Sparse decomposition of head related impulse responses with applications to spatial audio rendering
This application describes methods of signal processing and spatial audio synthesis. One such method includes accepting an auditory signal and generating an impression of auditory virtual reality by processing the auditory signal to impute a spatial characteristic on it via convolution with a plurality of head-related impulse responses. The processing is performed in a series of steps, the steps including: performing a first convolution of an auditory signal with a characteristic-independent, mixed-sign filter and performing a second convolution of the result of first convolution with a characteristic-dependent, sparse, non-negative filter. In some described methods, the first convolution can be pre-computed and the second convolution can be performed in real-time, thereby resulting in a reduction of computational complexity in said methods of signal processing and spatial audio synthesis.
1. A method of signal processing, comprising:
accepting a physical signal having a characteristic indicative of a physical property in a first state; and
processing the physical signal to effect a transformation of the physical signal from the first state to a second state by applying a representation of a base filter to the physical signal;
wherein the representation of the base filter is a convolution of a plurality of filters, and the base filter is an impulse response dependent upon the characteristic and inclusive of mixed signs.
2. The method of claim 1 , wherein the characteristic is a direction associated with a location of an origin of the physical signal.
3. The method of claim 2 , wherein the impulse response is one of a plurality of head-related impulse responses parameterized by one of the location and the direction.
4. The method of claim 1 , wherein the convolution includes approximate decomposition of the characteristic-dependent, mixed-sign base filter into a characteristic-independent, mixed-sign filter represented as a mixed-sign, Toeplitz-structured matrix and a characteristic-dependent, non-negative filter represented as a non-negative matrix.
5. The method of claim 4 , wherein the non-negative matrix is made sparse.
6. The method of claim 5 , wherein the sparsity of the non-negative matrix is tuned using a non-negative least squares solver to achieve a target approximation error.
7. The method of claim 6 , wherein the approximation error is one of a root-mean square error and a spectral distortion.