We present a constructive algorithm for the design of real lapped equal-norm tight frame transforms. These transforms can be efficiently implemented through filter banks and have recently been proposed as a redundant counterpart to lapped orthogonal transforms, as well as an infinite-dimensional counterpart to harmonic tight frames. The proposed construction consists of two parts: First, we design a large class of new real lapped orthogonal transforms derived from submatrices of the discrete Fourier transform. Then, we seed these to obtain real lapped tight frame transforms corresponding to tight, equal-norm frames. We identify those frames that are maximally robust to erasures, and show that our construction leads to a large class of new lapped orthogonal transforms as well as new lapped tight frame transforms.

中文翻译：

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真实重叠紧框架变换的系统构建

我们提出了一种用于设计真实重叠等范紧框架变换的构造算法。这些变换可以通过滤波器组有效地实现，并且最近被提出作为重叠正交变换的冗余对应物，以及谐波紧框架的无限维对应物。所提出的结构由两部分组成：首先，我们设计了一大类从离散傅立叶变换的子矩阵导出的新的实重叠正交变换。然后，我们播种这些以获得与紧、等范数框架相对应的真实重叠紧框架变换。我们确定了那些对擦除具有最大鲁棒性的帧，并表明我们的构造导致了一大类新的重叠正交变换以及新的重叠紧密帧变换。