A method for constructing non-uniform filter banks is presented. Starting from a uniform system of translates, generated by a prototype filter, a non-uniform covering of the frequency axis is obtained by composition with a warping function. The warping function is a \({\mathcal {C}}^1\)-diffeomorphism that determines the frequency progression and can be chosen freely, apart from minor technical restrictions. The resulting functions are interpreted as filter frequency responses. Combined with appropriately chosen decimation factors, a non-uniform analysis filter bank is obtained. Classical Gabor and wavelet filter banks are special cases of the proposed construction. Beyond the state-of-the-art, we construct a filter bank adapted to a frequency scale derived from human auditory perception and families of filter banks that can be interpreted as an interpolation between linear (Gabor) and logarithmic (wavelet) frequency scales. We derive straightforward conditions on the prototype filter decay and the decimation factors, such that the resulting warped filter bank forms a frame. In particular, a simple and constructive method for obtaining tight frames with bandlimited filters is derived by invoking previous results on generalized shift-invariant systems.

中文翻译：

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一类针对非线性频率尺度定制的翘曲滤波器组框架

提出了一种构造非均匀滤波器组的方法。从原型滤波器生成的统一平移系统开始，通过具有翘曲函数的合成可以获得频率轴的不均匀覆盖。翘曲函数为\（{\ mathcal {C}} ^ 1 \）-决定频率变化的微变态，除了较小的技术限制外，还可以自由选择。结果函数被解释为滤波器频率响应。用适当地选择抽取因素结合在一起，获得了非均匀的分析滤波器组。经典的Gabor和小波滤波器组是拟议结构的特例。除了最先进的技术外，我们还构建了一个滤波器库，该滤波器库适用于从人类听觉感知和滤波器库系列中推导出的频率标度，这些滤波器库可以解释为线性（Gabor）和对数（小波）频率标度之间的插值。我们得出关于原型滤波器衰减和抽取因子的简单条件，以使最终的变形滤波器组形成一个框架。尤其是，