Quadratic Phase Multiresolution Analysis and the Construction of Orthonormal Wavelets in <i>L</i>²(ℝ)

Abstract

The multi-resolution analysis (MRA) associated with quadratic phase Fourier transform (QPFT) serves as a tool to construct orthogonal bases of the L2(R). Consequently, it assumes a pivotal role in facilitating potential applications of QPFT. Inspired by the sampling theorem applicable to band-limited signals in the QPFT domain, this paper formulates the development of the MRA linked with QPFT. Subsequently, we develop a method for constructing orthogonal bases for L2(R), followed by some examples.

Keywords

• Fourier transform
• quadratic phase Fourier transform
• Shannon’s sampling theorem
• multiresolution analysis
• quadratic phase wavelet transform
• orthonormal basis