Complex Modulated Filterbank for Short-Response Audio Filtering
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Solution Overview
Problem
Current filter systems for audio signals, particularly in HRTF-related applications, face inefficiencies in processing due to long impulse responses and limitations in computational complexity, especially when trying to model intricate phase characteristics and adapt to individual hearing needs.
Innovation Solution
A filter apparatus and method utilizing a complex analysis and synthesis filter bank with intermediate filters having shorter impulse responses, allowing for parallel processing and efficient conversion of time domain signals into the subband domain, enabling flexible and high-quality filtering with reduced computational effort.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If a filter with non-uniform amplitude/frequency characteristic is implemented directly in time domain, then the filter characteristic is accurately achieved, but the impulse response becomes very long increasing computational complexity and memory usage
Solution Approach 1:
The filter is segmented into multiple subband filters operating in parallel. Each subband filter processes a specific frequency range with shorter impulse responses, while collectively they reproduce the characteristics of the original long impulse response filter. This segmentation reduces computational complexity while maintaining filter accuracy.
Solution Approach 2:
The solution transitions from time-domain processing to frequency-domain processing by using a complex modulated filter bank. The filter operation is moved to the frequency domain where convolution becomes multiplication, dramatically reducing computational complexity from O(N*M) to O(N*log(N)) while maintaining spectral precision.
2Measurement precision
If a complex modulated filter bank is used for spectral processing, then frequency resolution is enhanced, but the filter bank resolution may still be insufficient for accurate phase characteristic modeling
Solution Approach 1:
Different subband filters are designed with locally optimized characteristics tailored to their specific frequency ranges. Each subband filter has impulse responses adapted to its frequency region, allowing accurate phase characteristic modeling in each local frequency band while maintaining overall high frequency resolution across the spectrum.
3Adaptability or versatility
If HRTF filtering is performed in time domain, then individual hearing characteristics can be modeled, but processing efficiency is reduced due to long filter impulse responses
Solution Approach 1:
The HRTF filters are pre-computed and transformed into the frequency domain before actual audio processing. The complex modulated filter bank coefficients are prepared in advance, allowing efficient real-time processing of audio signals while maintaining accurate individual hearing characteristics through pre-characterized frequency responses.
Data Source
Figure 1a~1c
Figure 1d~1e
Figure 2~4
AI summary
A filter apparatus for filtering a time domain input signal to obtain a time domain output signal, which is a representation of the time domain input signal filtered using a filter characteristic having an non-uniform amplitude/frequency characteristic, comprises a complex analysis filter bank for generating a plurality of complex subband signals from the time domain input signals, a plurality of intermediate filters, wherein at least one of the intermediate filters of the plurality of the intermediate filters has a non-uniform amplitude/frequency characteristic, wherein the plurality of intermediate filters have a shorter impulse response compared to an impulse response of a filter having the filter characteristic, and wherein the non-uniform amplitude/frequency characteristics of the plurality of intermediate filters together represent the non-uniform filter characteristic, and a complex synthesis filter bank for synthesizing the output of the intermediate filters to obtain the time domain output signal.