# Approximation of Derivatives of IIR Filter design Method MCQ [Free PDF] – Objective Question Answer for Approximation of Derivatives of IIR Filter design Method Quiz

1. An analog filter can be converted into a digital filter by approximating the differential equation by an equivalent difference equation.

A. True
B. False

One of the simplest methods for converting an analog filter into a digital filter is to approximate the differential equation by an equivalent difference equation.

2. 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

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).

3. Which of the following is true relation among s-domain and z-domain?

A. s=(1+z-1)/T
B. s=(1+z )/T
C. s=(1-z-1)/T
D. None of the mentioned

The analog differentiator with output dy(t)/dt has the system function H(s)=s, while the digital system that produces the output [y(n)-y(n-1)]/T has the system function H(z) =(1-z-1)/T. Thus the relation between s-domain and z-domain is given as
s=(1-z-1)/T.

4. 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)]/T2
C. [y(n)+2y(n-1)+y(n-2)]/T
D. [y(n)+2y(n-1)+y(n-2)]/T2

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)]/T2.

5. Which of the following in z-domain is equal to s-domain of second order derivate?

A. $$(\frac{1-z^{-1}}{T})^2$$

B. $$(\frac{1+z^{-1}}{T})^2$$

C. $$(\frac{1+z^{-1}}{T})^{-2}$$

D. None of the mentioned

We know that for a second order derivative

d2y(t)/dt2=[y(n)-2y(n-1)+y(n-2)]/T2

=>s2 = $$\frac{1-2z^{-1}+z^{-2}}{T^2} = (\frac{1-z^{-1}}{T})^2$$

6. If s=jΩ and if Ω varies from -∞ to ∞, then what is the corresponding locus of points in the z-plane?

A. Circle of radius 1 with center at z=0
B. Circle of radius 1 with center at z=1
C. Circle of radius 1/2 with center at z=1/2
D. Circle of radius 1 with center at z=1/2

We know that
s=(1-z-1)/T
=> z=1/(1-sT)
Given s= jΩ => z = 1/(1- jΩT)
Thus from the above equation if Ω varies from -∞ to ∞, then the corresponding locus of points in the z-plane is a circle of radius 1/2 with a center at z=1/2.

7. Which of the following mapping is true between the s-plane and z-domain?

A. Points in LHP of the s-plane into points inside the circle in the z-domain
B. Points in RHP of the s-plane into points outside the circle in the z-domain
C. Points on the imaginary axis of the s-plane into points onto the circle in z-domain
D. All of the mentioned

The mapping is true between the s-plane and z-domain when

A. Points in LHP of the s-plane into points inside the circle in the z-domain
B. Points in RHP of the s-plane into points outside the circle in the z-domain
C. Points on an imaginary axis of the s-plane into points onto the circle in z-domain

8. This mapping is restricted to the design of low pass filters and bandpass filters having relatively small resonant frequencies.

A. True
B. False

The possible location of poles of the digital filter are confined to relatively small frequencies and as a consequence, the mapping is restricted to the design of low pass filters and bandpass filters having relatively small resonant frequencies.

9. Which of the following filter transformation is not possible?

A. High pass analog filter to low pass digital filter
B. High pass analog filter to high pass digital filter
C. Low pass analog filter to low pass digital filter
D. None of the mentioned

We know that only low pass and bandpass filters with low resonant frequencies in the digital can be designed. So, it is not possible to transform a high pass analog filter into a corresponding high pass digital filter.

10. It is possible to map the jΩ-axis into the unit circle.

A. True
B. False