1. Which of the following is the first method proposed for the design of FIR filters?
A. Chebyshev approximation
B. Frequency sampling method
C. Windowing technique
D. None of the mentioned
Answer: C
The design method based on the use of windows to truncate the impulse response h(n) and obtain the desired spectral shaping, was the first method proposed for designing linear phase FIR filters.
2. The lack of precise control of cutoff frequencies is a disadvantage of which of the following designs?
A. Window design
B. Chebyshev approximation
C. Frequency sampling
D. None of the mentioned
Answer: A
The major disadvantage of the window design method is the lack of precise control of the critical frequencies.
3. The values of cutoff frequencies, in general, depend on which of the following?
A. Type of the window
B. Length of the window
C. Type & Length of the window
D. None of the mentioned
Answer: D
The values of the cutoff frequencies of a filter in general by the windowing technique depend on the type of the filter and the length of the filter.
4. In the frequency sampling method, the transition band is a multiple of which of the following?
A. π/M
B. 2π/M
C. π/2M
D. 2πM
Answer: B
In the frequency sampling technique, the transition band is a multiple of 2π/M.
5. The frequency sampling design method is attractive when the FIR filter is realized in the frequency domain by means of the DFT.
A. True
B. False
Answer: A
The frequency sampling design method is particularly attractive when the FIR is realized either in the frequency domain by means of the DFT or in any of the frequency sampling realizations.
6. Which of the following values can a frequency response take in the frequency sampling technique?
A. Zero
B. One
C. Zero or One
D. None of the mentioned
Answer: C
The attractive feature of the frequency sampling design is that the frequency response can take either zero or one at all frequencies, except in the transition band.
7. Which of the following technique is more preferable for the design of a linear phase FIR filter?
A. Window design
B. Chebyshev approximation
C. Frequency sampling
D. None of the mentioned
Answer: B
The Chebyshev approximation method provides total control of the filter specifications, and as a consequence, it is usually preferable to the other two methods.
8. By optimal filter design, the maximum sidelobe level is minimized.
A. True
B. False
Answer: A
By spreading the approximation error over the passband and stopband of the filter, this method results in an optimal filter design and using this the maximum sidelobe level is minimized.
9. Which of the following is the correct expression for transition band Δf?
A. (ωp– ωs)/2π
B. (ωp+ωs)/2π
C. (ωp.ωs)/2π
D. (ωs– ωp)/2π
Answer: D
The expression for Δf i.e., for the transition band is given as
Δf=(ωs-ωp)/2π.
10. If the resulting δ exceeds the specified δ2, then the length can be increased until we obtain a side lobe level that meets the specification.
A. True
B. False
Answer: A
The estimate is used to carry out the design and if the resulting δ exceeds the specified δ2, then the length can be increased until we obtain a side lobe level that meets the specification.
11. What is the duration of the unit sample response of a digital filter?
A. Finite
B. Infinite
C. Impulse(very small)
D. Zero
Answer: B
Digital filters are the filters that can be designed from analog filters which have infinite duration unit sample response.
12. Which of the following methods are used to convert the analog filter into a digital filter?
A. Approximation of Derivatives
B. Bilinear transformation
C. Impulse invariance
D. All of the mentioned
Answer: D
There are many techniques that are used to convert analog filters into digital filters of which some of which are Approximation of derivatives, bilinear transformation, impulse invariance, and many other methods.
13. Which of the following is the difference equation of the FIR filter of length M, input x(n) and output y(n)?
A. y(n)=\(\sum_{k=0}^{M+1} b_k x(n+k)\)
B. y(n)=\(\sum_{k=0}^{M+1} b_k x(n-k)\)
C. y(n)=\(\sum_{k=0}^{M-1} b_k x(n-k)\)
D. None of the mentioned
Answer: C
An FIR filter of length M with input x(n) and output y(n) is described by the difference equation
y(n)=\(\sum_{k=0}^{M-1} b_k x(n-k)\)
where {bk} is the set of filter coefficients.
14. What is the relation between h(t) and Ha(s)?
A. Ha(s)=\( \int_{-\infty}^{\infty} h(t)e^{-st} dt\)
B. Ha(s)=\(\int_0^{\infty} h(t)e^{st} dt\)
C. Ha(s)=\( \int_{-\infty}^{\infty} h(t)e^{st} dt\)
D. None of the mentioned
Answer: A
We know that the impulse response h(t) and the Laplace transform Ha(s) are related by the equation.
15. Which of the following is a representation of system function?
A. Normal system function
B. Laplace transform
C. Rational system function
D. All of the mentioned
Answer: D
There are many ways how we represent a system function of which one is normal representation i.e., output/input and other ways like Laplace transform and rational system function.
16. For an analog LTI system to be stable, where should the poles of system function H(s) lie?
A. Right half of s-plane
B. Left half of s-plane
C. On the imaginary axis
D. At origin
Answer: B
An analog linear time-invariant system with system function H(s) is stable if all its poles lie on the left half of the s-plane.
17. If the conversion technique is to be effective, the jΩ axis in the s-plane should map into the unit circle in the z-plane.
A. True
B. False
Answer: A
If the conversion technique is to be effective, the jΩ axis in the s-plane should map into the unit circle in the z-plane. Thus there will be a direct relationship between the two frequency variables in the two domains.
18. If the conversion technique is to be effective, then the LHP of the s-plane should be mapped into _________
A. Outside of unit circle
B. Unit circle
C. Inside unit circle
D. Does not matter
Answer: C
If the conversion technique is to be effective, then the LHP of the s-plane should be mapped into the inside of the unit circle in the z-plane. Thus a stable analog filter will be converted to a stable digital filter.
19. Physically realizable and stable IIR filters cannot have a linear phase.
A. True
B. False
Answer: A
If an IIR filter is stable and if it can be physically realizable, then the filter cannot have a linear phase.
20. What is the condition on the system function of a linear phase filter?
A. H(z)=\(z^{-N} H(z^{-1})\)
B. H(z)=\(z^N H(z^{-1})\)
C. H(z)=\(±z^N H(z^{-1})\)
D. H(z)=\(±z^{-N} H(z^{-1})\)
Answer: D
A linear phase filter must have a system function that satisfies the condition
H(z)=\(±z^{-N} H(z^{-1})\)
where z(-N) represents a delay of N units of time.
