Dispersion Operators Algebra and Linear Canonical Transformations

This work intends to present a study on relations between a Lie algebra called dispersion operators algebra, linear canonical transformation and a phase space representation of quantum mechanics that we have introduced and studied in previous works. The paper begins with a brief recall of our previous works followed by the description of the dispersion operators algebra which is performed in the framework of the phase space representation. Then, linear canonical transformations are introduced and linked with this algebra. A multidimensional generalization of the obtained results is given.

A Fast Algorithm of Linear Canonical Transformation for Radar Signal Processing System

Linear canonical transformation is a new signal processing tools developing in recent years. As a unified multi-parameter linear integral transform, linear canonical transformation has its unique advantages when dealing with non-stationary signal. However, from the existing literatures, the basic theoretical system is not perfect, some of the theories associated with signal processing needs to be further established or strengthened, the research of linear canonical transformation has important theoretical significance and practical significance, but linear canonical transformation needs a lot of calculation, it is not like Fourier transform, fractional Fourier transform, Fresnel transform and scale operator, they have already been widely used in various fields of expertise, in order to reduce the amount of calculation, this paper puts forward a fast algorithm which uses duality theorem of linear canonical transformation to reduce the amount of calculation, it can quickly complete the operation when we use linear canonical transformation to process the signal during radar signal processing, the time for normal algorithm is 5s, the fast algorithm needs only 0.2s.