Oversampled DFT Filter Bank Synthesis Window Optimization
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Solution Overview
Problem
Existing oversampled DFT filter banks lack an effective technique for optimizing their operation, particularly in achieving improved performance through better synthesis window design, which is crucial for applications like subband adaptive filtering and dynamic range compression.
Innovation Solution
A system and method that utilize a null space generator to produce a basis of the null space of a perfect reconstruction condition matrix, allowing for the construction of an optimized synthesis window using various optimization criteria such as minimum delay, minimum out-of-band, least-square, and minimum quantization-error designs.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If minimum-norm solution is used for synthesis window design, then device complexity is reduced, but manufacturing precision deteriorates
Solution Approach 1:
The patent changes the optimization parameter from minimum-norm to minimum-delay criterion. This parameter change allows the synthesis window to achieve perfect reconstruction with reduced delay, improving both time-domain performance and reconstruction precision without increasing system complexity
Solution Approach 2:
The patent introduces dynamic optimization by allowing the synthesis window to be adapted based on the null space basis vectors. This enables the system to dynamically adjust window parameters to achieve optimal performance for different signal processing scenarios while maintaining perfect reconstruction
2Measurement precision
If oversampling is implemented to mitigate aliasing, then measurement precision improves, but device complexity increases
Solution Approach 1:
The patent extracts and utilizes the null space basis vectors from the perfect reconstruction condition matrix. By separating the reconstruction conditions into a structured form with identifiable null space components, the system can efficiently implement oversampled filter banks with reduced computational complexity
Solution Approach 2:
The patent segments the synthesis window design into multiple components based on the null space basis vectors. This segmentation allows independent optimization of different window parameters (such as main lobe width, side lobe levels, and delay characteristics) while maintaining perfect reconstruction, thereby managing complexity through modular design
3Productivity
If extensive subband sample processing is performed, then productivity improves, but object-generated harmful factors increase
Solution Approach 1:
The patent applies preliminary action by designing the synthesis window in advance to satisfy perfect reconstruction conditions. The null space basis vectors are pre-computed and used to construct windows that inherently prevent aliasing, allowing extensive subband processing without introducing harmful artifacts during the processing stage
Data Source
AI summary
A system for, and method of optimizing an operation of an oversampled filter bank and an oversampled discrete Fourier transform (DFT) filter bank designed by the system or the method. In one embodiment, the system includes: (1) a null space generator configured to produce a basis of a null space of a perfect reconstruction condition matrix based on a first window of the oversampled filter bank and (2) an optimizer associated with the basis generator and configured to employ the null space and an optimization criterion to construct a second window of the oversampled filter bank.