Minimum-Phase Frequency Response Matching for Real-Time Audio Filtering
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Solution Overview
Problem
Existing methods for dynamically adjusting the frequency response of audio signals to match a target magnitude frequency response are inefficient and prone to audible artefacts, particularly in real-time applications, due to computational complexity and non-linear decomposition issues.
Innovation Solution
The method recasts the concatenation of minimum phase filters as a linear equation in the logarithmic domain, using constrained basis functions that satisfy the minimum phase constraint, allowing for a deterministic and efficient calculation of gain parameters to match an arbitrary target magnitude frequency response.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If iterative methods are used to match target magnitude frequency response, then adaptability is improved, but computational complexity increases and convergence cannot be guaranteed
Solution Approach 1:
The patent transforms the frequency response matching problem from the linear domain to the logarithmic domain by applying parameter transformation. This changes the mathematical nature of the problem, converting a complex non-linear optimization problem into a simpler linear system that can be solved directly without iteration, thereby reducing computational complexity while maintaining adaptability
Solution Approach 2:
The patent replaces the iterative computational mechanism with a direct algebraic solution mechanism. By substituting the iterative optimization process with a closed-form mathematical solution in the logarithmic domain, the system eliminates the need for complex computational iterations while achieving the same adaptive matching goal
2Stability of the object's composition
If linear phase equalisation is used, then phase preservation is improved, but pre-ringing artefacts occur
Solution Approach 1:
The patent employs asymmetric filter design by using minimum phase filters instead of symmetric linear phase filters. This asymmetry in the impulse response allows the filter to achieve phase preservation while eliminating the symmetric pre-ringing artifacts that characterize linear phase equalization, as the energy is concentrated in the causal direction rather than being smeared symmetrically in both time directions
3Manufacturing precision
If minimum phase filters are concatenated to match target response, then manufacturing precision is improved, but non-linear decomposition problems arise
Solution Approach 1:
The patent applies parameter transformation by working in the logarithmic domain rather than the linear domain. This transformation linearizes the concatenation operation, converting the non-linear decomposition problem into a simple linear system where the gain parameters can be directly calculated without complex iterative decomposition algorithms
Solution Approach 2:
The patent introduces the logarithmic domain as an intermediary mathematical space. By transforming the frequency response parameters into the logarithmic domain, the complex non-linear relationships between concatenated minimum phase filters are simplified into linear relationships, making the decomposition and calculation of gain parameters straightforward
4Adaptability or versatility
If dynamic adjustment of frequency response is implemented, then adaptability is improved, but temporal oscillations and artefacts increase
Solution Approach 1:
The patent uses parameter transformation to the logarithmic domain to enable dynamic adjustment of frequency response parameters. This transformation allows gain parameters to be calculated directly from the target magnitude frequency response without iterative processes, ensuring stable and artifact-free dynamic adjustments that adapt to changing requirements in real-time
Data Source
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AI summary
The invention provides a method and apparatus for filtering a temporal signal. A target magnitude frequency response H T (f) is specified (101,201) of frequency f in terms of a column vector l of K weights l k where log H T (f) = l T W(f) and W(f) is a column vector of K magnitude basis functions Wk(f). A constrained frequency response H c (f) is computed (102,214) defined by log H c (f) = g T V(f) , where V(f) is a column vector of N constrained basis functions V n (f) for which each exp g n V n (f) satisfies a constraint preserved by concatenation, and g is a column vector of N coefficients satisfying a matching criterion between l T W(f) and g T V(f). An input temporal signal is received (103,212) and filtered (104,210) with the constrained frequency response H c (f) to form a filtered temporal signal; and the filtered temporal signal is output (105,211).