Nonuniform multiresolution analysis associated with linear canonical transform

The linear canonical transform (LCT) has attained respectable status within a short span and is being broadly employed across several disciplines of science engineering including signal processing, optical radar systems, electrical communication quantum physics etc, mainly due to the extra degrees freedom simple geometrical manifestation. In this article, we introduce novel multiresolution analysis (LCT-NUMRA) on spectrum \(\Omega = \big \{0,{r}/{N}\big \}+2\mathbb {Z},\) where \(N \geqq 1\) an integer r odd with \( 1 \leqq 2N-1,\) such that N are relatively prime, by intertwining ideas nonuniform MRA transforms. We first develop associated LCT then drive algorithm construct LCT-NUMRA starting from low-pass filter \(\Lambda _{0}^{M}(\omega )\) suitable conditions. Nevertheless, extend scope present study, wavelet packets for investigate their properties means