The metaplectic transform (MT), a generalization of the Fourier sometimes called linear canonical transform, is tool used ubiquitously in modern optics, for example, when calculating transformations light beams paraxial optical systems. MT also an essential ingredient geometrical-optics modeling caustics that was recently proposed by authors. In particular, this application relies on near-ident...

The two-dimensional discrete cosine transform (DCT) can be found in the heart of many image compression algorithms. Specifically, the JPEG format uses a lossy form of compression based on that transform. Since the standardization of the JPEG, many other transforms become practical in lossy data compression. This article aims to analyze the use of these transforms as the DCT replacement in the J...

The quaternionic offset linear canonical transform (QOLCT) can be defined as a generalization of the (QLCT). In this paper, we define QOLCT, derive relationship between QOLCT and quaternion Fourier (QFT). Based on fact, prove Rayleigh formula some properties related to QOLCT. Then, generalize different uncertainty principles (UPs), including Heisenberg-Weyl's UP, Hardy's Beurling's logarithmic ...

In this paper, we investigate the (two-sided) quaternion windowed linear canonical transform (QWLCT) and study uncertainty principles associated with QWLCT. First, several important properties of QWLCT such as bounded, shift, modulation orthogonality relations are presented based on spectral representation quaternionic (QLCT). Second, Pitt’s inequality Lieb for explored. Moreover, different kin...

Abstract Linear canonical transform as a general integration has been considered into Wigner-Ville distribution (WVD) to show more powerful ability for non-stationary signal processing. In this paper, new WVD associated with linear (WVDL) and form of WVDL (IWVDL) are presented. First, the definition is derived based on autocorrelation function some properties investigated in details. It removes...

In this paper, we generalize the linear canonical transform (LCT) to quaternion-valued signals, known as the quaternionic linear canonical transform (QLCT). Using the properties of the LCT we establish an uncertainty principle for the QLCT. This uncertainty principle prescribes a lower bound on the product of the effective widths of quaternion-valued signals in the spatial and frequency domains...

In a recent paper the authors have introduced the windowed linear canonical transform and shown its good properties together with some applications such as Poisson summation formulas, sampling interpolation and series expansion. In this paper we prove the Paley-Wiener theorems and the uncertainty principles for the (inverse) windowed linear canonical transform. They are new in literature and ha...