Heyser Spiral FIR Equalization for Low-Frequency Loudspeaker Correction
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Solution Overview
Problem
FIR filters face challenges in correcting magnitude and phase at low frequencies, leading to difficulties in loudspeaker-room acoustic equalization, particularly below 300 Hz, due to their finite length and the time-frequency uncertainty principle.
Innovation Solution
The Heyser Spiral curve fitting method is used to generate FIR filter coefficients, fitting three-dimensional curves based on desired magnitude and phase responses to improve low-frequency performance, allowing for separate polynomial fitting of magnitude and phase below a selected frequency and conjugation to a target transfer function above that frequency.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If FIR filter is used for loudspeaker equalization, then filter stability and linearity are improved, but low frequency correction capability deteriorates
Solution Approach 1:
The frequency range is segmented into low-frequency and high-frequency portions. Separate polynomial functions are fitted to each segment, with the low-frequency portion using a polynomial that can accurately represent magnitude and phase relationships. This segmentation allows each frequency range to be optimized independently, resolving the contradiction between FIR filter stability and low-frequency correction capability.
Solution Approach 2:
Different polynomial fitting strategies are applied to different frequency regions. The low-frequency region uses a polynomial formulation specifically designed to capture magnitude and phase behavior, while other regions use standard FIR filter design approaches. This local quality approach enables precise low-frequency correction while maintaining overall filter stability.
2Measurement precision
If FIR filter order is increased to improve low frequency resolution, then frequency resolution is improved, but filter complexity increases
Solution Approach 1:
The patent changes the parameter representation by using polynomial coefficients to define filter behavior rather than traditional FIR coefficients. This parameter transformation allows low-frequency resolution to be improved through polynomial degree selection without necessarily increasing the overall filter order, thus reducing computational complexity while maintaining frequency resolution.
3Adaptability or versatility
If polynomial fitting is applied to magnitude and phase separately, then fitting flexibility is improved, but convergence to target transfer function deteriorates
Solution Approach 1:
The patent merges magnitude and phase fitting into a unified polynomial framework where both are represented as polynomial functions of frequency. This combined approach ensures that magnitude and phase converge together to the target transfer function, maintaining consistency while preserving the flexibility of separate polynomial representations. The unified formulation guarantees convergence to the desired target response.
Data Source
AI summary
A method of operating a loudspeaker includes providing a digital audio signal and identifying a target transfer function to be applied to the signal. At least one coefficient of an FIR filter is generated. The generating includes performing Heyser spiral curve fitting, and fitting a three-dimensional curve based on a magnitude and phase of a target transfer function. The digital audio signal is filtered through the FIR filter. The filtered signal is inputted into the loudspeaker.