Hilbert Transformers Design MCQ [Free PDF] – Objective Question Answer for Hilbert Transformers Design Quiz

An ideal Hilbert transformer is an all-pass filter.

An ideal Hilbert transformer is an all-pass filter that imparts a 90° phase shift on the signal at its input.

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

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.

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

h(n)=\(\frac{2}{\pi} \frac{(sin(\frac{πn}{2}))^{2}}{n}\); n≠0

h(n)=0; n=0

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

h(n)=\(\frac{2}{\pi} \frac{(sin(\frac{πn}{2}))^{2}}{n}\); n≠0

h(n)=0; n=0

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

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

h(n)=\(\frac{2}{\pi} \frac{(sin(\frac{πn}{2}))^{2}}{n}\); n≠0

h(n)=0; n=0

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.

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).

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

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.