Method and apparatus for higher order ambisonics encoding and decoding using singular value decomposition

The encoding and decoding of HOA signals using Singular Value Decomposition includes forming (11) based on sound source direction values and an Ambisonics order corresponding ket vectors (| Y (© s )Œª) of spherical harmonics and an encoder mode matrix (ž O x S ). From the audio input signal (| x (© s )Œª) a singular threshold value ( à µ ) determined. On the encoder mode matrix a Singular Value Decomposition (13) is carried out in order to get related singular values which are compared with the threshold value, leading to a final encoder rank ( r fin e ) . Based on direction values (© l ) of loudspeakers and a decoder Ambisonics order ( N l ), corresponding ket vectors (|Y(© l )Œª) and a decoder mode matrix (¨ O x L ) are formed (18). On the decoder mode matrix a Singular Value Decomposition (19) is carried out, providing a final decoder rank ( r fin d ). From the final encoder and decoder ranks a final rank is determined, and from this final rank and the encoder side Singular Value Decomposition an adjoint pseudo inverse (ž + ) € of the encoder mode matrix (ž O x S ) and an Ambisonics ket vector (|a' s Œª) are calculated. The number of components of the Ambisonics ket vector is reduced (16) according to the final rank so as to provide an adapted Ambisonics ket vector (|a' l Œª). From the adapted Ambisonics ket vector, the output values of the decoder side Singular Value Decomposition and the final rank an adjoint decoder mode matrix (¨) € is calculated (15), resulting in a ket vector (| y (© l )Œª) of output signals for all loudspeakers.