This set of Digital Signal Processing Multiple Choice Questions & Answers (MCQs) focuses on “Design of IIR Filters in Frequency Domain”.

1. Filter parameter optimization technique is used for designing of which of the following?

a) FIR in time domain

b) FIR in frequency domain

c) IIR in time domain

d) IIR in frequency domain

View Answer

Explanation: We describe a filter parameter optimization technique carried out in the frequency domain that is representative of frequency domain design methods.

2. In this type of designing, the system function of IIR filter is expressed in which form?

a) Parallel form

b) Cascade form

c) Mixed form

d) Any of the mentioned

View Answer

Explanation: The design is most easily carried out with the system function for the IIR filter expressed in the cascade form as

H(z)=G.A(z).

3. It is more convenient to deal with the envelope delay as a function of frequency.

a) True

b) False

View Answer

Explanation: Instead of dealing with the phase response ϴ(ω), it is more convenient to deal with the envelope delay as a function of frequency.

4. Which of the following gives the equation for envelope delay?

a) dϴ(ω)/dω

b) ϴ(ω)

c) -dϴ(ω)/dω

d) -ϴ(ω)

View Answer

Explanation: Instead of dealing with the phase response ϴ(ω), it is more convenient to deal with the envelope delay as a function of frequency, which is

Tg(ω)= -dϴ(ω)/dω.

5. What is the error in magnitude at the frequency ωk?

a) G.A(ω_{k}) + A_{d}(ω_{k})

b) G.A(ω_{k}) – A_{d}(ω_{k})

c) G.A(ω_{k}) – A(ω_{k})

d) None of the mentioned

View Answer

Explanation: The error in magnitude at the frequency ω

_{k}is G.A(ω

_{k}) – A

_{d}(ω

_{k}) for 0 ≤ |ω| ≤ π, where A

_{d}(ω

_{k}) is the desired magnitude response at ω

_{k}.

6. What is the error in delay at the frequency ω_{k}?

a) T_{g}(ω_{k})- T_{d}(ω_{k})

b) T_{g}(ω_{k})+ T_{d}(ω_{k})

c) T_{d}(ω_{k})

d) None of the mentioned

View Answer

Explanation: Similarly as in the previous question, the error in delay at ωk is defined as T

_{g}(ω

_{k})- T

_{d}(ω

_{k}), where T

_{d}(ω

_{k}) is the desired delay response.

7. The choice of T_{d}(ω_{k}) for error in delay is complicated.

a) True

b) False

View Answer

Explanation: We know that the error in delay is defined as T

_{g}(ω

_{k})- T

_{d}(ω

_{k}). However, the choice of T

_{d}(ω

_{k}) for error in delay is complicated by the difficulty in assigning a nominal delay of the filter.

8. If the error in delay is defined as T_{g}(ω_{k})- T_{g}(ω_{0})- T_{d}(ωk_{k}), then what is T_{g}(ω_{0})?

a) Filter delay at nominal frequency in stop band

b) Filter delay at nominal frequency in transition band

c) Filter delay at nominal frequency

d) Filter delay at nominal frequency in pass band

View Answer

Explanation: We are led to define the error in delay as T

_{g}(ω

_{k})- T

_{g}(ω

_{0})- T

_{d}(ω

_{k}), where T

_{g}(ω

_{0}) is the filter delay at some nominal centre frequency in the pass band of the filter.

9. We cannot choose any arbitrary function for the errors in magnitude and delay.

a) True

b) False

View Answer

Explanation: As a performance index for determining the filter parameters, one can choose any arbitrary function of the errors in magnitude and delay.

10. What does ‘p’ represents in the arbitrary function of error?

a) 2K- dimension vector

b) 3K- dimension vector

c) 4K- dimension vector

d) None of the mentioned

View Answer

Explanation: In the error function ‘p’ denotes the 4K dimension vector of the filter coefficients.

11. What should be the value of λ for the error to be placed entirely on delay?

a) 1

b) 1/2

c) 0

d) None of the mentioned

View Answer

Explanation: The emphasis on the errors affecting the design may be placed entirely on the delay by taking the value of λ as 1.

12. What should be the value of λ for the error to be placed equally on magnitude and delay?

a) 1

b) 1/2

c) 0

d) None of the mentioned

View Answer

Explanation: The emphasis on the errors affecting the design may be equally weighted between magnitude and delay by taking the value of λ as 1/2.

13. Which of the following is true about the squared-error function E(p,G)?

a) Linear function of 4K parameters

b) Linear function of 4K+1 parameters

c) Non-Linear function of 4K parameters

d) Non-Linear function of 4K+1 parameters

View Answer

Explanation: The squared error function E(p,G) is a non-linear function of 4K+1 parameters.

14. Minimization of the error function over the remaining 4K parameters is performed by an iterative method.

a) True

b) False

View Answer

Explanation: Due to the non-linear nature of E(p,G), its minimization over the remaining 4K parameters is performed by an iterative numerical optimization method.

15. The iterative process may converge to a global minimum.

a) True

b) False

View Answer

Explanation: The major difficulty with any iterative procedure that searches for the parameter values that minimize a non-linear function is that the process may converge to a local minimum instead of a global minimum.

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