Question

What is the system function of the integrator that is modeled by the discrete time system?

(a) H(z)=\(\frac{z^{-1}}{1-z^{-1}}\)

(b) H(z)=\(\frac{z^{-1}}{1+z^{-1}}\)

(c) H(z)=\(\frac{z^{z^1}}{1-z^1}\)

(d) H(z)=\(\frac{z^{z^1}}{1+z^1}\)

The question was asked by my school principal while I was bunking the class.

My doubt stems from Discrete-Time Processing of Continuous Time Signals topic in portion Discrete Time Systems Implementation of Digital Signal Processing

Answer 1

Right option is (a) H(z)=\(\frac{z^{-1}}{1-z^{-1}}\)

To elaborate: The integrator is modeled by the discrete time system with system function

H(z)=\(\frac{z^{-1}}{1-z^{-1}}\)