Matrix Decomposition for Adaptive Audio Codec Systems
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Solution Overview
Problem
High-definition audio codec systems, such as Dolby TrueHD, require large precision calculations for downmix and upmix operations, leading to the need for a method to decompose downmix specification matrices into primitive matrices with limited coefficient values to reduce bit requirements and enable efficient transmission of adaptive audio content.
Innovation Solution
The method involves decomposing downmix or upmix matrices into a sequence of unit primitive matrices and a permutation matrix, with absolute coefficient values in non-trivial rows constrained within the audio processing system's limits, allowing for finite precision implementations and efficient matrix operations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If large precision calculations are used for downmix and upmix operations, then audio reproduction accuracy is improved, but bit requirements and system complexity increase
Solution Approach 1:
The patent segments the downmix specification matrix into a sequence of primitive matrices, each with simple coefficient structures (typically identity matrices with one modified row). This segmentation allows complex matrix operations to be broken down into simpler, more manageable steps that reduce computational precision requirements while maintaining audio reproduction accuracy.
Solution Approach 2:
The patent changes the parameter representation by constraining matrix coefficients to specific quantized values (e.g., integers or limited precision floats) rather than using full precision real numbers. This parameter transformation enables efficient fixed-point arithmetic and reduces bit requirements while preserving sufficient audio quality through carefully designed quantization schemes.
2Measurement precision
If large precision calculations are used for downmix and upmix operations, then audio reproduction accuracy is improved, but transmission efficiency decreases
Solution Approach 1:
By segmenting the transformation matrix into primitive matrices with simple structures, the patent reduces the number of bits required to represent each matrix coefficient. This segmentation enables more efficient encoding and transmission of matrix data while maintaining the ability to achieve accurate audio reproduction through the sequence of simpler operations.
Solution Approach 2:
The patent uses approximate representations (primitive matrices with quantized coefficients) that are computationally cheaper and require fewer bits to transmit. While each individual primitive matrix is an approximation, the sequence of such matrices collectively achieves the desired transformation with significantly reduced transmission requirements compared to full-precision matrices.
3Measurement precision
If full precision matrices are transmitted, then decoding accuracy is improved, but legacy device compatibility decreases
Solution Approach 1:
The patent transforms the matrix representation into a form with constrained parameters (primitive matrices with limited coefficient values) that can be processed by legacy devices with fixed-point arithmetic capabilities. This parameter transformation maintains sufficient decoding accuracy for legacy devices while enabling new devices to achieve lossless decoding when full precision is available.
Solution Approach 2:
The patent creates a universal matrix representation format (sequence of primitive matrices) that can be processed by both legacy devices and modern high-definition audio decoders. This multi-functional format allows legacy devices to perform downmix operations with limited precision while new devices can reconstruct the full precision original signal, achieving backward compatibility and forward capability simultaneously.
Data Source
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AI summary
A method of decomposing a matrix of dimension L-by-N, where L is less than or equal to N, into a sequence of N-by-N unit primitive matrices and a permutation matrix comprising a sequence that is the product of the primitive matrices and the permutation matrix, containing L rows that are substantially close to the provided L-by-N matrix, where the choice of the permutation matrix and the indices of the non-trivial rows in the primitive matrices are chosen to limit the coefficient values in the primitive matrices.