摘要：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.
