Digital Filters Design MCQ [Free PDF] – Objective Question Answer for Digital Filters Design Quiz

176. In this section, we confine our attention to FIR designs in which h(n)=-h(M-1-n).

A. True
B. False

Answer: A

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

 

177. Which of the following is the condition that a differentiator should satisfy?

A. Infinite response at zero frequency
B. Finite response at zero frequency
C. Negative response at zero frequency
D. Zero response at zero frequency

Answer: D

For an FIR filter, when M is odd, the real-valued frequency response of the FIR filter Hr(ω) has the characteristic that Hr(0)=0. A zero response at zero frequency is just the condition that the differentiator should satisfy.

 

178. Full band differentiators can be achieved with an FIR filter having an odd number of coefficients.

A. True
B. False

Answer: B

Full band differentiators cannot be achieved with FIR filters having an odd number of coefficients, since Hr(π)=0 for M odd.

 

179. If fp is the bandwidth of the differentiator, then the desired frequency characteristic should be linear in the range of _____________

A. 0 ≤ ω ≤ 2π

B. 0 ≤ ω ≤ 2fp

C. 0 ≤ ω ≤ 2πfp

D. None of the mentioned

Answer: C

In most cases of practical interest, the desired frequency response characteristic need only be linear over the limited frequency range 0 ≤ ω ≤ 2πfp, where fp is the bandwidth of the differentiator.

 

180. What is the desired response of the differentiator in the frequency range 2πfp ≤ ω ≤ π?

A. Left unconstrained
B. Constrained to be zero
C. Left unconstrained or Constrained to be zero
D. None of the mentioned

Answer: C

In the frequency range 2πfp ≤ ω ≤ π, the desired response may be either left unconstrained or constrained to be zero.

 

181. What is the weighting function used in the design of FIR differentiators based on the Chebyshev approximation criterion?

A. 1/ω
B. ω
C. 1+ω
D. 1-ω

Answer: A

In the design of FIR differentiators based on the Chebyshev approximation criterion, the weighting function W(ω) is specified in the program as

W(ω)=1/ω

in order that the relative ripple in the pass band is a constant.

 

182. The absolute error between the desired response ω and the approximation Hr(ω) decreases as ω varies from 0 to 2πfp.

A. True
B. False

Answer: B

We know that the weighting function is

W(ω)=1/ω

in order that the relative ripple in the pass band is a constant. Thus, the absolute error between the desired response ω and the approximation Hr(ω) increases as ω varies from 0 to 2πfp.

 

183. Which of the following is the important parameter in a differentiator?

A. Length
B. Bandwidth
C. Peak relative error
D. All of the mentioned

Answer: D

The important parameters in a differentiator are its length, its bandwidth, and the peak relative error of the approximation. The interrelationship among these three parameters can be easily displayed parametrically.

 

184. In this section, we confine our attention to FIR designs in which h(n)=h(M-1-n).

A. True
B. False

Answer: B

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

 

185. What is the maximum value of fp with which good designs are obtained for M odd?

A. 0.25
B. 0.45
C. 0.5
D. 0.75

Answer: B

Designs based on M odd are particularly poor if the bandwidth exceeds 0.45. The problem is basically the zero in the frequency response at ω=π(f=1/2). When fp < 0.45, good designs are obtained for M odd.

 

186. 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.

An all-pass filter is that which passes all frequency components of the input signal without attenuation but provides predictable phase shifts for different frequencies of the input signals.

 

187. 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.

 

188. 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

 

189. 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.

 

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

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

A. True
B. False

Answer: A

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

 

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

A. True
B. False

Answer: B

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.

 

192. The unit sample response of Hilbert transform is _________

A. Zero
B. Symmetric
C. Anti-symmetric
D. None of the mentioned

Answer: C

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.

 

193. 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).

 

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

A. Complex
B. Purely imaginary
C. Purely real
D. Zero

Answer: B

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

 

195. 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.

 

196. 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 flu?

A. -1
B. -0.5
C. 0
D. 1

Answer: D

The bandwidth of the 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.

 

197. 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

Answer: C

The unit sample response of the Hilbert transformer is given as

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

h(n)=0; n=0
From the above equation, it is clear that h(n) becomes zero for even values of ‘n’.

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