With the wide application of spectral and algebraic theory in discrete signal processing techniques field graph processing, an increasing number methods have been proposed, such as Fourier transform, wavelet transform windowed transform. In this paper, we propose design definition linear canonical on graphs (GLCT), which is extension (DLCT), just (GFT) (DFT). First, based centrality scalability...

Sampling rate conversion (SRC) is one of important issues in modern sampling theory. It can be realized by up-sampling, filtering, and down-sampling operations, which need large complexity. Although some efficient algorithms have been presented to do the sampling rate conversion, they all need to compute the N-point original signal to obtain the up-sampling or the down-sampling signal in the tim...

Fabry-Perot cavities are central to many optical measurement systems. In high precision experiments, such as aLIGO and AdV, coupled often required leading complex dynamics, particularly when imperfections considered. We show, for the first time, that discrete LCTs can be used compute circulating fields in which optics have arbitrary apertures, reflectance transmittance profiles, shape. compare ...

This work builds on an existing model of discrete canonical evolution and applies it to the case a linear dynamical system, i.e., finite-dimensional system with vector configuration space equations motion. The is assumed evolve in time steps. most distinctive feature that motion can be irregular. After analysis arising constraints symplectic form, we introduce adjusted coordinates phase space, ...