Complex Modulated Filterbank for High-Resolution Subband Filtering
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Solution Overview
Problem
Existing methods for filtering audio signals, particularly in the context of HRTF (head related transfer function) related filtering, face challenges in achieving sufficient frequency resolution and accurately modeling the intricate phase characteristics of filters, especially when dealing with complex gain modifications and subband filtering.
Innovation Solution
A method is introduced that involves converting an impulse response signal into intermediate filter definition signals using a complex modulated filter bank, allowing for efficient filtering in the subband domain. This method utilizes a filter converter that employs a complex analysis filter bank to derive subband filters from a given time domain filter, enabling high-quality approximation of filtering operations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If simple gain modifications in each subband are applied, then computational complexity is reduced, but frequency resolution and phase accuracy become insufficient
Solution Approach 1:
The audio signal is divided into multiple frequency subbands using a complex modulated filter bank, where each subband can be processed independently. This segmentation allows selective application of complex filtering operations only in subbands where high frequency resolution and phase accuracy are critical, while simpler operations can be used in other subbands, thus resolving the contradiction between computational complexity and measurement precision.
Solution Approach 2:
Different filtering strategies are applied to different subbands based on their specific requirements. In subbands where intricate phase characteristics are important for perceived audio quality, full complex filtering is applied. In other subbands, simpler gain modifications suffice. This local differentiation optimizes the balance between computational complexity and frequency resolution/phase accuracy.
2Measurement precision
If fast convolution methods based on DFT are applied as post-process, then frequency resolution is improved, but computational complexity and algorithmic integration increase
Solution Approach 1:
The complex modulated filter bank structure merges the filtering and frequency transformation operations into a unified framework. By using complex exponentials as modulation functions, the system combines the advantages of frequency domain resolution with efficient time-domain implementation, eliminating the need for separate post-processing convolution steps and reducing overall computational complexity.
Solution Approach 2:
The patent replaces traditional mechanical convolution operations with a mathematically equivalent but computationally more efficient approach using complex modulated filter banks. The filtering operation is performed through modulation and multiplication in the frequency domain followed by inverse transformation, substituting the mechanical convolution process with algebraic operations that are computationally superior.
3Reliability
If HRTF filtering is performed in time domain, then phase accuracy is maintained, but processing efficiency and integration with subband domain decrease
Solution Approach 1:
The patent transitions the HRTF filtering operation from the time domain to the frequency subband domain, effectively changing the dimensional space in which filtering is performed. By representing the filter in the subband domain through complex modulated filter banks, the system maintains phase accuracy while enabling parallel processing of multiple subbands simultaneously, thus improving processing efficiency and integration with subband-based audio processing pipelines.
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.