Uncertainty Principle On A Kind Of Hartley Transform

The classic uncertainty principle can better analyze the relationship between the time domain and the frequency domain resolution of the signal in the field of signal processing,The relevant conclusions have been extended from the classical fourier transform to the quaternion fourier transform and the quaternion linear canonical transform,and has become one of the research hot spots in recent years.Hartley transform is an integral transform that converts a real-valued function to a real-valued function,since the Hartley transform can greatly improve the speed and efficiency in the calculation process,attracted the attention of scholars.Hartley transform and fourier transform are both orthogonal sinusoidal transforms.Quaternion fourier transform is a generalization of the classical fourier transform on the high-dimensional space,it can convert a two-dimensional signal into a quaternion-valued frequency-domain signal.Firstly,this paper establishes the relationship between the quaternion fourier transform and the two-dimensional Hartley transform,based on this conclusion,the uncertainty principle of the two-dimensional Hartley transform is further given.Quaternion linear canonical transform is a more generalized integral transform,based on the kernel function of quaternion linear canonical transform,we give a kind of Hartley transform based on the quaternion linear canonical transform,explore its real number property and uncertainty principle.Hartley transform has limitations in dealing with the local characteristics of the signal,therefore,this paper further explores its real number property and uncertainty principle of the windowed Hartley transform.The main work of thesis can be summarized as follows:(1)Introduce the knowledge of Hartley transform,quaternion,quaternion fourier transform,quaternion linear canonical transform and the uncertainty principle.(2)Establish the relationship between the two-dimensional Hartley transform and the quaternion fourier transform,and give the uncertainty principle of two-dimensional Hartley transform.Based on the relationship between the quaternion fourier transform and the quaternion linear canonical transform,it defines the Hartley transform in linear canonical transform domain,discussed its real number property and established the uncertainty principle of the Hartley transform in quaternion linear canonical transform domain.(3)Define a two-dimensional windowed Hartley transform,establish the relationship between the windowed 2D Hartley transform and the windowed quaternion fourier transform,and give the uncertainty principle of two-dimensional windowed Hartley transform.Based on the windowed quaternion linear canonical transform'kernel function,it defines the windowed Hartley transform in windowed quaternion linear canonical transform domain,further address the real number property of the Hartley transform in windowed quaternion linear canonical transform domain in the case of windowing and its uncertainty principle.