MDCT Window Functions for Perfect Reconstruction and Low Complexity
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Solution Overview
Problem
Current audio and video coding systems face challenges in achieving flexible and computationally efficient window functions for MDCT applications, particularly in maintaining perfect input reconstruction and optimizing energy compaction, due to the limitations of existing window functions such as sine, KBD, and Vorbis windows.
Innovation Solution
The development of a new class of window functions that extend the sine window by incorporating weighted sinusoids with specific angular frequencies, allowing for adjustable characteristics and reduced computational complexity, while ensuring continuity and improved side lobe attenuation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If predetermined time/space invariant windows are used for MDCT, then perfect input reconstruction is achieved, but flexibility and adaptability are limited
Solution Approach 1:
The patent applies dynamics by making the window function adaptable and variable rather than fixed. The window function is defined by a mathematical expression with adjustable parameters that can be modified based on signal characteristics, allowing the system to adapt to different audio content while maintaining the perfect reconstruction property through the fundamental expression structure.
Solution Approach 2:
The patent implements parameter changes by introducing adjustable parameters into the window function definition. The mathematical expression w(n) = sin(πn/N) * (1 + a*cos(2πn/N) + b*cos(4πn/N)) allows parameters a and b to be changed to modify window characteristics such as main lobe width and side lobe attenuation, providing flexibility while preserving the power complementarity property essential for perfect reconstruction.
2Measurement precision
If KBD window is used, then stopband attenuation is improved, but computational complexity increases due to Bessel function, hyperbolic sine, square root, and division operations
Solution Approach 1:
The patent replaces the computationally expensive KBD window function with a simpler mathematical expression that uses only basic trigonometric functions and arithmetic operations. This 'cheaper' alternative achieves comparable or superior stopband attenuation without requiring complex Bessel functions, square roots, or division operations, making it suitable for real-time processing on resource-constrained devices.
Solution Approach 2:
The patent substitutes the mechanical/mathematical complexity of the KBD window (based on Bessel functions and hyperbolic sine) with a simpler trigonometric-based window function. This substitution maintains the essential filtering functionality while dramatically reducing computational complexity by replacing complex mathematical operations with simpler sine and cosine calculations.
3Productivity
If sine window is used, then computational efficiency is maintained, but passband selectivity and stopband rejection are insufficient
Solution Approach 1:
The patent creates a composite window function by combining multiple trigonometric components: the base sine term sin(πn/N) provides the fundamental windowing effect, while additional cosine terms a*cos(2πn/N) and b*cos(4πn/N) are superimposed to enhance spectral characteristics. This composite structure improves passband selectivity and stopband rejection compared to the simple sine window, while maintaining computational efficiency since all operations remain basic trigonometric and arithmetic calculations.
Data Source
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AI summary
A signal processor for providing a processed version of an input signal in dependence on the input signal comprises a windower configured to window a portion of the input signal, or of a pre-processed version thereof, in dependence on a signal processing window described by signal processing window values for a plurality of window value index values, in order to obtain the processed version of the input signal. The signal processor also comprises a window provider for providing the signal processing window values for a plurality of window value index values in dependence on one or more window shape parameters.