Based on the generalized discrete Fourier transform, the generalized orthogonal discrete W transform and its fast algorithm are proposed and derived in this paper. The orthogonal discrete W transform proposed by Zhongde Wang has only four types. However, the generalized orthogonal discrete W transform proposed by us has infinite types and subsumes a family of symmetric transforms. The generalized orthogonal discrete W transform is a real-valued orthogonal transform, and the real-valued orthogonal transform of a real sequence has the advantages of simple operation and facilitated transmission and storage. The generalized orthogonal discrete W transforms provide more basis functions with new frequencies and phases and hence lead to more powerful analysis and processing tools for communication, signal processing, and numerical computing.

中文翻译：

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广义正交离散W变换及其快速算法

在广义离散傅里叶变换的基础上，提出并推导了广义正交离散W变换及其快速算法。Wang Zhongde Wang提出的正交离散W变换只有四种类型。但是，我们提出的广义正交离散W变换具有无限的类型，并且包含一族对称变换。广义正交离散W变换是实值正交变换，实序列的实值正交变换具有操作简单，便于传输和存储的优点。广义正交离散W变换为新的频率和相位提供了更多的基函数，因此导致了用于通信，信号处理和数值计算的更强大的分析和处理工具。