Audio Precompensation Filter for Spatial Robustness
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Solution Overview
Problem
Current digital audio precompensation filters struggle to achieve robust and perceptually acceptable sound reproduction across multiple listening positions, as they often introduce pre-ringings and post-ringings due to their inability to effectively handle non-minimum phase dynamics and spatial variations in acoustic responses.
Innovation Solution
A discrete-time audio precompensation filter is designed using a Single-Input Multiple Output (SIMO) linear model that accounts for non-minimum phase zeros outside the stability region, allowing for the creation of a mixed-phase compensator that minimizes pre-ringings by using a product of a characteristic scalar magnitude response and a causal Finite Impulse Response (FIR) filter, optimized to control residual pre-ringings at all listening positions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If a digital precompensation filter is designed to compensate for measured properties of the sound generating system, then the phase and amplitude response of the compensated system can be made close to an ideal response, but pre-ringings and post-ringings occur due to non-minimum phase dynamics
Solution Approach 1:
The precompensation filter is divided into two separate filters: a minimum phase filter that handles magnitude compensation without creating pre-ringings, and a non-causal filter that handles phase compensation. This segmentation allows each filter to specialize in one aspect, preventing the pre-ringing problem while achieving both magnitude and phase accuracy.
Solution Approach 2:
A delay element is introduced as an intermediary between the minimum phase filter and the non-causal filter. This delay allows the non-causal filter to access future samples without creating pre-ringings in the final output, as the delay shifts the pre-ringing artifacts to occur after the main signal arrival.
2Measurement precision
If equalization is optimized for one single measuring point in space, then the response at that position can be made ideal, but the behavior deviates at other listening positions
Solution Approach 1:
The precompensation filter is designed to handle both magnitude and phase compensation simultaneously, making it universally applicable to achieve ideal response across multiple listening positions rather than being optimized for a single position. The filter structure allows it to address multiple objectives at once.
Solution Approach 2:
The problem is extended from single-point optimization to multi-point optimization by considering spatial dimensions. The filter design incorporates measurements from multiple listening positions and optimizes the frequency and phase response to be robust across this spatial volume, adding the dimension of spatial robustness to the design criteria.
3Object-generated harmful factors
If a minimum phase filter is used for precompensation, then pre-ringings are avoided, but the phase response cannot be accurately controlled
Solution Approach 1:
The compensation task is segmented into two independent functions: magnitude compensation handled by the minimum phase filter (which avoids pre-ringings) and phase compensation handled by the non-causal filter. This segmentation allows each filter to optimize its specific function without compromising the other.
Solution Approach 2:
A delay element serves as an intermediary that allows the non-causal filter to perform phase compensation using future samples. The delay ensures that any pre-ringing artifacts generated by the non-causal filter are shifted to occur after the main signal arrival, effectively hiding them from the listener while maintaining phase accuracy.
Data Source
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AI summary
A discrete-time audio precompensation filter is designed based on a linear model that describes the dynamic response of a sound generating system at p > 1 listening positions. The filter construction is based on providing information (S2) representative of n non-minimum phase zeros {zi} that are outside of the stability region lzl = 1 in the complex frequency domain. A causal Finite Impulse Response (FIR) filter, of user-specified degree d, having coefficients corresponding to a causal part of a delayed non-causal impulse response is determined (S4) based on the information representative of n non-minimum phase zeros. The resulting precompensation filter is determined (S5) as the product of at least two scalar dynamic systems, represented by an inverse of a characteristic scalar magnitude response (S3) in the frequency domain that represents the power gains at the listening positions, and the causal Finite Impulse Response (FIR) filter designed (S4) to approximately invert only non-minimum phase zeros that can be safely inverted.