UM ETheses Collection (澳門大學電子學位論文庫)
 Title

Linear canonical transform in timefrequency analysis
 English Abstract

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The class of the linear canonical transforms is a fourparameter class of linear integral transforms (LCT s), with wide application in optical, acoustical, electromagnetic, and other wave propagation problems. The Fourier transform is well known as a special case of the LCT s. In signal processing, the timefrequency analysis gives us the information of a signal in both the time and frequency domains simultaneously. The thesis is devoted to the linear canonical transform (LCT) in timefrequency analysis. We will extent some operators in the LCT domain to show how powerful it is in some calculations. We also discuss these operators work on a signal of its complex form, which gives simple calculation methods in some cases. In Chapter 2, we will discuss the frequency operator in the LCT domain. The method is used to get the mean frequency, the average square frequency, and the bandwidth of a signal. Chapter 3 is about the time frequency operator in the LCT domain, similar results is presented. Chapter 4 is about the translation operators in the LCT domain. Operators on a signal of its complex form is discussed in Chapter 5. We denote a signal in its complex form, and use the operator methods to get some results we need when we want to learn about a signal. Some easy results of the characteristic function for density in time and in frequency are presented in Chapter 6. The main results discussed in this thesis are listed in Chapter 7 by table form.
 Issue date

2016
 Author

Li, Xiao Jun
 Faculty

Faculty of Science and Technology
 Degree

M.Sc.
 Subject

Signal processing  Digital techniques
Timeseries analysis
Mathematics  Department of Mathematics
 Supervisor

Kou, Kit Ian
 Files In This Item
 Location
 1/F Zone C
 Library URL
 991001933089706306