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Test: Hilbert Transformers Design


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10 Questions MCQ Test Signals and Systems | Test: Hilbert Transformers Design

Test: Hilbert Transformers Design for Electrical Engineering (EE) 2022 is part of Signals and Systems preparation. The Test: Hilbert Transformers Design questions and answers have been prepared according to the Electrical Engineering (EE) exam syllabus.The Test: Hilbert Transformers Design MCQs are made for Electrical Engineering (EE) 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Hilbert Transformers Design below.
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Test: Hilbert Transformers Design - Question 1

 What kind of filter is an ideal Hilbert transformer?

Detailed Solution for Test: Hilbert Transformers Design - Question 1

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

Test: Hilbert Transformers Design - Question 2

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

Detailed Solution for Test: Hilbert Transformers Design - Question 2

Explanation: An ideal Hilbert transformer is a all pass filter that imparts a 90o phase shift on the signal at its input.

Test: Hilbert Transformers Design - Question 3

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

Detailed Solution for Test: Hilbert Transformers Design - Question 3

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.

Test: Hilbert Transformers Design - Question 4

The unit sample response of an ideal Hilbert transform is

Detailed Solution for Test: Hilbert Transformers Design - Question 4

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

Test: Hilbert Transformers Design - Question 5

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

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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.

Test: Hilbert Transformers Design - Question 6

The unit sample response of Hilbert transform is:

Detailed Solution for Test: Hilbert Transformers Design - Question 6

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.

Test: Hilbert Transformers Design - Question 7

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

Detailed Solution for Test: Hilbert Transformers Design - Question 7

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).

Test: Hilbert Transformers Design - Question 8

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

Detailed Solution for Test: Hilbert Transformers Design - Question 8

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

Test: Hilbert Transformers Design - Question 9

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

Detailed Solution for Test: Hilbert Transformers Design - Question 9

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.

Test: Hilbert Transformers Design - Question 10

 If fl and fu are the cutoff frequencies, then what is the desired real valued frequency response of a Hilbert transform filter in the frequency range 2π fl < ω < 2πfu

Detailed Solution for Test: Hilbert Transformers Design - Question 10

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 fl < ω < 2πfu
where fl and fu are the cutoff frequencies.

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