Laboratory Roberval CNRS UMR 6253, University of Technology of Compiegne, 60200 Compiegne, France.
J Acoust Soc Am. 2010 Feb;127(2):884-95. doi: 10.1121/1.3273888.
This paper addresses the design of digital fractional-octave-band filters with energy conservation and perfect reconstruction--i.e., whose outputs to each fractional-octave-band correctly sum up to the original signal and whose partial energies at each output correctly sum up to the overall signal energy--a combination of properties that cannot be met by any current design despite its considerable importance in many applications. A solution is devised based on the introduction of complex basis functions that span the outputs of the fractional-octave bands and whose real and imaginary parts form two individually--but not mutually--orthogonal bases. This imposes a "partition-of-unity" condition on the design of the filter frequency gains such that they exactly sum up to one over the frequency axis. The practical implementation of the proposed solution uses the discrete Fourier transform, and a fast algorithm is implemented using the fast Fourier transform. The proposed filters are well suited to any application involving the post-processing of finite-energy signals. They closely match the international standard templates, except for a small departure at the bandedge frequencies which can be made arbitrarily small.
本文讨论了具有能量守恒和完美重构特性的数字分数倍频带滤波器的设计，即其每个分数倍频带的输出正确地总和为原始信号，并且每个输出的部分能量正确地总和为整个信号能量。尽管在许多应用中非常重要，但目前的任何设计都无法满足这些特性的组合要求。我们设计了一种基于引入复数基函数的解决方案，这些基函数跨越分数倍频带的输出，其实数和虚数部分形成两个单独的但不是相互正交的基。这对滤波器频率增益的设计施加了“单位分解”条件，使得它们在频率轴上精确地总和为一。所提出解决方案的实际实现使用离散傅里叶变换，并使用快速傅里叶变换实现了快速算法。所提出的滤波器非常适合涉及有限能量信号后处理的任何应用。它们与国际标准模板非常匹配，除了在频带边缘频率处略有偏离，该偏离可以任意小。
