Transformations for Data Linearization The technique of data linearization has been used to fit curves. Once the curve has been chosen,a suitable transformation of the variables must be found so that a linear relation is obtained. Function,y=f(x) Linearized form,Y=4X+B Change of variable(s)and constants A y=x+B y=A+B X=,Y=y 0 X=xy,Y=y y= y=名)+ -1 x+C C= B =A 1 y= X=x,Y= Ax+B =Ax+B y y x 1 1 1 (c)y=Ax+B =A+B y X=Y=jTransformations for Data Linearization ◼ The technique of data linearization has been used to fit curves. ◼ Once the curve has been chosen, a suitable transformation of the variables must be found so that a linear relation is obtained. Function, y = f (x) Linearized form, Y=AX+B Change of variable(s) and constants 𝑦 = 𝐴 𝑥 + 𝐵 𝑦 = 𝐴 1 𝑥 +B 𝑋 = 1 𝑥 , 𝑌 = 𝑦 𝑦 = 𝐷 𝑥 + 𝐶 𝑦 = −1 𝐶 𝑥𝑦 + 𝐷 𝐶 X = xy, Y = y 𝐶 = −1 𝐴 ,𝐷 = −𝐵 𝐴 𝑦 = 1 𝐴𝑥 + 𝐵 1 𝑦 = 𝐴𝑥 + 𝐵 𝑋 = 𝑥, 𝑌 = 1 𝑦 𝑦 = 𝑥 𝐴𝑥 + 𝐵 1 𝑦 = 𝐴 1 𝑥 + 𝐵 𝑋 = 1 𝑥 , 𝑌 = 1 𝑦 (c)