# Digital Filters Design Consideration MCQ’s

This set of Digital Signal Processing Multiple Choice Questions & Answers (MCQs) focuses on “Digital Filters Design Consideration”.

1. If h(n) is absolutely summable, i.e., BIBO stable, then the equation for the frequency response H(ω) is given as?

a) H_{I}(ω)-j H_{R}(ω)

b) H_{R}(ω)-j H_{I}(ω)

c) H_{R}(ω)+j H_{I}(ω)

d) H_{I}(ω)+j H_{R}(ω)

2. The magnitude |H(ω)| cannot be constant in any finite range of frequencies and the transition from pass-band to stop-band cannot be infinitely sharp.

a) True

b) False

3. Which of the following represents the bandwidth of the filter?

a) ω_{P}+ ω_{S}

b) -ω_{P}+ ω_{S}

c) ω_{P}-ω_{S}

d) None of the mentioned

4. If h(n) is causal and h(n)=h_{e}(n)+h_{o}(n),then what is the expression for h(n) in terms of only h_{e}(n)?

a) h(n)=2h_{e}(n)u(n)+h_{e}(0)δ(n), n ≥ 0

b) h(n)=2h_{e}(n)u(n)+h_{e}(0)δ(n), n ≥ 1

c) h(n)=2h_{e}(n)u(n)-h_{e}(0)δ(n), n ≥ 1

d) h(n)=2h_{e}(n)u(n)-h_{e}(0)δ(n), n ≥ 0

5. The following diagram represents the unit sample response of which of the following filters?

a) Ideal high pass filter

b) Ideal low pass filter

c) Ideal high pass filter at ω=π/4

d) Ideal low pass filter at ω=π/4

6. If h(n) has finite energy and h(n)=0 for n<0, then which of the following are true?

a) ∫π−π|ln|H(ω)||dω>−∞

b) ∫π−π|ln|H(ω)||dω<∞

c) ∫π−π|ln|H(ω)||dω=∞

d) None of the mentioned

7. If h(n) is causal and h(n)=h_{e}(n)+h_{o}(n),then what is the expression for h(n) in terms of only h_{o}(n)?

a) h(n)=2h_{o}(n)u(n)+h(0)δ(n), n ≥ 0

b) h(n)=2h_{o}(n)u(n)+h(0)δ(n), n ≥ 1

c) h(n)=2h_{o}(n)u(n)-h(0)δ(n), n ≥ 1

d) h(n)=2h_{o}(n)u(n)-h(0)δ(n), n ≥ 0

8. The frequency ω_{P} is called as ______________

a) Pass band ripple

b) Stop band ripple

c) Pass band edge ripple

d) Stop band edge ripple

9. The ideal low pass filter cannot be realized in practice.

a) True

b) False

10. H_{R}(ω) and H_{I}(ω) are interdependent and cannot be specified independently when the system is causal.

a) True

b) False

11. What is the Fourier transform of the unit step function U(ω)?

a) πδ(ω)-0.5-j0.5cot(ω/2)

b) πδ(ω)-0.5+j0.5cot(ω/2)

c) πδ(ω)+0.5+j0.5cot(ω/2)

d) πδ(ω)+0.5-j0.5cot(ω/2)

12. The H_{I}(ω) is uniquely determined from H_{R}(ω) through the integral relationship. This integral is called as Continuous Hilbert transform.

a) True

b) False

13. If |H(ω)| is square integrable and if the integral ∫π−π|ln|H(ω)||dω is finite, then the filter with the frequency response H(ω)=|H(ω)|e^{jθ(ω)} is?

a) Anti-causal

b) Constant

c) Causal

d) None of the mentioned

14. The magnitude function |H(ω)| can be zero at some frequencies, but it cannot be zero over any finite band of frequencies.

a) True

b) False

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