# Approximation of Derivatives design Method

This set of Digital Signal Processing Questions for entrance exams focuses on “IIR Filter Design by Approximation of Derivatives”.

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

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

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

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

5. Which of the following in z-domain is equal to s-domain of second order derivate?
a) (1−z−1T)2
b) (1+z−1T)2
c) (1+z−1T)−2
d) None of the mentioned

6. If s=jΩ and if Ω varies from -∞ to ∞, then what is the corresponding locus of points in z-plane?
a) Circle of radius 1 with centre at z=0
b) Circle of radius 1 with centre at z=1
c) Circle of radius 1/2 with centre at z=1/2
d) Circle of radius 1 with centre at z=1/2

7. Which of the following mapping is true between s-plane and z-domain?
a) Points in LHP of the s-plane into points inside the circle in z-domain
b) Points in RHP of the s-plane into points outside the circle in z-domain
c) Points on imaginary axis of the s-plane into points onto the circle in z-domain
d) All of the mentioned

8. This mapping is restricted to the design of low pass filters and band pass filters having relatively small resonant frequencies.
a) True
b) False

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

10. It is possible to map the jΩ-axis into the unit circle.
a) True
b) False