Complex-Exponential Filter Bank for Low-Delay Alias Suppression
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Solution Overview
Problem
Existing digital filter banks face challenges in minimizing aliasing artifacts and achieving low system delay while maintaining near-perfect reconstruction properties, especially when subband signals are modified, which is crucial for real-time applications like audio and video streaming.
Innovation Solution
The design of a low delay complex-exponential modulated filter bank using an improved alias term minimization method for asymmetric prototype filters, which optimizes the filter bank to reduce aliasing and pass band errors, and incorporates a specific 64-channel filter bank design with a 319-sample system delay.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If cosine modulated filter bank is used, then implementation is effective and widely used in audio coding, but aliasing artifacts appear when subband samples are modified
Solution Approach 1:
The patent employs complex exponential modulation instead of symmetric cosine modulation, creating asymmetric filter characteristics that eliminate the main alias terms. The analysis and synthesis filters use complex exponential functions with different parameters, breaking the symmetry that causes aliasing in conventional cosine modulated filter banks while maintaining implementation efficiency.
Solution Approach 2:
The patent changes the modulation parameter from real cosine function to complex exponential function. By using complex exponential modulation with appropriately chosen parameters (different from conventional designs), the filter bank achieves aliasing-free operation while maintaining computational efficiency and near-perfect reconstruction properties.
2Object-affected harmful factors
If prototype filter length is increased to reduce aliasing, then aliasing suppression improves, but system delay increases
Solution Approach 1:
The patent uses asymmetric complex exponential modulated filters where the analysis and synthesis filters have different characteristics. This asymmetry allows the system to achieve aliasing suppression with shorter filter lengths compared to symmetric designs, reducing the group delay while maintaining near-perfect reconstruction.
Solution Approach 2:
By changing from cosine modulation to complex exponential modulation and optimizing the specific parameters of the prototype filter, the patent achieves aliasing suppression with a compact filter length of 640 coefficients, resulting in a system delay of only 319 samples, which is significantly lower than conventional designs.
3Object-affected harmful factors
If complex exponential modulated filter bank is used, then main alias terms are eliminated, but other alias terms remain requiring sophisticated design
Solution Approach 1:
The patent employs asymmetric complex exponential modulation where the analysis and synthesis filters use different modulation parameters. This asymmetric design completely eliminates all alias terms (not just main alias terms) while maintaining a simple and elegant filter structure, avoiding the need for sophisticated iterative optimization procedures.
Solution Approach 2:
By carefully selecting specific parameters for the complex exponential modulation in the analysis and synthesis filters, the patent achieves complete aliasing elimination with a simple closed-form solution. The parameter selection ensures that all alias terms vanish without requiring complex iterative optimization, thus reducing design sophistication while maintaining effectiveness.
4Loss of time
If low delay filter bank is designed, then real-time application performance improves, but aliasing suppression and reconstruction quality deteriorate
Solution Approach 1:
The patent uses asymmetric complex exponential modulated filters that are specifically designed to achieve near-perfect reconstruction with low delay. The asymmetric structure allows the system to maintain high reconstruction quality (aliasing suppression of -76 dB) while achieving a low system delay of 319 samples, outperforming symmetric low-delay designs.
Solution Approach 2:
By optimizing the parameters of the complex exponential modulation and the prototype filter, the patent achieves a optimal balance between delay and reconstruction quality. The specific parameter selection results in a system delay of 319 samples while maintaining aliasing suppression of -76 dB and pass band reconstruction error of -72 dB, exceeding conventional low-delay filter banks.
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.