# Digital Filters Design Consideration

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

1. The ideal low pass filter cannot be realized in practice.
a) True
b) False

2. 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

3. 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

4. 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)|ejθ(ω) is?
a) Anti-causal
b) Constant
c) Causal
d) None of the mentioned

5. 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

6. If h(n) is causal and h(n)=he(n)+ho(n),then what is the expression for h(n) in terms of only he(n)?
a) h(n)=2he(n)u(n)+he(0)δ(n), n ≥ 0
b) h(n)=2he(n)u(n)+he(0)δ(n), n ≥ 1
c) h(n)=2he(n)u(n)-he(0)δ(n), n ≥ 1
d) h(n)=2he(n)u(n)-he(0)δ(n), n ≥ 0
.

7. If h(n) is causal and h(n)=he(n)+ho(n),then what is the expression for h(n) in terms of only ho(n)?
a) h(n)=2ho(n)u(n)+h(0)δ(n), n ≥ 0
b) h(n)=2ho(n)u(n)+h(0)δ(n), n ≥ 1
c) h(n)=2ho(n)u(n)-h(0)δ(n), n ≥ 1
d) h(n)=2ho(n)u(n)-h(0)δ(n), n ≥ 0

8. If h(n) is absolutely summable, i.e., BIBO stable, then the equation for the frequency response H(ω) is given as?
a) HI(ω)-j HR(ω)
b) HR(ω)-j HI(ω)
c) HR(ω)+j HI(ω)
d) HI(ω)+j HR(ω)

9. HR(ω) and HI(ω) are interdependent and cannot be specified independently when the system is causal.
a) True
b) False

10. 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)

11. The HI(ω) is uniquely determined from HR(ω) through the integral relationship. This integral is called as Continuous Hilbert transform.
a) True
b) False

12. 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

13. The frequency ωP is called as ______________
a) Pass band ripple
b) Stop band ripple
c) Pass band edge ripple
d) Stop band edge ripple

14. Which of the following represents the bandwidth of the filter?
a) ωP+ ωS
b) -ωP+ ωS
c) ωPS
d) None of the mentioned