1. Filter parameter optimization technique is used for designing which of the following?
A. FIR in time domain
B. FIR in frequency domain
C. IIR in time domain
D. IIR in the frequency domain
Answer: D
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 design, the system function of the IIR filter is expressed in which form?
A. Parallel form
B. Cascade form
C. Mixed form
D. Any of the mentioned
Answer: B
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
Answer: A
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)
Answer: C
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(ωk) + Ad(ωk)
B. G.A(ωk) – Ad(ωk)
C. G.A(ωk) – A(ωk)
D. None of the mentioned
Answer: B
The error in magnitude at the frequency ωk is G.A(ωk) – Ad(ωk) for 0 ≤ |ω| ≤ π, where Ad(ωk) is the desired magnitude response at ωk.
6. What is the error in delay at the frequency ωk?
A. Tg(ωk)-Td(ωk)
B. Tg(ωk)+Td(ωk)
C. Td(ωk)
D. None of the mentioned
Answer: A
Similarly, as in the previous question, the error in delay at ωk is defined as Tg(ωk)-Td(ωk), where Td(ωk) is the desired delay response.
7. The choice of Td(ωk) for error in the delay is complicated.
A. True
B. False
Answer: A
We know that the error in the delay is defined as Tg(ωk) – Td(ωk). However, the choice of Td(ωk) for error in the delay is complicated by the difficulty in assigning a nominal delay of the filter.
8. If the error in the delay is defined as Tg(ωk) – Tg(ω0) – Td(ωkk), then what is Tg(ω0)?
A. Filter delay at nominal frequency in stopband
B. Filter delay at nominal frequency in the transition band
C. Filter delay at nominal frequency
D. Filter delay at the nominal frequency in passband
Answer: D
We are led to define the error in delay as Tg(ωk) – Tg(ω0) – Td(ωk), where Tg(ω0) is the filter delay at some nominal center frequency in the passband of the filter.
9. We cannot choose any arbitrary function for the errors in magnitude and delay.
A. True
B. False
Answer: B
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
Answer: C
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
Answer: A
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
Answer: B
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
Answer: D
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
Answer: A
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
Answer: B
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.
16. What is the region between origin and the passband frequency in the magnitude frequency response of a low pass filter?
A. Stopband
B. Passband
C. Transition band
D. None of the mentioned
Answer: B
From the magnitude frequency response of a low pass filter, we can state that the region before passband frequency is known as ‘pass band’ where the signal is passed without huge losses.
17. What is the region between stopband and the passband frequencies in the magnitude frequency response of a low pass filter?
A. Stopband
B. Passband
C. Transition band
D. None of the mentioned
Answer: C
From the magnitude frequency response of a low pass filter, we can state that the region between passband and stopband frequencies is known as the ‘transition band’ where no specifications are provided.
18. What is the region after the stopband frequency in the magnitude frequency response of a low pass filter?
A. Stopband
B. Passband
C. Transition band
D. None of the mentioned
Answer: A
From the magnitude frequency response of a low pass filter, we can state that the region after stop band frequency is known as ‘stop band’ where the signal is stopped or restricted.
19. If δP is the forbidden magnitude value in the passband and δS is the forbidden magnitude value in the stopband, then which of the following is true in the passband region?
A. 1-δS≤|H(jΩ)|≤1
B. δP≤|H(jΩ)|≤1
C. 0≤|H(jΩ)|≤ δS
D. 1-δP≤|H(jΩ)|≤1
Answer: D
From the magnitude frequency response of the low pass filter, the hatched region in the passband indicates a forbidden magnitude value whose value is given as
1- δP≤|H(jΩ)|≤1.
20. If δP is the forbidden magnitude value in the passband and δS is the forbidden magnitude value in the stopband, then which of the following is true in the stopband region?
A. 1- δP≤|H(jΩ)|≤1
B. δP≤|H(jΩ)|≤1
C. 0≤|H(jΩ)|≤ δS
D. 1- δP≤|H(jΩ)|≤1
Answer: C
From the magnitude frequency response of the low pass filter, the hatched region in the stopband indicate a forbidden magnitude value whose value is given as
0≤|H(jΩ)|≤ δS.
21. What is the value of passband ripple in dB?
A. -20log(1- δP)
B. -20log(δP)
C. 20log(1- δP)
D. None of the mentioned
Answer: A
1-δP is known as the passband ripple or the passband attenuation, and its value in dB is given as -20log(1-δP).
22. What is the value of stopband ripple in dB?
A. -20log(1-δS)
B. -20log(δS)
C. 20log(1-δS)
D. None of the mentioned
Answer: B
δS is known as the stopband attenuation, and its value in dB is given as -20log(δS).
23. What is the passband gain of a low pass filter with 1- δP as the passband attenuation?
A. -20log(1- δP)
B. -20log(δP)
C. 20log(δP)
D. 20log(1- δP)
Answer: D
If 1-δP is the passband attenuation, then the passband gain is given by the formula 20log(1-δP).
24. What is the stopband gain of a low pass filter with δS as the passband attenuation?
A. -20log(1- δS)
B. -20log(δS)
C. 20log(δS)
D. 20log(1- δS)
Answer: C
If δS is the stopband attenuation, then the stopband gain is given by the formula 20log(δS).
25. What is the cutoff frequency of a normalized filter?
A. 2 rad/sec
B. 1 rad/sec
C. 0.5 rad/sec
D. None of the mentioned
Answer: B
A filter is said to be normalized if the cutoff frequency of the filter, Ωc is 1 rad/sec.
