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

A. Low pass
B. High pass
C. Bandpass
D. All pass

Answer: D

An ideal Hilbert transformer is an all-pass filter.

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

A. 45°
B. 90°
C. 135°
D. 180°

Answer: B

An ideal Hilbert transformer is an all-pass filter that imparts a 90° 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

Answer: A

The frequency response of an ideal Hilbert transform is given as
H(ω) = -j ;0 ≤ ω ≤ π
H(ω) = 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

Answer: D

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

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

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

A. True
B. False

Answer: A

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

Answer: B

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

Answer: A

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.