Digital Electronic MCQ Set 1
1. If we down-sample a signal x(n), then the resulting signal will be an aliased version of x(n).
a) True
b) False
Answer
Answer: a [Reason:] We know that if we reduce the sampling rate simply by selecting every Dth value of x(n), the signal will be an aliased version of x(n).
2. What is the folding frequency for the aliased version of x(n) with sampling rate F?
a) F/D
b) F/4D
c) F/2
d) F/2D
Answer
Answer: d [Reason:] We know that if we reduce the sampling rate simply by selecting every Dth value of x(n), the signal will be an aliased version of x(n), with a folding frequency of F/2D.
3. To what value should the bandwidth of x(n) has to be reduced in order to avoid aliasing?
a) F/D
b) F/2D
c) F/4D
d) None of the mentioned
Answer
Answer: b [Reason:] To avoid aliasing, we must reduce the bandwidth of x(n) to Fmax=F/2D. Then we may down-sample by D and thus avoid sampling.
4. Which process has a block diagram as shown in the figure below?
a) Sampling rate conversion
b) Interpolation
c) Decimation
d) None of the mentioned
Answer
Answer: c [Reason:] The block diagram shown in the figure is of sampling rate conversion by decimation by a factor D technique.
5. Which of the following is true about the filtering operation on x(n)?
a) Linear
b) Time variant
c) None of the mentioned
d) Linear and time invariant
Answer
Answer: d [Reason:] Although the filtering operation on x(n) is linear and time invariant, the down-sampling operation in combination with the filtering results in a time variant system.
6.If x(n) produces y(m), then x(n-n0)) does imply y(n-n0) for any value of n0).
a) True
b) False
Answer
Answer: b [Reason:] Given the fact that x(n) produces y(m), we note that x(n-n0)) does not imply y(n-n0)) unless n0) is a multiple of D.
7. The linear filtering operation followed by down sampling on x(n) is not time invariant.
a) True
b) False
Answer
Answer: a [Reason:] Given the fact that x(n) produces y(m), we note that x(n-n0)) does not imply y(n-n0)) unless n0) is a multiple of D. Consequently, the overall linear operation, that is linear filtering followed by down sampling on x(n) is not time invariant.
8. Which of the following gives the equation for y(m)?
a) v(mD)
b) p(mD)
c) v(mD).p(mD)
d) None of the mentioned
Answer
Answer: c [Reason:] We know that the equation for y(m) is given as
y(m)= v ̅(mD)= v(mD).p(mD).
9. We need not relate the spectrum of y(m) to spectrum of x(n) to obtain frequency response characteristic of y(m).
a) True
b) False
Answer
Answer: b [Reason:] The frequency domain characteristic of the output sequence y(m) can be obtained by relating the spectrum of y(m) to the spectrum of the input sequence x(n).
10. The sequence v ̅(n) can be obtained by multiplying v(n) with a signal p(n) of period D.
a) True
b) False
Answer
Answer: a [Reason:] v ̅(n) can be viewed as a sequence obtained by multiplying v(n) with a periodic train of impulses p(n) with period D.
11. If HD(ω) is the frequency response of the low pass filter, then for what value of ω, HD(ω)=1?
a) |ω| = π/D
b) |ω| ≥ π/D
c) |ω| ≤ π/D
d) None of the mentioned
Answer
Answer: c [Reason:] The input sequence x(n) is passed through a low pass filter, characterized by the impulse response h(n) and a frequency response HD(ω), which ideally satisfies the condition,
HD(ω)=1, |ω| ≤ π/D
=0, otherwise.
12. The filter eliminates the spectrum of X(ω) in the range π/D < ω < π.
a) True
b) False
Answer
Answer: a [Reason:] The input sequence x(n) is passed through a low pass filter, characterized by the impulse response h(n) and a frequency response HD(ω), which ideally satisfies the condition,
HD(ω)=1, |ω| ≤ π/D
=0, otherwise
Thus the filter eliminates the spectrum of X(ω) in the range π/D < ω < π.
Digital Electronic MCQ Set 2
1. How is the frequency response of an ideal differentiator related to the frequency?
a) Inversely proportional
b) Linearly proportional
c) Quadratic
d) None of the mentioned
Answer
Answer: b [Reason:] An ideal differentiator has a frequency response that is linearly proportional to the frequency.
2. Which of the following is the frequency response of an ideal differentiator, Hd(ω)?
a) -jω ; -π ≤ ω ≤ π
b) -jω ; 0 ≤ ω ≤ π
c) jω ; 0 ≤ ω ≤ π
d) jω ; -π ≤ ω ≤ π
Answer
Answer: d [Reason:] An ideal differentiator is defined as one that has the frequency response
Hd(ω)= jω ; -π ≤ ω ≤ π.
3. What is the unit sample response corresponding to Hd(ω)?
Answer
Answer: a [Reason:] We know that, for an ideal differentiator, the frequency response is given as
Hd(ω)= jω ; -π ≤ ω ≤ π
Thus, we get the unit sample response corresponding to the ideal differentiator is given as
h(n)=cosπn/n.
4. The ideal differentiator ahs which of the following unit sample response?
a) Symmetric
b) Anti-symmetric
c) Cannot be explained
d) None of the mentioned
Answer
Answer: b [Reason:] We know that the unit sample response of an ideal differentiator is given as
h(n)=cosπn/n
So, we can state that the unit sample response of an ideal differentiator is anti-symmetric because cosπn is also an anti-symmetric function.
5. If hd(n) is the unit sample response of an ideal differentiator, then what is the value of hd(0)?
a) 1
b) -1
c) 0
d) 0.5
Answer
Answer: c [Reason:] Since we know that the unit sample response of an ideal differentiator is anti-symmetric,
=>hd(0)=0.
6. In this section, we confine our attention to FIR designs in which h(n)=-h(M-1-n).
a) True
b) False
Answer
Answer: a [Reason:] 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).
7. Which of the following is the condition that an 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
Answer: d [Reason:] 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.
8. Full band differentiators can be achieved with an FIR filters having odd number of coefficients.
a) True
b) False
Answer
Answer: b [Reason:] Full band differentiators cannot be achieved with an FIR filters having odd number of coefficients, since Hr(π)=0 for M odd.
9. If fp is the bandwidth of the differentiator, then the desired frequency characteristic should be linear in the range:
a) 0 ≤ ω ≤ 2π
b) 0 ≤ ω ≤ 2fp
c) 0 ≤ ω ≤ 2πfp
d) None of the mentioned
Answer
Answer: c [Reason:] 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.
10. What is the desired response of the differentiator in the frequency range 2πfp ≤ ω ≤ π?
a) Left unconstrained
b) Constrained to be zero
c) Either of the mentioned
d) None of the mentioned
Answer
Answer: c [Reason:] In the frequency range 2πfp ≤ ω ≤ π, the desired response may be either left unconstrained or constrained to be zero.
11. 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
Answer: a [Reason:] 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 be a constant.
12. 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
Answer: b [Reason:] We know that the weighting function is
W(ω)=1/ω
in order that the relative ripple in the pass band be a constant. Thus, the absolute error between the desired response ω and the approximation Hr(ω) increases as ω varies from 0 to 2πfp.
13. 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
Answer: d [Reason:] The important parameters in a differentiator are its length, its bandwidth and the peak relative error of the approximation. The inter relationship among these three parameters can be easily displayed parametrically.
14. In this section, we confine our attention to FIR designs in which h(n)=h(M-1-n).
a) True
b) False
Answer
Answer: b [Reason:] 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).
15. 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
Answer: b [Reason:] 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.
Digital Electronic MCQ Set 3
1. Which of the following is the difference equation of the FIR filter of length M, input x(n) and output y(n)?
d) None of the mentioned
Answer
Answer: c [Reason:] An FIR filter of length M with input x(n) and output y(n) is described by the difference equation
where {bk} is the set of filter coefficients.
2. The lower and upper limits on the convolution sum reflect the causality and finite duration characteristics of the filter.
a) True
b) False
Answer
Answer: a [Reason:] We can express the output sequence as the convolution of the unit sample response h(n) of the system with the input signal. The lower and upper limits on the convolution sum reflect the causality and finite duration characteristics of the filter.
3. Which of the following condition should the unit sample response of a FIR filter satisfy to have a linear phase?
a) h(M-1-n) n=0,1,2…M-1
b) ±h(M-1-n) n=0,1,2…M-1
c) -h(M-1-n) n=0,1,2…M-1
d) None of the mentioned
Answer
Answer: b [Reason:] An FIR filter has an linear phase if its unit sample response satisfies the condition
h(n)= ±h(M-1-n) n=0,1,2…M-1.
4. If H(z) is the z-transform of the impulse response of an FIR filter, then which of the following relation is true?
Answer
Answer: d [Reason:] We know that 
and h(n)= ±h(M-1-n) n=0,1,2…M-1
When we incorporate the symmetric and anti-symmetric conditions of the second equation into the first equation and by substituting z -1 for z, and multiply both sides of the resulting equation by z -(M-1) we get
5. The roots of the polynomial H(z) are identical to the roots of the polynomial H(z -1).
a) True
b) False
Answer
Answer: a [Reason:] We know that . This result implies that the roots of the polynomial H(z) are identical to the roots of the polynomial H(z -1).
6. The roots of the equation H(z) must occur in:
a) Identical
b) Zero
c) Reciprocal pairs
d) Conjugate pairs
Answer
Answer: c [Reason:] We know that the roots of the polynomial H(z) are identical to the roots of the polynomial H(z -1). Consequently, the roots of H(z) must occur in reciprocal pairs.
7. If the unit sample response h(n) of the filter is real, complex valued roots need not occur in complex conjugate pairs.
a) True
b) False
Answer
Answer: b [Reason:] We know that the roots of the polynomial H(z) are identical to the roots of the polynomial H(z -1). This implies that if the unit sample response h(n) of the filter is real, complex valued roots must occur in complex conjugate pairs.
8. What is the value of h(M-1/2) if the unit sample response is anti-symmetric?
a) 0
b) 1
c) -1
d) None of the mentioned
Answer
Answer: a [Reason:] When h(n)=-h(M-1-n), the unit sample response is anti-symmetric. For M odd, the center point of the anti-symmetric is n=M-1/2. Consequently, h(M-1/2)=0.
9. What is the number of filter coefficients that specify the frequency response for h(n) symmetric?
a) (M-1)/2 when M is odd and M/2 when M is even
b) (M-1)/2 when M is even and M/2 when M is odd
c) (M+1)/2 when M is even and M/2 when M is odd
d) (M+1)/2 when M is odd and M/2 when M is even
Answer
Answer: d [Reason:] We know that, for a symmetric h(n), the number of filter coefficients that specify the frequency response is (M+1)/2 when M is odd and M/2 when M is even.
10. What is the number of filter coefficients that specify the frequency response for h(n) anti-symmetric?
a) (M-1)/2 when M is even and M/2 when M is odd
b) (M-1)/2 when M is odd and M/2 when M is even
c) (M+1)/2 when M is even and M/2 when M is odd
d) (M+1)/2 when M is odd and M/2 when M is even
Answer
Answer: b [Reason:] We know that, for a anti-symmetric h(n) h(M-1/2)=0 and thus the number of filter coefficients that specify the frequency response is (M-1)/2 when M is odd and M/2 when M is even.
11. Which of the following is not suitable either as low pass or a high pass filter?
a) h(n) symmetric and M odd
b) h(n) symmetric and M even
c) h(n) anti-symmetric and M odd
d) h(n) anti-symmetric and M even
Answer
Answer: c [Reason:] If h(n)=-h(M-1-n) and M is odd, we get H(0)=0 and H(π)=0. Consequently, this is not suitable as either a low pass filter or a high pass filter.
12. The anti-symmetric condition with M even is not used in the design of which of the following linear-phase FIR filter?
a) Low pass
b) High pass
c) Band pass
d) Bans stop
Answer
Answer: a [Reason:] When h(n)=-h(M-1-n) and M is even, we know that H(0)=0. Thus it is not used in the design of a low pass linear phase FIR filter.
13. The anti-symmetric condition is not used in the design of low pass linear phase FIR filter.
a) True
b) False
Answer
Answer: a [Reason:] We know that if h(n)=-h(M-1-n) and M is odd, we get H(0)=0 and H(π)=0. Consequently, this is not suitable as either a low pass filter or a high pass filter and when h(n)=-h(M-1-n) and M is even, we know that H(0)=0. Thus it is not used in the design of a low pass linear phase FIR filter. Thus the anti-symmetric condition is not used in the design of low pass linear phase FIR filter.
Digital Electronic MCQ Set 4
1. What kind of filter is an ideal Hilbert transformer?
a) Low pass
b) High pass
c) Band pass
d) All pass
Answer
Answer: d [Reason:] An ideal Hilbert transformer is a all pass filter.
2. How much phase shift does an Hilbert transformer impart on the input?
a) 45o
b) 90o
c) 135o
d) 180o
Answer
Answer: b [Reason:] An ideal Hilbert transformer is a all pass filter that imparts a 90o phase shift on the signal at its input.
3. 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
Answer: a [Reason:] The frequency response of an ideal Hilbert transform is given as
H(ω)= -j ;0 < ω < π j ;-π < ω < 0
4. 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
Answer: d [Reason:] 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.
5. The unit sample response of an ideal Hilbert transform is
a) True
b) False
Answer
Answer: a [Reason:] 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
6. The unit sample response of Hilbert transform is infinite in duration and causal.
a) True
b) False
Answer
Answer: b [Reason:] We know that the unit sample response of the Hilbert transform is given as
it sample response of an ideal Hilbert transform is infinite in duration and non-causal.
7. The unit sample response of Hilbert transform is:
a) Zero
b) Symmetric
c) Anti-symmetric
d) None of the mentioned
Answer
Answer: c [Reason:] We know that the unit sample response of the Hilbert transform is given as
Thus from the above equation, we can tell that h(n)=-h(-n). Thus the unit sample response of Hilbert transform is anti-symmetric in nature.
8. In this section, we confine our attention on the design of FIR Hilbert transformers with h(n)=-h(M-1-n).
a) True
b) False
Answer
Answer: a [Reason:] 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).
9. Which of the following is true regarding the frequency response of Hilbert transform?
a) Complex
b) Purely imaginary
c) Purely real
d) Zero
Answer
Answer: b [Reason:] Our choice of an anti-symmetric unit sample response is consistent with having a purely imaginary frequency response characteristic.
10. It is impossible to design an all-pass digital Hilbert transformer.
a) True
b) False
Answer
Answer: a [Reason:] 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.
11. 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 fl < ω < 2πfu?
a) -1
b) -0.5
c) 0
d) 1
Answer
Answer: d [Reason:] The bandwidth of 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.
12. 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
Answer: c [Reason:] The unit sample response of the Hilbert transformer is given as
From the above equation, it is clear that h(n) becomes zero for even values of ‘n’.
Digital Electronic MCQ Set 5
1. What is the duration of the unit sample response of a digital filter?
a) Finite
b) Infinite
c) Impulse(very small)
d) Zero
Answer
Answer: b [Reason:] Digital filters are the filters which can be designed from analog filters which have infinite duration unit sample response.
2. Which of the following methods are used to convert analog filter into digital filter?
a) Approximation of Derivatives
b) Bilinear transformation
c) Impulse invariance
d) All of the mentioned
Answer
Answer: d [Reason:] There are many techniques which are used to convert analog filter into digital filter of which some of them are Approximation of derivatives, bilinear transformation, impulse invariance and many other methods.
3. Which of the following is the difference equation of the FIR filter of length M, input x(n) and output y(n)?
d) None of the mentioned
Answer
Answer: c [Reason:] An FIR filter of length M with input x(n) and output y(n) is described by the difference equation
where {bk} is the set of filter coefficients.
4. What is the relation between h(t) and Ha(s)?
d) None of the mentioned
Answer
Answer: a [Reason:] We know that the impulse response h(t) and the Laplace transform Ha(s) are related by the equation
5. 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
Answer: d [Reason:] 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.
6. 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
Answer: b [Reason:] 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.
7. 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
Answer: a [Reason:] 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.
8. If the conversion technique is to be effective, then the LHP of s-plane should be mapped into:
a) Outside of unit circle
b) Unit circle
c) Inside unit circle
d) Does not matter
Answer
Answer: c [Reason:] If the conversion technique is to be effective, then the LHP of 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.
9. Physically realizable and stable IIR filters cannot have linear phase.
a) True
b) False
Answer
Answer: a [Reason:] If an IIR filter is stable and if it can be physically realizable, then the filter cannot have linear phase.
10. What is the condition on the system function of a linear phase filter?
Answer
Answer: d [Reason:] A linear phase filter must have a system function that satisfies the condition
where z(-N) represents a delay of N units of time.
11. If the filter is in linear phase, then filter would have a mirror-image pole outside the unit circle for every pole inside the unit circle.
a) True
b) False
Answer
Answer: a [Reason:] For a linear phase filter, we know that
where z(-N) represents a delay of N units of time. But if this were the case, the filter would have a mirror image pole outside the unit circle for every pole inside the unit circle. Hence the filter would be unstable.
12. What is the order of operations to be performed in order to realize linear phase IIR filter?
(i) Passing x(-n) through a digital filter H(z)
(ii) Time reversing the output of H(z)
(iii) Time reversal of the input signal x(n)
(iv) Passing the result through H(z)
a) (i),(ii),(iii),(iv)
b) (iii),(i),(ii),(iv)
c) (ii),(iii),(iv),(i)
d) (i),(iii),(iv),(ii)
Answer
Answer: b [Reason:] If the restriction on physical reliability is removed, it is possible to obtain a linear phase IIR filter, at least in principle. This approach involves performing a time reversal of the input signal x(n), passing x(-n) through a digital filter H(z), time reversing the output of H(z), and finally, passing the result through H(z) again.
13. When an application requires a linear phase filter, it should be an FIR filter.
a) True
b) False
Answer
Answer: a [Reason:] The signal processing is computationally cumbersome and appear to offer no advantages over linear phase FIR filters. Consequently, when an application requires a linear phase, it should be an FIR filter.
