Linear-Phase FIR Audio Filter With Lower Latency Subfilter Convolution
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Solution Overview
Problem
Linear-phase FIR filters in audio technology face high latency issues due to the need for a higher number of coefficients, which is problematic in live transmissions where delays can be noticeable, and current solutions either accept this latency or compromise phase linearity by using IIR filters.
Innovation Solution
A method for generating a linear-phase digital FIR filter by combining two subfilters through linear convolution and truncating the resulting sum set using a window function, maintaining phase linearity while reducing the number of coefficients and latency, particularly suitable for medium to high-frequency ranges.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If the number of coefficients in linear-phase FIR filters is increased to reduce latency, then phase linearity is improved, but the filter complexity and computing time increase
Solution Approach 1:
The filter is divided into multiple subfilters with smaller coefficient sets. Each subfilter processes a portion of the frequency spectrum independently, allowing the overall system to achieve the desired phase linearity and frequency response without requiring a single large coefficient set. This segmentation reduces the complexity of individual filter stages while maintaining overall performance.
Solution Approach 2:
Multiple subfilters are combined through multiplication in the frequency domain (or convolution in the time domain) to create the final filter response. By merging the effects of several smaller subfilters, the system achieves the equivalent performance of a larger filter with fewer coefficients, resolving the contradiction between phase linearity and computational complexity.
2Loss of time
If the number of coefficients in linear-phase FIR filters is reduced to decrease latency, then latency is improved, but filtering precision deteriorates
Solution Approach 1:
The filtering task is segmented across multiple subfilters, each with reduced coefficient sets that introduce minimal latency. The segmentation allows the system to achieve the overall filtering effect with smaller individual coefficient sets, thereby reducing total latency while maintaining filtering precision through the combined effect of all subfilters.
Solution Approach 2:
Each subfilter performs a partial filtering action on a specific portion of the frequency spectrum rather than attempting to perform the complete filtering task with a single large coefficient set. This partial action approach allows each subfilter to use fewer coefficients, reducing latency, while the cumulative effect of all subfilters achieves the required filtering precision.
3Loss of time
If IIR filters are used to reduce latency, then latency is improved, but phase linearity is compromised
Solution Approach 1:
The patent replaces the traditional IIR filter mechanism (which uses feedback and can achieve low latency but poor phase linearity) with an alternative approach using multiple FIR subfilters. By substituting the IIR feedback mechanism with a parallel/sequential combination of FIR subfilters, the system achieves low latency through reduced coefficient counts while maintaining the phase linearity characteristic of FIR filters.
Data Source
AI summary
Systems and methods for producing a linear-phase digital FIR filter from two sub-filters for an audio signal. In one method, the sub-filters are provided as sub-sets having numbers of coefficients, a lower cutoff frequency of the particular sub-filter being greater than the sampling frequency of the audio signal divided by the number. The sub-sets are linearly convoluted with one another so as to form a total set having a number of coefficients greater than the numbers, and the total set is symmetrically reduced to a number less than the number, so as to form a reduced total set of the filter. A linear-phase digital FIR filter for an audio signal is created by the method.