Integer MDCT Transform Rounding Error Compensation
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Current audio coding methods, such as MPEG Layer3 and MPEG AAC, face challenges in achieving lossless coding due to accumulating rounding errors in integer transforms, particularly in the MDCT with overlap and add, which affect coding efficiency and introduce approximation errors in the higher frequency range.
Innovation Solution
The development of an integer MDCT (IntMDCT) transform that decomposes the MDCT into Givens rotations and applies a lifting scheme, reducing rounding errors by combining and shaping the rounding error in the frequency domain, where signal energy is present, and placing it in regions with low signal energy, thus reducing the bit rate and improving coding efficiency.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If integer transforms are used in audio coding, then hardware implementation efficiency is improved, but rounding errors accumulate and affect coding precision
Solution Approach 1:
The patent applies error feedback by feeding back the rounding error from the integer transform back to the input signal. The rounding error is calculated as the difference between the original floating-point transform result and the integer transform result, then added to the input signal before transformation. This feedback mechanism compensates for the rounding errors accumulated during integer transform operations, thereby maintaining coding precision while preserving hardware implementation efficiency.
Solution Approach 2:
The patent converts the harmful rounding error into a beneficial component by spectrally shaping it to match the signal's frequency characteristics. Instead of treating rounding error as pure noise to be eliminated, the patent shapes its spectral distribution to concentrate error energy in frequency regions where the signal has low energy content. This transforms the rounding error from a harmful artifact into a less perceptible component, effectively improving coding precision without sacrificing integer transform efficiency.
2Measurement precision
If rounding errors are reduced through multiple rounding operations, then coding precision is improved, but computational complexity increases
Solution Approach 1:
The patent extracts the rounding error as a separate component from the main transform operation. Instead of performing multiple rounding operations within the transform chain, the patent performs a single rounding operation to generate the integer transform result, then separately calculates and processes the rounding error through spectral shaping. This extraction approach reduces computational complexity by eliminating redundant rounding operations while maintaining coding precision through the separate error compensation path.
Solution Approach 2:
The patent applies preliminary spectral shaping to the rounding error before it is added back to the signal. By pre-shaping the error spectrum to match signal characteristics, the patent ensures that error energy is optimally distributed before combination, reducing the need for subsequent correction operations and thereby lowering overall computational complexity while maintaining high coding precision.
3Reliability
If rounding error is spectrally shaped to match signal energy distribution, then lossless coding performance is improved, but transform complexity increases
Solution Approach 1:
The patent changes the spectral parameters of the rounding error to match the signal's frequency characteristics. By applying spectral shaping that modifies the error's frequency distribution according to the signal's energy profile, the patent optimizes the error placement in the frequency domain. This parameter change approach improves lossless coding performance by minimizing perceptible error while using efficient spectral shaping techniques that avoid excessive transform complexity.
Data Source
AI summary
For the reduction of the rounding error, a first and a second non-integer input value are provided and combined, for example by addition, in non-integer state to obtain a non-integer result value which is rounded and added to a third input value. Thus, the rounding error may be reduced at an interface between two rotations divided into lifting steps or between a first rotation divided into lifting steps and a first lifting step of a subsequent multi-dimensional lifting sequence.