1. What is the duration of the unit sample response of a digital filter?

A. Finite
B. Infinite
C. Impulse(very small)
D. Zero

Answer: B

Digital filters are the filters that can be designed from analog filters which have infinite duration unit sample response.

2. Which of the following methods are used to convert the analog filter into a digital filter?

A. Approximation of Derivatives
B. Bilinear transformation
C. Impulse invariance
D. All of the mentioned

Answer: D

There are many techniques that are used to convert analog filters into digital filters of which some of which are Approximation of derivatives, bilinear transformation, impulse invariance, and many other methods.

3. Which of the following is the difference equation of the FIR filter of length M, input x(n) and output y(n)?

A. y(n)=\(\sum_{k=0}^{M+1} b_k x(n+k)\)

B. y(n)=\(\sum_{k=0}^{M+1} b_k x(n-k)\)

C. y(n)=\(\sum_{k=0}^{M-1} b_k x(n-k)\)

D. None of the mentioned

Answer: C

An FIR filter of length M with input x(n) and output y(n) is described by the difference equation

y(n)=\(\sum_{k=0}^{M-1} b_k x(n-k)\)

where {bk} is the set of filter coefficients.

4. What is the relation between h(t) and Ha(s)?

A. Ha(s)=\( \int_{-\infty}^{\infty} h(t)e^{-st} dt\)

B. Ha(s)=\(\int_0^{\infty} h(t)e^{st} dt\)

C. Ha(s)=\( \int_{-\infty}^{\infty} h(t)e^{st} dt\)

D. None of the mentioned

Answer: A

We know that the impulse response h(t) and the Laplace transform Ha(s) are related by the equation.

5. Which of the following is a representation of system function?

A. Normal system function
B. Laplace transform
C. Rational system function
D. All of the mentioned

Answer: D

There are many ways how we represent a system function of which one is normal representation i.e., output/input and other ways like Laplace transform and rational system function.

6. For an analog LTI system to be stable, where should the poles of system function H(s) lie?

A. Right half of s-plane
B. Left half of s-plane
C. On the imaginary axis
D. At origin

Answer: B

An analog linear time-invariant system with system function H(s) is stable if all its poles lie on the left half of the s-plane.

7. If the conversion technique is to be effective, the jΩ axis in the s-plane should map into the unit circle in the z-plane.

A. True
B. False

Answer: A

If the conversion technique is to be effective, the jΩ axis in the s-plane should map into the unit circle in the z-plane. Thus there will be a direct relationship between the two frequency variables in the two domains.

8. If the conversion technique is to be effective, then the LHP of the s-plane should be mapped into _____________

A. Outside of unit circle
B. Unit circle
C. Inside unit circle
D. Does not matter

Answer: C

If the conversion technique is to be effective, then the LHP of the s-plane should be mapped into the inside of the unit circle in the z-plane. Thus a stable analog filter will be converted to a stable digital filter.

9. Physically realizable and stable IIR filters cannot have a linear phase.

A. True
B. False

Answer: A

If an IIR filter is stable and if it can be physically realizable, then the filter cannot have a linear phase.

10. What is the condition on the system function of a linear phase filter?

A. H(z)=\(z^{-N} H(z^{-1})\)

B. H(z)=\(z^N H(z^{-1})\)

C. H(z)=\(±z^N H(z^{-1})\)

D. H(z)=\(±z^{-N} H(z^{-1})\)

Answer: D

A linear phase filter must have a system function that satisfies the condition

H(z)=\(±z^{-N} H(z^{-1})\)

where z(-N) represents a delay of N units of time.