电子科线女学光电科学与工程学院 SCHOOL OF OPTOELECTRONIC SCIENCE AND ENGINEERING OF UESTC 1.Background ■Derivative An approximation to the first-order derivative at point x of a one-dimensional function f(x)by expanding the function f(x+x)into a Taylor series about x letting Ax=1 and keeping only the linear terms (Problem 10.1).The result is the digital difference Y=f'(x)=f(x+1)-f(x) a ==x++1--2 2ff'（☒=f'(x+)-f'() 0x2 Ox =f(x+2)-f(x+1)-f(x+1)+f(x) =f(x+2)-2f(x+1)+f(x)An approximation to the first-order derivative at point x of a one-dimensional function f (x) by expanding the function f (x+Δx) into a Taylor series about x letting Δx=1 and keeping only the linear terms (Problem 10.1).The result is the digital difference ( ) ( 1) ( ) f f x f x f x x  = = + −   ◼ Derivative ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 2 1 2 1 1 2 2 1 f f x f x f x x x f x f x f x f x f x f x f x    = = + −     = + − + − + + = + − + + ( ) ( ) ( ) ( ) 2 2 1 1 2 f f x f x f x f x x  = = + + − −   1. Background