Shelving Filter Structure for Fixed-Phase Audio Equalization
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Solution Overview
Problem
Existing digital filters used in sound systems for audio equalization often distort the magnitude response when attempting to maintain a well-defined phase response, making it difficult to independently adjust these parameters, leading to issues like 'pre-ringing' and 'temporal diffusion'.
Innovation Solution
A filter structure comprising a series of shelving filters with fixed phase response, where each shelving filter consists of a cascade of fourth-order low-pass and high-pass filters with pre-defined cut-off frequencies and Q factors, allowing for independent adjustment of broadband gains to modify the magnitude response without altering the phase response.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If linear phase filters are used to maintain fixed phase response, then phase relations between audio channels are preserved, but pre-ringing and temporal diffusion occur
Solution Approach 1:
The filter is segmented into multiple second-order sections (biquad filters) connected in cascade, where each section contributes to the overall fourth-order transfer function. This segmentation allows the filter to achieve the desired magnitude response while maintaining a fixed phase response characteristic, avoiding the harmful effects of linear phase filters.
Solution Approach 2:
The filter design changes the parameters of second-order sections (cut-off frequencies and Q factors) to create a fourth-order filter with specific magnitude and phase characteristics. By carefully selecting these parameters, the filter achieves a fixed phase response that avoids pre-ringing and temporal diffusion while providing the desired equalization.
2Reliability
If digital filters are designed to provide well-defined phase response, then phase relations are maintained, but magnitude response is distorted
Solution Approach 1:
The filter design allows dynamic adjustment of the magnitude response through variable gain stages while maintaining a fixed phase response. The fourth-order filter structure provides independent control over magnitude characteristics without affecting the phase relations, enabling precise equalization.
Solution Approach 2:
The fourth-order filter structure acts as an intermediary between the input audio signal and the output, providing a fixed phase response that mediates the signal transmission while allowing flexible magnitude adjustment. This intermediary structure decouples the phase and magnitude control, solving the contradiction between phase definition and magnitude precision.
3Adaptability or versatility
If filter parameters are adjusted to tune magnitude response, then equalization is achieved, but phase response changes
Solution Approach 1:
The filter is divided into multiple independent second-order sections that can be adjusted individually. Each section contributes to the overall magnitude response but maintains the fixed phase characteristic when properly configured. This segmentation enables versatile magnitude tuning without compromising phase consistency.
Solution Approach 2:
The filter design uses asymmetric configuration of the second-order sections with different cut-off frequencies and Q factors to achieve the desired magnitude response. This asymmetric arrangement allows independent control of magnitude characteristics while preserving the symmetric fixed phase response characteristic of the overall fourth-order filter.
Data Source
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AI summary
An equalization filter structure for filtering an audio signal within an audio system is disclosed. The equalization filter comprises a first and a second shelving filter each having a fixed first and a fixed second phase response, each of which is determined by a respective cut-off frequency and Q factor which represent the transfer characteristic of the corresponding shelving filter. The first and the second shelving filters are coupled in series and each shelving filter comprises at least one fourth order low-pass filter having a cut-off frequency, a Q factor, and a first broadband gain and further at least one fourth order high-pass filter having a second broadband gain and the same cut-off frequency and the same Q factor as the low-pass filter. The fourth order low-pass filter and the fourth order high-pass filter are connected in parallel, such that both filters receive the same input signal and the corresponding filtered signals are summed to form a respective shelving filter output signal. Each fourth order low-pass and high-pass filter is composed of a cascade of two second order low-pass or high-pass filters, respectively, and each second order filter has the same cut-off frequency and Q factor as the corresponding shelving filter.