Question

Which of the following is the backward difference for the derivative of y(t) with respect to ‘t’ for t=nT?

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

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

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

(d) [y(n)-y(n-1)]/T

The question was posed to me by my school teacher while I was bunking the class.

The query is from IIR Filter Design by Approximation of Derivatives topic in division Digital Filters Design of Digital Signal Processing

Answer 1

Right choice is (d) [y(n)-y(n-1)]/T

The explanation is: For the derivative dy(t)/dt at time t=nT, we substitute the backward difference [y(nT)-y(nT-T)]/T. Thus

dy(t)/dt =[y(nT)-y(nT-T)]/T

=[y(n)-y(n-1)]/T

where T represents the sampling interval and y(n)=y(nT).