Frequency-Domain Adaptive Filter Step Size for Faster Deep Convergence
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Solution Overview
Problem
Adaptive filters face challenges in achieving quick and deep convergence, as existing methods often prioritize speed over depth or vice versa, leading to suboptimal performance in applications like active noise control and noise cancellation.
Innovation Solution
A frequency domain adaptation block that analyzes the movement direction of filter coefficients and adjusts the step size accordingly, dynamically varying the step size to enhance convergence speed and depth by maintaining separate statistics for real and imaginary parts and adjusting parameters such as leakage inversely proportionally to the predominance of coefficient movement direction.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Speed
If a fixed step size is used in frequency domain adaptive filter, then the filter parameters are simple to control, but the convergence speed and depth cannot be simultaneously optimized
Solution Approach 1:
The patent implements dynamic step size adjustment by tracking the movement direction of filter coefficients in the frequency domain. The step size parameter is modified based on whether coefficients are moving in the same direction (indicating convergence progress) or changing direction (indicating potential overshooting), allowing the filter to adapt its convergence behavior in real-time to achieve both speed and depth optimization
Solution Approach 2:
The patent introduces a feedback mechanism that monitors the movement direction of adaptive filter coefficients and uses this information to adjust the step size. By counting direction changes and comparing current movement with historical movement, the system provides feedback control that modulates the step size to optimize both convergence speed and depth simultaneously
2Speed
If the step size is increased to improve convergence speed, then the filter converges faster, but the convergence depth deteriorates due to overshooting
Solution Approach 1:
The patent dynamically adjusts the step size based on the movement direction statistics of filter coefficients. When coefficients show consistent movement in one direction, the step size is maintained or increased for faster convergence. When direction changes are detected (indicating potential overshooting), the step size is reduced to prevent instability, thus maintaining both speed and reliability
Solution Approach 2:
The patent changes the step size parameter adaptively based on observed coefficient movement patterns. By modifying this critical parameter in response to convergence behavior, the system achieves faster convergence when appropriate while preventing overshooting and maintaining stability, thus resolving the contradiction between speed and reliability
3Manufacturing precision
If the step size is decreased to improve convergence depth, then the filter converges deeper, but the convergence speed deteriorates
Solution Approach 1:
The patent uses dynamic step size adjustment to overcome the trade-off between convergence depth and time. By monitoring coefficient movement directions and adapting the step size accordingly, the filter achieves deep convergence when needed while maintaining faster overall convergence through intelligent parameter modulation, thus reducing total convergence time while achieving sufficient depth
4Productivity
If frequency domain adaptation is used to improve convergence performance, then the filter efficiency increases, but the computational complexity increases due to frequency transformation
Solution Approach 1:
The patent applies segmentation by operating on frequency bins independently after FFT transformation. Each frequency bin's coefficient movement is tracked and adjusted separately, allowing parallel processing and efficient utilization of frequency domain properties while managing computational complexity through structured organization of the adaptation process
Data Source
AI summary
An adaptive filter includes a frequency domain adaptation block that analyzes a statistic of coefficient movement in the frequency domain. The adaption block adjusts, in the frequency domain, a parameter (step size or leakage factor) that affects speed of convergence of the adaptive filter based on the analyzed statistic of filter coefficient movement. The filter includes an associated coefficient, statistic of coefficient movement, and parameter for each frequency bin. The coefficients may be complex numbers, and separate real and imaginary statistics and parameters are maintained. The statistic may be direction counts of the filter coefficient movement. The step size may be adjusted to a predetermined minimum value when the current direction of movement of the filter coefficient is different than the predominant direction and otherwise the step size is adjusted approximately proportionally to an amount of predominance by a value based on a direction count of the filter coefficient movement.