%% Wave Number Domain Subscript
\sflinkkeychoice{subscript}{k}{k}
%% Circular Harmonics Subscript
\sflinkkeychoice{subscript}{cylm}{cylm}
\sflinkkeychoice{subscript}{cylmu}{cylmu}
%% Spherical Harmonics Subscript
\sflinkkeychoice{subscript}{sphn}{sphn}
\sflinkkeychoice{subscript}{sphnu}{sphnu}
%% Time Subscript
\sflinkkeychoice{subscript}{t}{t}
%% Error
\sflinkkeychoice{subscript}{err}{err}  % error
%% Misc. %%
\sflinkkeychoice{subscript}{eta}{eta} 
\sflinkkeychoice{subscript}{zeta}{zeta}

%%% Sound Field Synthesis %%%
\sflinkkeychoice{subscript}{pressure}{pressure}
\sflinkkeychoice{subscript}{greens}{greens}
\sflinkkeychoice{subscript}{driving}{driving}
\sflinkkeychoice{subscript}{virtualsource}{virtualsource}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% List of Elementary Superscript %%%%

\sfnewkeychoice{superscript}{sampled}{\mathrm{S}} % sampled
\sfnewkeychoice{superscript}{truncated}{\mathrm{tr}}  % truncated
\sfnewkeychoice{superscript}{sbl}{\mathrm{B}}  % spatial bandwidth limited

%%% Operations %%%
\sfnewkeychoice{superscript}{timereverse}{*} % time reversal/phase conjugation
\sfnewkeychoice{superscript}{transpose}{T} % transpose
\sfnewkeychoice{superscript}{inverse}{-1} 
\sfnewkeychoice{superscript}{prime}{\prime}
\sfnewkeychoice{superscript}{dprime}{\prime\prime}
\sfnewkeychoice{superscript}{shift}{\dagger}  % shifted coordinate frame
\sfnewkeychoice{superscript}{spp}{\ddagger}  % stationary phase point

%% Hankel Functions
\sfnewkeychoice{superscript}{firstkind}{(1)}
\sfnewkeychoice{superscript}{secondkind}{(2)}

%%% Sound Field Synthesis %%%
%% Techniques
\sfnewkeychoice{superscript}{SFS}{\mathrm{SFS}}
\sfnewkeychoice{superscript}{WFS}{\mathrm{WFS}}
\sfnewkeychoice{superscript}{LWFS}{\mathrm{LWFS}}
\sfnewkeychoice{superscript}{LWFS-SBL}{\mathrm{LWFS-SBL}}
\sfnewkeychoice{superscript}{LWFS-VSS}{\mathrm{LWFS-VSS}}
\sfnewkeychoice{superscript}{HOA}{\mathrm{HOA}}
\sfnewkeychoice{superscript}{NFCHOA}{\mathrm{NFCHOA}}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% List of Superscript derived from Elementary Symbols %%%%

%% Spherical Harmonics Superscript
\sflinkkeychoice{superscript}{sphm}{sphm}
\sflinkkeychoice{superscript}{sphmu}{sphmu}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% Extension of Symbols %%%%

%%% Vectors %%%

%% Unit Vector %%
\sfextendsymbol[subscript=x]{unit}{x}  % unit vector in x-direction
\sfextendsymbol[subscript=y]{unit}{y}  % unit vector in y-direction
\sfextendsymbol[subscript=z]{unit}{z}  % unit vector in z-direction
%% Wave Vector %%
\sfextendsymbol[prefix=vec]{k}{vec}  % wave number vector
\sfextendsymbol[subscript=x]{k}{x}  % wave vector component in x-direction
\sfextendsymbol[subscript=y]{k}{y}  % wave vector component in y-direction
\sfextendsymbol[subscript=z]{k}{z}  % wave vector component in z-direction
\sfextendsymbol[subscript=cylr]{k}{cylr}  % wave vector component in x-y-plane
% polar and azimuth angle of wave vector
\sfextendsymbol[subscript=k]{sphphi, sphtheta}{k}

%%% Transforms %%%
%% Fourier %%
\sfextendsymbol[subscript=x]{fourier}{x}  % fourier transform w.r.t. x
\sfextendsymbol[subscript=y]{fourier}{y}  % fourier transform w.r.t. y
\sfextendsymbol[subscript=z]{fourier}{z}  % fourier transform w.r.t. z
\sfextendsymbol[subscript={x,y}]{fourier}{xy}  % fourier transform w.r.t. x, y
\sfextendsymbol[subscript={y,z}]{fourier}{yz}  % fourier transform w.r.t. y, z
\sfextendsymbol[subscript={x,z}]{fourier}{xz}  % fourier transform w.r.t. x, z
\sfextendsymbol[subscript={x,y,z}]{fourier}{xyz}  % fourier transform w.r.t. 
% x,y,z
\sfextendsymbol[subscript=t]{fourier}{t}  % fourier transform w.r.t. t
%% SHT %%
\sfextendsymbol[superscript=inverse]{sht, cht, fourier}{inv}

%% Spatial Transforms
\sfextendsymbol[prefix=pwd]{normal, greens, driving, hrtf, virtualsource}{pwd}

%%% Differential Operators %%%
\sfextendsymbol[prefix=differential]{x, y, z, cylr, cylphi, sphr, sphphi, 
  sphtheta, t, volume, area, line, kx, ky, kz}{diff}
\sfextendsymbol[prefix=pdiff]{x, y, z, cylr, cylphi, sphr, sphphi, sphtheta}%
{pdiff}
\sfextendsymbol[prefix=pdifftwo]{x, y, z, cylr, cylphi, sphr, sphphi, sphtheta}%
{pdifftwo}
\sfextendsymbol[subscript=pos]{grad, laplace}{pos}  % w.r.t. x
\sfextendsymbol[subscript=possec]{grad, laplace}{possec}  % w.r.t. x0

%%% Error %%%
\sfextendsymbol[subscript=err]{pressure}{err} 

%%% Sound Field Synthesis %%%

%% Sound Fields (inhom., hom., Density, Phase, Amplitude) %%
\sfextendsymbol[subscript=pressure]{inh, hom, density, phase, amp,  kvec, 
  kvecnorm}{P}
\sfextendsymbol[subscript=greens]{inh, hom, density, phase, amp, kvec, 
  kvecnorm}{G}
\sfextendsymbol[subscript=virtualsource]{inh, hom, density, phase, amp, kvec, 
  kvecnorm}{S}
\sfextendsymbol[subscript=driving]{phase, amp}{D}
\sfextendsymbol[superscript=prime]
  {phase, phaseP, phaseG, phaseS}{p}
\sfextendsymbol[superscript=dprime]
  {phase, phaseP, phaseG, phaseS}{pp}
%% Source Types %%%
\sfextendsymbol[subscript=s]%
  {pos, normal, driving, areadiff, set, x, y, z, N}{s}
\sfextendsymbol[subscript=pw]%
  {pos, normal, driving, cylphi, sphtheta, sphphi, pressure, kvec, N, dist}{pw}
\sfextendsymbol[subscript=ps]
  {pos, normal, driving, pressure, sphr, sphtheta, sphphi, N, dist}{ps}
\sfextendsymbol[subscript=dps]
  {pos, normal, driving, pressure, sphr, sphtheta, sphphi, N}{dps}
\sfextendsymbol[subscript=ls]{pos, normal, driving, pressure,cylr, cylphi}{ls}
\sfextendsymbol[subscript=fs]
  {pos, normal, driving, greens, density, inh, hom, set, N}{fs}
%% Dimensionality %%%
\sfextendsymbol[subscript=twoD]{greens, driving}{twoD}
\sfextendsymbol[subscript=twohalfD]{pressure, driving}{twohalfD}
\sfextendsymbol[subscript=threeD]{greens, driving}{threeD}
%% Domains %%
\sfextendsymbol[subscript=sec]{pos, normal, tangent, greens, select, 
  driving, set, boundary, area, volume, line, areadiff, volumediff, linediff, 
  laplace, xdiff, ydiff, zdiff, x, y, z, cylrdiff, cylphidiff, cylr, cylphi, 
  sphr, sphrdiff, sphphi, sphphidiff, sphtheta, sphthetadiff, N, R}{sec}
\sfextendsymbol[subscript=local]{pos, normal, driving, select, set, boundary, 
  area, volume, areadiff, volumediff, cylr, cylphi, sphr, sphphi, sphtheta, 
  sphrdiff, N, circle, R, region, contour}{local}
\sfextendsymbol[subscript=h]{pos, cylphi, circle, set, boundary, 
  region, contour, normal, R}{h}
%% HRTFs and BRTFs %%
\sfextendsymbol[subscript=left]{hrtf, brtf}{left}
\sfextendsymbol[subscript=right]{hrtf, brtf}{right}
\sfextendsymbol[subscript=leftright]{hrtf, brtf}{leftright}
%% Sound Field Representations
% spherical coordinates
\sfextendsymbol[prefix=rcb, subscript=cylm]{pressure}{rcb}
\sfextendsymbol[prefix=scb, subscript=cylm]{pressure}{scb}
% spherical coordinates
\sfextendsymbol[prefix=rsb, subscript=sphn, superscript=sphm]{pressure}{rsb}
\sfextendsymbol[prefix=ssb, subscript=sphn, superscript=sphm]{pressure}{ssb}
%% Boundary Conditions %%%
\sfextendsymbol[subscript=neumann]{greens, pressure}{N}
\sfextendsymbol[subscript=dirichlet]{greens, pressure}{D}
%%% Others %%%
\sfextendsymbol[subscript=c]{pos, normal, driving, circle, set, R}{c}
\sfextendsymbol[subscript=ref]{pos, sphr}{ref}
\sfextendsymbol[subscript=samp]{f, omega, T}{samp}
\sfextendsymbol[subscript=scatter]{pressure}{sc}
\sfextendsymbol[subscript=incoming]{pressure}{in}
\sfextendsymbol[subscript=pre]{filter}{pre}
\sfextendsymbol[prefix=norm]{f, k}{norm}
\sfextendsymbol[superscript=sampled]{driving, f, fnorm}{S}
\sfextendsymbol[superscript=truncated]{driving, f, fnorm}{tr}
\sfextendsymbol[superscript=sbl]{virtualsource, driving, f, fnorm}{B}
\sfextendsymbol[superscript=shift]{pos, possec}{shift}
\sfextendsymbol[superscript=spp]{pos, x}{spp}

%% Distances %%
\sfextendsymbol[subscript=x]{delta}{x}
\sfextendsymbol[subscript=y]{delta}{y}
\sfextendsymbol[subscript=z]{delta}{z}
\sfextendsymbol[subscript=cylphi]{delta}{cylphi}