convert_N3D_SN3D.m

function outsig = convert_N3D_SN3D(insig, type)
%CONVERT_N3D_TO_SN3D Converts between N3D/SN3D HOA normalization conventions
% CONVERT_N3D_TO_SN3D Converts from orthonormalized (N3D) HOA signals to 
% Schmidt semi-normalized (SN3D) HOA signals, and the opposite. 
%
% Inputs:
%   insig:  The N3D or SN3D HOA signals
%   type:   'sn2n' to convert from SN3D to N3D, or 'n2sn' to do the
%           opposite
%
% Outputs:
%   outsig:  the converted signals
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%   Archontis Politis, 15/11/2015
%   archontis.politis@aalto.fi
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

order = sqrt(size(insig,2))-1;

switch lower(type)
    case 'sn2n'
        SN3Dsig = insig;
        N3Dsig = zeros(size(SN3Dsig));
        % transformation between N3D and SN3D is a simple scaling of same
        % order components
        for no=0:order
            idx_order = no^2 + (1:2*no+1);
            N3Dsig(:, idx_order) = sqrt(2*no+1) * SN3Dsig(:, idx_order);
        end
        outsig = N3Dsig;
        
    case 'n2sn'
        N3Dsig = insig;
        SN3Dsig = zeros(size(N3Dsig));
        % transformation between N3D and SN3D is a simple scaling of same
        % order components
        for no=0:order
            idx_order = no^2 + (1:2*no+1);
            SN3Dsig(:, idx_order) = N3Dsig(:, idx_order)/sqrt(2*no+1);
        end        

        outsig = SN3Dsig;
end

end