Complex-Exponential Filter Bank for Low-Delay HFR Reconstruction
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Solution Overview
Problem
Digital filter banks face challenges in reducing aliasing artifacts and maintaining low system delay while achieving near-perfect reconstruction, especially when subband signals are modified, due to limitations in existing design methods that prioritize either aliasing suppression or delay reduction.
Innovation Solution
The proposed method employs an improved alias term minimization (IATM) technique for optimizing asymmetric or symmetric prototype filters, allowing for the design of low delay complex-exponential modulated filter banks with reduced aliasing and pass band errors, using a composite objective function that balances these properties.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of operation
If cosine modulated filter banks are used for effective implementation, then ease of operation is improved, but aliasing artifacts increase when subband signals are modified
Solution Approach 1:
The patent applies asymmetry by using complex exponential modulation instead of symmetric cosine modulation. The analysis filters use complex exponentials e^(-j2πkl/M) which break the symmetry of traditional cosine modulated filter banks, enabling better aliasing cancellation properties when subband signals are modified while maintaining implementation efficiency.
Solution Approach 2:
The patent converts the harmful aliasing artifacts into a beneficial property by designing the complex exponential modulated filter bank such that the aliasing terms naturally cancel out when subband signals are modified. The modulation scheme transforms what would be harmful aliasing into a mechanism that actually suppresses aliasing artifacts in the output signal.
2Manufacturing precision
If prototype filter length is increased to reduce aliasing, then manufacturing precision is improved, but system delay increases
Solution Approach 1:
The patent changes the fundamental parameter of filter modulation from cosine to complex exponential, which fundamentally alters the aliasing cancellation mechanism. This parameter change enables achieving better aliasing suppression with shorter filter lengths, as the complex exponential modulation provides more effective aliasing cancellation properties compared to traditional cosine modulation.
3Adaptability or versatility
If subband samples are modified for equalization or compression, then adaptability is improved, but aliasing artifacts increase
Solution Approach 1:
The patent converts the harmful aliasing artifacts into a beneficial property by designing the complex exponential modulated filter bank such that the aliasing terms naturally cancel out when subband signals are modified. The modulation scheme transforms what would be harmful aliasing into a mechanism that actually suppresses aliasing artifacts in the output signal.
Solution Approach 2:
The patent employs an optimization process that iteratively adjusts the prototype filter coefficients to minimize aliasing error terms. This feedback mechanism continuously refines the filter design based on the actual aliasing performance, ensuring optimal suppression even when subband signals undergo various modifications for equalization or compression.
Data Source
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AI summary
The document relates to modulated sub-sampled digital filter banks, as well as to methods and systems for the design of such filter banks. In particular, the present document proposes a method and apparatus for the improvement of low delay modulated digital filter banks. The method employs modulation of an asymmetric low-pass prototype filter and a new method for optimizing the coefficients of this filter. Further, a specific design for a 64 channel filter bank using a prototype filter length of 640 coefficients and a system delay of 319 samples is given. The method substantially reduces artifacts due to aliasing emerging from independent modifications of subband signals, for example when using a filter bank as a spectral equalizer. The method is preferably implemented in software, running on a standard PC or a digital signal processor (DSP), but can also be hardcoded on a custom chip. The method offers improvements for various types of digital equalizers, adaptive filters, multiband companders and spectral envelope adjusting filter banks used in high frequency reconstruction (HFR) or parametric stereo systems.