Composition of wavelet and Fourier transforms
Mariusz Ziółko, Marcin Witkowski, Jakub Gałka · Roczniki Polskiego Towarzystwa Matematycznego. Seria 3, Matematyka Stosowana/Matematyka Stosowana/Mathematica Applicanda · 2018
The paper presents the basic properties of the serial composition of two transformations: and Fourier. Two types of transformations were obtained because and Fourier transformations do not commute. The consequences of a phenomenon known as a wavelet crime are presented. Using wavelets with compact support in the frequency domain (e.g. Meyer wavelets) leads to the representation of signals as sparse matrices. Speech signals were used to test the presented transforms.