Asymmetric MDCT Windowing Function for Continuous Differentiation
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Solution Overview
Problem
Existing audio coding techniques using asymmetric modified discrete cosine transform (MDCT) and modified discrete sine transform (MDST) windows face suboptimal frequency responses due to non-continuous differentiation, which affects the temporal modulation of quantization error and frequency response.
Innovation Solution
The use of a modulated lapped transform tool with an asymmetric analysis windowing function that meanders across a linear function at four points, defined as being greater in certain intervals and lesser in others, ensuring continuous differentiation and improved frequency response.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If asymmetric MDCT/MDST windows are used to improve frequency response, then frequency response is improved, but continuous differentiation is lost leading to suboptimal temporal modulation of quantization error
Solution Approach 1:
The patent modifies the window function parameters by introducing a meandering portion with specific mathematical formulation that ensures continuous differentiation. The window function w(n) is defined with different segments including a meandering portion that smoothly transitions between regions, maintaining C1 continuity while achieving the desired asymmetric shape for improved frequency response.
Solution Approach 2:
The patent applies curvature principles by designing the meandering portion of the window function to follow a smooth curved path rather than straight line transitions. The meandering portion uses sinusoidal or polynomial curves to ensure continuous first and second derivatives, creating a smoothly varying window shape that avoids abrupt changes while maintaining asymmetry.
2Ease of operation
If conventional asymmetric window shapes are used, then temporal shaping of quantization noise is achieved, but stop band attenuation is insufficient
Solution Approach 1:
The patent applies local quality by designing different portions of the window function with distinct characteristics. The meandering portion has specific properties for temporal noise shaping, while the transition regions are designed with optimized curvature and derivative properties to enhance stop band attenuation. Each segment of the window function is locally optimized for its specific function.
Solution Approach 2:
The patent introduces dynamic characteristics through the meandering portion that adapts the window shape to better match the signal characteristics. The continuous differentiation and smooth transitions allow the window to dynamically respond to signal variations while maintaining optimal stop band attenuation properties across different operating conditions.
3Stability of the object's composition
If symmetric window shapes are used, then continuous differentiation is maintained, but frequency response is suboptimal for low delay applications
Solution Approach 1:
The patent deliberately introduces asymmetry into the window function through the meandering portion design. The window function is defined as asymmetric with different behaviors in the first half and second half of the window, allowing optimization for low delay applications while maintaining continuous differentiation through careful mathematical formulation of the transition regions.
Data Source
AI summary
There are provided methods and apparatus for performing modified cosine transformation (MDCT) with an analysis/synthesis windowing function, using an analysis windowing function having a meandering portion which passes a linear function in correspondence of at least four points.