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

1. What kind of filter is an ideal Hilbert transformer?

a) Low pass

b) High pass

c) Band pass

d) All pass

View Answer

Explanation: An ideal Hilbert transformer is a all pass filter.

2. How much phase shift does an Hilbert transformer impart on the input?

a) 45^{o}

b) 90^{o}

c) 135^{o}

d) 180^{o}

View Answer

Explanation: An ideal Hilbert transformer is a all pass filter that imparts a 90

^{o}phase shift on the signal at its input.

3. Which of the following is the frequency response of the ideal Hilbert transform?

a) -j ;0 < ω < π j ;-π < ω < 0 b) j ;0 < ω < π -j ;-π < ω < 0 c) -j ;-π < ω < π d) None of the mentioned

Explanation: The frequency response of an ideal Hilbert transform is given as

H(ω)= -j ;0 < ω < π j ;-π < ω < 0

4. In which of the following fields, Hilbert transformers are frequently used?

a) Generation of SSB signals

b) Radar signal processing

c) Speech signal processing

d) All of the mentioned

View Answer

Explanation: Hilbert transforms are frequently used in communication systems and signal processing, as, for example, in the generation of SSB modulated signals, radar signal processing and speech signal processing.

5. The unit sample response of an ideal Hilbert transform is

a) True

b) False

View Answer

Explanation: We know that the frequency response of an ideal Hilbert transformer is given as

H(ω)= -j ;0 < ω < π

j ;-π < ω < 0

Thus the unit sample response of an ideal Hilbert transform is obtained as

6. The unit sample response of Hilbert transform is infinite in duration and causal.

a) True

b) False

View Answer

Explanation: We know that the unit sample response of the Hilbert transform is given as

it sample response of an ideal Hilbert transform is infinite in duration and non-causal.

7. The unit sample response of Hilbert transform is:

a) Zero

b) Symmetric

c) Anti-symmetric

d) None of the mentioned

View Answer

Explanation: We know that the unit sample response of the Hilbert transform is given as

Thus from the above equation, we can tell that h(n)=-h(-n). Thus the unit sample response of Hilbert transform is anti-symmetric in nature.

8. In this section, we confine our attention on the design of FIR Hilbert transformers with h(n)=-h(M-1-n).

a) True

b) False

View Answer

Explanation: In view of the fact that the ideal Hilbert transformer has an anti-symmetric unit sample response, we shall confine our attention to FIR designs in which h(n)=-h(M-1-n).

9. Which of the following is true regarding the frequency response of Hilbert transform?

a) Complex

b) Purely imaginary

c) Purely real

d) Zero

View Answer

Explanation: Our choice of an anti-symmetric unit sample response is consistent with having a purely imaginary frequency response characteristic.

10. It is impossible to design an all-pass digital Hilbert transformer.

a) True

b) False

View Answer

Explanation: We know that when h(n) is anti-symmetric, the real valued frequency response characteristic is zero at ω=0 for both M odd and even and at ω=π when M is odd. Clearly, then, it is impossible to design an all-pass digital Hilbert transformer.

11. If f_{l} and f_{u} are the cutoff frequencies, then what is the desired real valued frequency response of a Hilbert transform filter in the frequency range 2π f_{l} < ω < 2πf_{u}?

a) -1

b) -0.5

c) 0

d) 1

View Answer

Explanation: The bandwidth of Hilbert transformer need only cover the bandwidth of the signal to be phase shifted. Consequently, we specify the desired real valued frequency response of a Hilbert transformer filter is

H(ω)=1; 2π f

_{l}< ω < 2πf

_{u}

where fl and fu are the cutoff frequencies.

12. What is the value of unit sample response of an ideal Hilbert transform for ‘n’ even?

a) -1

b) 1

c) 0

d) None of the mentioned

View Answer

Explanation: The unit sample response of the Hilbert transformer is given as

From the above equation, it is clear that h(n) becomes zero for even values of ‘n’.

**Sanfoundry Global Education & Learning Series – Digital Signal Processing.**

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