Interplay between windowed Boas transform and windowed Hilbert transform
Abstract
To analyse the localized behaviour of a signal, the more general ‘windowed Boas transform’ is introduced in this article. Various properties of the windowed Boas transform are discussed, including convolution and correlation. An interplay between windowed Boas and windowed Hilbert transform is given. Also, the inversion formula for the windowed Boas transform is provided. Furthermore, we establish the relation between the windowed Boas transform and the Fourier transform. Lastly, the spectral energy and the energy difference of both the transforms is derived.
Fields of Study & Subjects
Mathematical Analysis and Transform Methods
Digital Filter Design and Implementation
Holomorphic and Operator Theory
Publication details
- Journal / source
- Integral Transforms and Special Functions
- Publisher
- Informa UK Limited
- Pages
- 1–14
- Publication date
- 3 April 2026
- Language
- EN