1. A method of rendering sound fields in a left ear and a right ear of a human listener, the sound fields being produced by a plurality of virtual loudspeakers, the method comprising: obtaining, by processing circuitry of a sound rendering computer configured to render the sound fields in the left ear and the right ear of the head of the human listener, a plurality of head-related impulse responses (HRIRs), each of the plurality of HRIRs being associated with a virtual loudspeaker of the plurality of virtual loudspeakers and the left or right ear of the human listener, each of the plurality of HRIRs including samples of a sound field produced at a specified sampling rate in the left or right ear produced in response to an audio impulse produced by that virtual loudspeaker; generating a first state space representation of each of the plurality of HRIRs, the first state space representation including a matrix, a column vector, and a row vector, each of the matrix, the column vector, and the row vector of the first state space representation having a first size; performing a state space reduction operation to produce a second state space representation of each of the plurality of HRIRs, the second state space representation including a matrix, a column vector, and a row vector, each of the matrix, the column vector, and the row vector of the second state space representation having a second size that is less than the first size; and producing a plurality of head-related transfer functions (HRTFs) based on the second state space representation, each of the plurality of HRTFs corresponding to a respective HRIR of the plurality of HRIRs, an HRTF corresponding to the respective HRIR producing, upon multiplication by a frequency-domain sound field produced by the virtual loudspeaker with which the respective HRIR is associated, a component of the sound field rendered in the left or right ear of the human listener.