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

Abstract

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.

Stability estimates for phase retrieval from discrete linear canonical Gabor transformation measurements

“…In the recent 10 years, [16][17][18][19][20][21] the basic theories of LCT, such as uncertainty principle, the relationship between LCT and ambiguity function and Winger Ville distribution, have been gradually studied. Combined with these basic theories, LCT has been widely used in scientific research and engineering technology, for example, instantaneous frequency estimation, 22 signal detection and estimation, 23 linear regular domain filter design, 24,25 radar system, 26 image processing, 27 speech signal analysis, 28 and optics. [29][30][31] Now, LCT has become the focus of interdisciplinary research.…”