Abstract: Techniques of rendering audio involve applying a balanced-realization state space model to each head-related transfer function (HRTF) to reduce the order of an effective FIR or even an infinite impulse response (IIR) filter. Along these lines, each HRTF G(z) is derived from a head-related impulse response filter (HRIR) via, e.g., a z-transform. The data of the HRIR may be used to construct a first state space representation [A, B, C, D] of the HRTF via the relation G(z)=C(zI?A)?1B+D This first state space representation is not unique and so for an FIR filter, A and B may be set to simple, binary-valued arrays, while C and D contain the HRIR data. This representation leads to a simple form of a Gramian Q whose eigenvectors provide system states that maximize the system gain as measured by a Hankel norm.

Abstract: Techniques of rendering audio involve applying a balanced-realization state space model to each head-related transfer function (HRTF) to reduce the order of an effective FIR or even an infinite impulse response (IIR) filter. Along these lines, each HRTF G(z) is derived from a head-related impulse response filter (HRIR) via, e.g., a z-transform. The data of the HRIR may be used to construct a first state space representation [A, B, C, D] of the HRTF via the relation .G(z)=C(zI?A)?1B+D This first state space representation is not unique and so for an FIR filter, A and B may be set to simple, binary-valued arrays, while C and D contain the HRIR data. This representation leads to a simple form of a Gramian Q whose eigenvectors provide system states that maximize the system gain as measured by a Hankel norm. Further, a factorization of Q provides a transformation into a balanced state space in which the Gramian is equal to a diagonal matrix of the eigenvalues of Q.