哈工大信息光学Chapter2-2.pdfVIP

幻 灯 片 Chapter 2 1 Analysis of Two-Dimensional Signals and Systems Yancheng Zhao College of Science Harbin Engineering University 幻 Decomposition: 分解，腐烂 灯 The Fourier transform as a 片 decomposition 2 G(f X , f Y ) F {g } g (x ,y ) exp[j 2p (f X x f Y y )]dxdy (2 1) g (x ,y ) F -1 {G} G(f X , f Y ) exp[j 2p (f X x f Y y )]df X df Y (2 2) We may regard the two-dimensional Fourier transform as a decomposition of a function g(x,y) into a linear combination of elementary functions of the form exp[j2p(f x +f y )]. X Y Such functions have a number of interesting properties. 幻 灯 片 3 n For any particular frequency pair (f ,f ) the X Y corresponding elementary function has a phase that is zero or an integer multiple of 2p radians along lines described by the equation f X n y x f Y f Y n Where n is an integer. 幻 灯 片 4 n The lines of zero phase for the function exp[j2p(f x+f y )] X Y 1 1 f X f Y 1 y L 1 2 1 2 f 2 f 2 （ ） （ ） X Y