Question

What is the second difference that is used to replace the second order derivate of y(t)?

(a) [y(n)-2y(n-1)+y(n-2)]/T

(b) [y(n)-2y(n-1)+y(n-2)]/T^2

(c) [y(n)+2y(n-1)+y(n-2)]/T

(d) [y(n)+2y(n-1)+y(n-2)]/T^2

I have been asked this question by my school teacher while I was bunking the class.

I'm obligated to ask this question of IIR Filter Design by Approximation of Derivatives topic in section Digital Filters Design of Digital Signal Processing

Answer 1

The correct choice is (b) [y(n)-2y(n-1)+y(n-2)]/T^2

Easiest explanation: We know that dy(t)/dt =[ y(n)-y(n-1)]/T

Second order derivative of y(t) is d(dy(t)/dt)/dt=[y(n)-2y(n-1)+y(n-2)]/T^2.