Study On Basical Theories Of Octonion Linear Canonical Transform

As an integral transform,linear canonical transform is often used in time-frequency analysis and non-stationary signal processing.It plays an important role in applied mathematics and signal processing,and is a powerful tool in the field of signal processing.In recent years,with the increasing complexity of signal environment and the increasing improvement of signal processing requirements,it has gradually become an important development direction of modern signal processing to extract signal features from multiple angles and analyze signal transform to different domains.Therefore,based on the existing research results,dissertation expands the linear canonical transform in the octonion field and studies the basic properties of the octonion linear canonical transform.The main research contents are as follows:1.introduces the definition of wavelet transform and fractional Fourier transform,gives the definition of fractional wavelet transform and its convolution and correlation;introduces the definition of short-time linear canonical transform and linear canonical transform of eight-element offset,and discusses some important properties,including:boundedness,linear,reconstruction formula,parity and time shift.2.Convolution of linear canonical wavelet transform convolution and its properties.We study the convolution and correlation theorem of linear canonical wavelet transform based on linear canonical and wavelet transforms.We give the admissibility condition and canonical conditions for the linear canonical wavelet function.We derive a new class of linear canonical wavelet convolution theorem and correlation theorems.Using the obtained theorem,the filtering design of the linear canonical wavelet domain is studied.3.The properties of the linear canonical transform of octonion are studied.Starting from the octonion linear canonical transform,the short-time offset linear canonical transform of octonion and its properties are studied.Octonion short-time offset linear canonical transform is defined.We study the important properties of boundedness,linear properties,reconstruction formula,parity properties,and time shift.The convolution theorem and correlation theorem of the octonion short-time offset linear canonical transform are derived.