Representation of sound fields and driving functions as circular and spherical harmonics

SFS_general/besselh_derived.m

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+function out = besselh_derived(nu,k,z)
+% BESSELH_DERIVED derivative of cylindrical hankel function of k kind of order nu, and argument z
+%
+%   Usage: out = besselh_derived(nu,k,z)
+%
+%   Input parameters:
+%       nu  - order of bessel function
+%       z   - argument of bessel function
+%
+%   Output parameters:
+%       out - value of bessel function at point z
+%
+%   BESSELH_DERIVED(nu,z) derivation of cylindrical hankel function of 
+%   order nu, k kind, and argument z
+%
+%   References:
+%       (4.1-51) in Ziomek (1995) - "Fundamentals of acoustic field theory 
+%                                   and space-time signal processing"
+%
+%   see also: besselh
+
+%*****************************************************************************
+% Copyright (c) 2010-2014 Quality & Usability Lab, together with             *
+%                         Assessment of IP-based Applications                *
+%                         Telekom Innovation Laboratories, TU Berlin         *
+%                         Ernst-Reuter-Platz 7, 10587 Berlin, Germany        *
+%                                                                            *
+% Copyright (c) 2013-2014 Institut fuer Nachrichtentechnik                   *
+%                         Universitaet Rostock                               *
+%                         Richard-Wagner-Strasse 31, 18119 Rostock           *
+%                                                                            *
+% This file is part of the Sound Field Synthesis-Toolbox (SFS).              *
+%                                                                            *
+% The SFS is free software:  you can redistribute it and/or modify it  under *
+% the terms of the  GNU  General  Public  License  as published by the  Free *
+% Software Foundation, either version 3 of the License,  or (at your option) *
+% any later version.                                                         *
+%                                                                            *
+% The SFS is distributed in the hope that it will be useful, but WITHOUT ANY *
+% WARRANTY;  without even the implied warranty of MERCHANTABILITY or FITNESS *
+% FOR A PARTICULAR PURPOSE.                                                  *
+% See the GNU General Public License for more details.                       *
+%                                                                            *
+% You should  have received a copy  of the GNU General Public License  along *
+% with this program.  If not, see <http://www.gnu.org/licenses/>.            *
+%                                                                            *
+% The SFS is a toolbox for Matlab/Octave to  simulate and  investigate sound *
+% field  synthesis  methods  like  wave  field  synthesis  or  higher  order *
+% ambisonics.                                                                *
+%                                                                            *
+% http://github.com/sfstoolbox/sfs                      [email protected] *
+%*****************************************************************************
+
+
+%% ===== Checking input parameters =======================================
+nargmin = 3;
+nargmax = 3;
+narginchk(nargmin,nargmax);
+isargscalar(nu)
+isargscalar(k)
+isargnumeric(z)
+
+
+%% ===== Computation =====================================================
+out = 0.5*(besselh(nu-1,k,z) - besselh(nu+1,k,z)); 

SFS_general/besselj_derived.m

@@ -0,0 +1,62 @@
+function out = besselj_derived(nu,z)
+% BESSELJ_DERIVED derivative of cylindrical bessel function of order nu, and argument z
+%
+%   Usage: out = besselh_derived(nu,z)
+%
+%   Input parameters:
+%       nu  - order of bessel function
+%       z   - argument of bessel function
+%
+%   Output parameters:
+%       out - value of bessel function at point z
+%
+%   BESSELJ_DERIVED(nu,z) derivation of cylindrical bessel function of 
+%   order nu, and argument z
+%
+%   References:
+%       (4.1-51) in Ziomek (1995) - "Fundamentals of acoustic field theory 
+%                                   and space-time signal processing"
+%
+%   see also: besselj
+
+%*****************************************************************************
+% Copyright (c) 2010-2014 Quality & Usability Lab, together with             *
+%                         Assessment of IP-based Applications                *
+%                         Telekom Innovation Laboratories, TU Berlin         *
+%                         Ernst-Reuter-Platz 7, 10587 Berlin, Germany        *
+%                                                                            *
+% Copyright (c) 2013-2014 Institut fuer Nachrichtentechnik                   *
+%                         Universitaet Rostock                               *
+%                         Richard-Wagner-Strasse 31, 18119 Rostock           *
+%                                                                            *
+% This file is part of the Sound Field Synthesis-Toolbox (SFS).              *
+%                                                                            *
+% The SFS is free software:  you can redistribute it and/or modify it  under *
+% the terms of the  GNU  General  Public  License  as published by the  Free *
+% Software Foundation, either version 3 of the License,  or (at your option) *
+% any later version.                                                         *
+%                                                                            *
+% The SFS is distributed in the hope that it will be useful, but WITHOUT ANY *
+% WARRANTY;  without even the implied warranty of MERCHANTABILITY or FITNESS *
+% FOR A PARTICULAR PURPOSE.                                                  *
+% See the GNU General Public License for more details.                       *
+%                                                                            *
+% You should  have received a copy  of the GNU General Public License  along *
+% with this program.  If not, see <http://www.gnu.org/licenses/>.            *
+%                                                                            *
+% The SFS is a toolbox for Matlab/Octave to  simulate and  investigate sound *
+% field  synthesis  methods  like  wave  field  synthesis  or  higher  order *
+% ambisonics.                                                                *
+%                                                                            *
+% http://github.com/sfstoolbox/sfs                      [email protected] *
+%*****************************************************************************
+
+%% ===== Checking input parameters =======================================
+nargmin = 2;
+nargmax = 2;
+narginchk(nargmin,nargmax);
+isargscalar(nu)
+isargnumeric(z)
+
+%% ===== Computation =====================================================
+out = 0.5*(besselj(nu-1,z) - besselj(nu+1,z)); 

SFS_general/sphbesselh_derived.m

@@ -0,0 +1,65 @@
+function out = sphbesselh_derived(nu,k,z)
+% SPHBESSELH_DERIVED derivative of spherical hankel function of k kind of order nu, and argument z
+%
+%   Usage: out = sphbesselh_derived(nu,k,z)
+%
+%   Input parameters:
+%       nu  - order of bessel function
+%       z   - argument of bessel function
+%
+%   Output parameters:
+%       out - value of bessel function at point z
+%
+%   SPHBESSELH_DERIVED(nu,z) derivation of spherical hankel function of 
+%   order nu, k kind, and argument z
+%
+%   References:
+%       (4.1-51) in Ziomek (1995) - "Fundamentals of acoustic field theory 
+%                                   and space-time signal processing"
+%
+%   see also: sphbesselh
+
+%*****************************************************************************
+% Copyright (c) 2010-2014 Quality & Usability Lab, together with             *
+%                         Assessment of IP-based Applications                *
+%                         Telekom Innovation Laboratories, TU Berlin         *
+%                         Ernst-Reuter-Platz 7, 10587 Berlin, Germany        *
+%                                                                            *
+% Copyright (c) 2013-2014 Institut fuer Nachrichtentechnik                   *
+%                         Universitaet Rostock                               *
+%                         Richard-Wagner-Strasse 31, 18119 Rostock           *
+%                                                                            *
+% This file is part of the Sound Field Synthesis-Toolbox (SFS).              *
+%                                                                            *
+% The SFS is free software:  you can redistribute it and/or modify it  under *
+% the terms of the  GNU  General  Public  License  as published by the  Free *
+% Software Foundation, either version 3 of the License,  or (at your option) *
+% any later version.                                                         *
+%                                                                            *
+% The SFS is distributed in the hope that it will be useful, but WITHOUT ANY *
+% WARRANTY;  without even the implied warranty of MERCHANTABILITY or FITNESS *
+% FOR A PARTICULAR PURPOSE.                                                  *
+% See the GNU General Public License for more details.                       *
+%                                                                            *
+% You should  have received a copy  of the GNU General Public License  along *
+% with this program.  If not, see <http://www.gnu.org/licenses/>.            *
+%                                                                            *
+% The SFS is a toolbox for Matlab/Octave to  simulate and  investigate sound *
+% field  synthesis  methods  like  wave  field  synthesis  or  higher  order *
+% ambisonics.                                                                *
+%                                                                            *
+% http://github.com/sfstoolbox/sfs                      [email protected] *
+%*****************************************************************************
+
+
+%% ===== Checking input parameters =======================================
+nargmin = 3;
+nargmax = 3;
+narginchk(nargmin,nargmax);
+isargscalar(nu)
+isargscalar(k)
+isargnumeric(z)
+
+
+%% ===== Computation =====================================================
+out = 1/(2*nu+1) * (nu*sphbesselh(nu-1,k,z) - (nu+1)*sphbesselh(nu+1,k,z)); 

SFS_general/sphbesselj_derived.m

@@ -0,0 +1,64 @@
+function out = sphbesselj_derived(nu,z)
+% SPHBESSELJ_DERIVED derivative of spherical bessel function of first kind of order nu, and argument z
+%
+%   Usage: out = sphbesselj_derived(nu,z)
+%
+%   Input parameters:
+%       nu  - order of bessel function
+%       z   - argument of bessel function
+%
+%   Output parameters:
+%       out - value of bessel function at point z
+%
+%   SPHBESSELJ_DERIVED(nu,z) derivation of spherical bessel function of 
+%   order nu, first type, and argument z
+%
+%   References:
+%       (4.1-51) in Ziomek (1995) - "Fundamentals of acoustic field theory 
+%                                   and space-time signal processing"
+%
+%   see also: sphbesselj
+
+%*****************************************************************************
+% Copyright (c) 2010-2014 Quality & Usability Lab, together with             *
+%                         Assessment of IP-based Applications                *
+%                         Telekom Innovation Laboratories, TU Berlin         *
+%                         Ernst-Reuter-Platz 7, 10587 Berlin, Germany        *
+%                                                                            *
+% Copyright (c) 2013-2014 Institut fuer Nachrichtentechnik                   *
+%                         Universitaet Rostock                               *
+%                         Richard-Wagner-Strasse 31, 18119 Rostock           *
+%                                                                            *
+% This file is part of the Sound Field Synthesis-Toolbox (SFS).              *
+%                                                                            *
+% The SFS is free software:  you can redistribute it and/or modify it  under *
+% the terms of the  GNU  General  Public  License  as published by the  Free *
+% Software Foundation, either version 3 of the License,  or (at your option) *
+% any later version.                                                         *
+%                                                                            *
+% The SFS is distributed in the hope that it will be useful, but WITHOUT ANY *
+% WARRANTY;  without even the implied warranty of MERCHANTABILITY or FITNESS *
+% FOR A PARTICULAR PURPOSE.                                                  *
+% See the GNU General Public License for more details.                       *
+%                                                                            *
+% You should  have received a copy  of the GNU General Public License  along *
+% with this program.  If not, see <http://www.gnu.org/licenses/>.            *
+%                                                                            *
+% The SFS is a toolbox for Matlab/Octave to  simulate and  investigate sound *
+% field  synthesis  methods  like  wave  field  synthesis  or  higher  order *
+% ambisonics.                                                                *
+%                                                                            *
+% http://github.com/sfstoolbox/sfs                      [email protected] *
+%*****************************************************************************
+
+
+%% ===== Checking input parameters =======================================
+nargmin = 2;
+nargmax = 2;
+narginchk(nargmin,nargmax);
+isargscalar(nu)
+isargnumeric(z)
+
+
+%% ===== Computation =====================================================
+out = 1/(2*nu+1) * (nu*sphbesselj(nu-1,z) - (nu+1)*sphbesselj(nu+1,z));

SFS_general/sphbessely_derived.m

@@ -0,0 +1,64 @@
+function out = sphbessely_derived(nu,z)
+% SPHBESSELY_DERIVED derivative of spherical bessel function of second kind of order nu, and argument z
+%
+%   Usage: out = sphbessely_derived(nu,z)
+%
+%   Input parameters:
+%       nu  - order of bessel function
+%       z   - argument of bessel function
+%
+%   Output parameters:
+%       out - value of bessel function at point z
+%
+%   SPHBESSELY_DERIVED(nu,z) derivation of spherical bessel function of 
+%   order nu, second type, and argument z
+%
+%   References:
+%       (4.1-51) in Ziomek (1995) - "Fundamentals of acoustic field theory 
+%                                   and space-time signal processing"
+%
+%   see also: sphbesselj
+
+%*****************************************************************************
+% Copyright (c) 2010-2014 Quality & Usability Lab, together with             *
+%                         Assessment of IP-based Applications                *
+%                         Telekom Innovation Laboratories, TU Berlin         *
+%                         Ernst-Reuter-Platz 7, 10587 Berlin, Germany        *
+%                                                                            *
+% Copyright (c) 2013-2014 Institut fuer Nachrichtentechnik                   *
+%                         Universitaet Rostock                               *
+%                         Richard-Wagner-Strasse 31, 18119 Rostock           *
+%                                                                            *
+% This file is part of the Sound Field Synthesis-Toolbox (SFS).              *
+%                                                                            *
+% The SFS is free software:  you can redistribute it and/or modify it  under *
+% the terms of the  GNU  General  Public  License  as published by the  Free *
+% Software Foundation, either version 3 of the License,  or (at your option) *
+% any later version.                                                         *
+%                                                                            *
+% The SFS is distributed in the hope that it will be useful, but WITHOUT ANY *
+% WARRANTY;  without even the implied warranty of MERCHANTABILITY or FITNESS *
+% FOR A PARTICULAR PURPOSE.                                                  *
+% See the GNU General Public License for more details.                       *
+%                                                                            *
+% You should  have received a copy  of the GNU General Public License  along *
+% with this program.  If not, see <http://www.gnu.org/licenses/>.            *
+%                                                                            *
+% The SFS is a toolbox for Matlab/Octave to  simulate and  investigate sound *
+% field  synthesis  methods  like  wave  field  synthesis  or  higher  order *
+% ambisonics.                                                                *
+%                                                                            *
+% http://github.com/sfstoolbox/sfs                      [email protected] *
+%*****************************************************************************
+
+
+%% ===== Checking input parameters =======================================
+nargmin = 2;
+nargmax = 2;
+narginchk(nargmin,nargmax);
+isargscalar(nu)
+isargnumeric(z)
+
+
+%% ===== Computation =====================================================
+out = 1/(2*nu+1) * (nu*sphbessely(nu-1,z) - (nu+1)*sphbessely(nu+1,z));