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Linear canonical transform in time-frequency analysis

English Abstract

The class of the linear canonical transforms is a four-parameter 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 time-frequency 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 time-frequency 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.

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Li, Xiao Jun


Faculty of Science and Technology




Signal processing -- Digital techniques

Time-series analysis

Mathematics -- Department of Mathematics


Kou, Kit Ian

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