Digital Electronic MCQ Set 1
1. “For very large value of A, a high boost filtered image is approximately equal to the original image”. State whether the statement is true or false?
a) True
b) False
Answer
Answer: a [Reason:] As the value of A increases, sharpening process contribution becomes less important and so at some very large value A, the contribution becomes almost negligible and so high boost filtered image is approximately equal to the original image.
2. Subtracting Laplacian from an image is proportional to which of the following?
a) Unsharp masking
b) Box filter
c) Median filter
d) None of the mentioned
Answer
Answer: a [Reason:] subtracting Laplacian from an image gives:
f(x,y)- ∇2 f(x,y) = f(x, y) – [f(x + 1, y) + f(x – 1, y) + f(x, y + 1) + f(x, y – 1) – 4f(x, y)]
That on calculation gives 5[1.2 f(x, y) – f ̅(x, y)] ≈ 5[f(x, y) – f(x, y)]
Where f(x, y) – f(x, y) is the unsharp masking definition.
3. A First derivative in image processing is implemented using which of the following given operator(s)?
a) Magnitude of Gradient vector
b) The Laplacian
c) All of the mentioned
d) None of the mentioned
Answer
Answer: a [Reason:] Magnitude of Gradient vector is used for implementation of first derivative in image processing, while Laplacian is for second order implementation in image processing.
4. If for an image function f(x, y), the magnitude of gradient vector 
is given by: mag(∇f)=[G2x+G2y] (1/2), then which of the following fact is correct?
a) The component of Gradient vector are linear operator and also the magnitude of the vector
b) The component of Gradient vector are linear operator, but the magnitude are not
c) The component of Gradient vector are nonlinear operator and also the magnitude of the vector
d) The component of Gradient vector are nonlinear operator, but the magnitude are not
Answer
Answer: b [Reason:] The component of Gradient vector are linear operator because these are derivatives but the magnitude of the vector are not because of the squaring and square root operations.
5. What is the sum of the coefficient of the mask defined using gradient?
a) 1
b) -1
c) 0
d) None of the mentioned
Answer
Answer: c [Reason:] Since, first order derivative of a digital function must be zero in the areas of constant grey values. So, the mask using gradient has a sum 0, so to produce a zero result if applied on constant gray level areas.
6. Gradient is used in which of the following area(s)?
a) To aid humans in detection of defects
b) As a preprocessing step for automated inspections
c) All of the mentioned
d) None of the mentioned
Answer
Answer: c [Reason:] Gradient has a usage in both human analysis as well as a preprocessing step for automated inspections.
7. Gradient have some important features. Which of the following is/are some of them?
a) Enhancing small discontinuities in an otherwise flat gray field
b) Enhancing prominent edges
c) All of the mentioned
d) None of the mentioned
Answer
Answer: c [Reason:] Since gradient are used in fist order derivative image enhancement that enhances the discontinuities except for in flat areas and produces thick edge for constant slope ramp. So, Gradient has all the mentioned features.
8. An image has significant edge details. Which of the following fact(s) is/are true for the gradient image and the Laplacian image of the same?
a) The gradient image is brighter than the Laplacian image
b) The gradient image is brighter than the Laplacian image
c) Both the gradient image and the Laplacian image has equal values
d) None of the mentioned
Answer
Answer: a [Reason:] Because the gradient enhances prominent edges better than Laplacian, so, the Gradient image with significant edge detail has higher value than in Laplacian image.
Digital Electronic MCQ Set 2
1. Which of the following relation is true if the signal x(n) is real?
a) X*(ω)=X(ω)
b) X*(ω)=X(-ω)
c) X*(ω)= -X(ω)
d) None of the mentioned
Answer
Answer: b [Reason:] We know that,
2. For a signal x(n) to exhibit even symmetry, it should satisfy the condition | X(-ω)|=| X(ω)|.
a) True
b) False
Answer
Answer: a [Reason:] We know that, if a signal x(n) is real, then
X*(ω)=X(-ω)
If the signal is even symmetric, then the magnitude on both the sides should be equal.
So, |X*(ω)|=|X(-ω)| =>| X(-ω)|=| X(ω)|.
3. What is the energy density spectrum Sxx(ω) of the signal x(n)=anu(n), |a|<1?
a) 1/(1+2acosω+a2 )
b) 1/(1+2asinω+a2 )
c) 1/(1-2asinω+a2 )
d) 1/(1-2acosω+a2 )
Answer
Answer: d [Reason:] Since |a|<1, the sequence x(n) is absolutely summable, as can be verified by applying the geometric summation formula.
4. What is the Fourier transform of the signal x(n) which is defined as shown in the graph below?
d) None of the mentioned
Answer
Answer: c [Reason:] The Fourier transform of this signal is
5. Which of the following condition is to be satisfied for the Fourier transform of a sequence to be equal as the Z-transform of the same sequence?
a) |z|=1
b) |z|<1
c) |z|>1
d) Can never be equal
Answer
Answer: a [Reason:] Let us consider the signal to be x(n)
6. The sequence 
does not have both z-transform and Fourier transform.
a) True
b) False
Answer
Answer: b [Reason:] The given x(n) do not have Z-transform. But the sequence have finite energy. So, the given sequence x(n) has a Fourier transform.
7. If x(n) is a stable sequence so that X(z) converges on to a unit circle, then the complex cepstrum signal is defined as:
a) X(ln X(z))
b) ln X(z)
c) X-1(ln X(z))
d) None of the mentioned
Answer
Answer: c [Reason:] Let us consider a sequence x(n) having a z-transform X(z). We assume that x(n) is a stable sequence so that X(z) converges on to the unit circle. The complex cepstrum of the signal x(n) is defined as the sequence cx(n), which is the inverse z-transform of Cx(z), where Cx(z)=ln X(z)
=> cx(z)= X-1(ln X(z))
8. If cx(n) is the complex cepstrum sequence obtained from the inverse Fourier transform of ln X(ω), then what is the expression for cθ(n)?
Answer
Answer: d [Reason:] We know that,
9. What is the Fourier transform of the signal x(n)=u(n)?
Answer
Answer: d [Reason:] Given x(n)=u(n)
We know that the z-transform of the given signal is
ROC:|z|>1
X(z) has a pole p=1 on the unit circle, but converges for |z|>1.
If we evaluate X(z) on the unit circle except at z=1, we obtain
10. If a power signal has its power density spectrum concentrated about zero frequency, the signal is known as:
a) Low frequency signal
b) Middle frequency signal
c) High frequency signal
d) None of the mentioned
Answer
Answer: a [Reason:] We know that, for a low frequency signal, the power signal has its power density spectrum concentrated about zero frequency.
11. What are the main characteristics of Anti aliasing filter?
a) Ensures that bandwidth of signal to be sampled is limited to frequency range
b) To limit the additive noise spectrum and other interference, which corrupts the signal
c) All of the mentioned
d) None
Answer
Answer: c [Reason:] T he anti aliasing filter is an analog filter which has a twofold purpose. First, it ensures that the bandwidth of the signal to be sampled is limited to the desired frequency range. Using an anti aliasing filter is to limit the additive noise spectrum and other interference, which often corrupts the desired signal. Usually, additive noise is wide band and exceeds the bandwidth of the desired signal.
12. In general, a digital system designer has better control of tolerances in a digital signal processing system than an analog system designer who is designing an equivalent analog system.
a) True
b) False
Answer
Answer: a [Reason:] Analog signal processing operations cannot be done very precisely either, since electronic components in analog systems have tolerances and they introduce noise during their operation. In general, a digital system designer has better control of tolerances in a digital signal processing system than an analog system designer who is designing an equivalent analog system.
13. The term ‘bandwidth’ represents the quantitative measure of a signal.
a) True
b) False
Answer
Answer: a [Reason:] In addition to the relatively broad frequency domain classification of signals, it is often desirable to express quantitatively the range of frequencies over which the power or energy density spectrum is concentrated. This quantitative measure is called the ‘bandwidth’ of a signal.
14. If F1 and F2 are the lower and upper cutoff frequencies of a band pass signal, then what is the condition to be satisfied to call such a band pass signal as narrow band signal?
Answer
Answer: d [Reason:] If the difference in the cutoff frequencies is much less than the mean frequency, the such a band pass signal is known as narrow band signal.
15. What is the frequency range(in Hz) of Electroencephalogram(EEG)?
a) 10-40
b) 1000-2000
c) 0-100
d) None of the mentioned
Answer
Answer: c [Reason:] Electroencephalogram(EEG) signal has a frequency range of 0-100 Hz.
16. Which of the following electromagnetic signals has a frequency range of 30kHz-3MHz?
a) Radio broadcast
b) Shortwave radio signal
c) RADAR
d) Infrared signal
Answer
Answer: a [Reason:] Radio broadcast signal is an electromagnetic signal which has a frequency range of 30kHz-3MHz.
Digital Electronic MCQ Set 3
1. What is the binary equivalent of (-3/8)?
a) (10011)2
b) (0011)2
c) (1100)2
d) (1101)2
Answer
Answer: d [Reason:] The number (-3/8) is stored in the computer as the 2’s complement of (3/8)
We know that the binary equivalent of (3/8)=0011
Thus the twos complement of 0011=1101.
2. Which of the following is the correct representation of a floating point number X?
a) 2E
b) M.2E(1/2<M<1 )
c) 2M.2E(1/2<M<1 )
d) None of the mentioned
Answer
Answer: b [Reason:] The binary floating point representation commonly used in practice, consists of a mantissa M, which is the fractional part of the number and falls in the range 1/2<M<1, multiplied by the exponential factor 2E, where the exponent E is either a negative or positive integer. Hence a number X is represented as X= M.2E(1/2<M<1).
3. What is the mantissa and exponent respectively obtained when we add 5 and 3/8 in binary float point representation?
a) 0.101010,011
b) 0.101000,011
c) 0.101011,011
d) 0.101011,101
Answer
Answer: c [Reason:] We can represent the numbers in binary float point as
5=0.101000(2011)
3/8=0.110000(2101)=0.000011(2011)
=>5+3/8=(0.101000+0.000011)(2011)=(0.101011)(2011)
Therefore mantissa=0.101011 and exponent=011.
4. What is the largest floating point number that can be represented using a 32-bit word?
a) 3*1038
b) 1.7*1038
c) 0.2*1038
d) 0.3*1038
Answer
Answer: b [Reason:] Let the mantissa be represented by 23 bits plus a sign bit and let the exponent be represented by 7 bits plus a sign bit.
5. If E=0 and M=0, then which of the following statement is true about X?
a) Not a number
b) Infinity
c) Defined
d) Zero
Answer
Answer: d [Reason:] According to the IEEE 754 standard, for a 32-bit machine, single precision floating point number is represented as X=(-1)s.2E-127(M).
From the above equation we can interpret that,
If E=0 and M=0, then the value of X is 0.
6. The truncation error for the sign magnitude representation is symmetric about zero.
a) True
b) False
Answer
Answer: a [Reason:] The truncation error for the sign magnitude representation is symmetric about zero and falls in the range
-(2-b-2-bm) ≤ Et ≤ (2-b-2-bm).
7. What is the range of round-off error for a foxed point representation?
a) [-0.5(2-b+2-bm), 0.5(2-b+2-bm)].
b) [0, (2-b+2-bm)].
c) [0, (2-b-2-bm)].
d) [-0.5(2-b-2-bm), 0.5(2-b-2-bm-bm)].
Answer
Answer: d [Reason:] The round-off error is independent of the type of fixed point representation. The maximum error that can be introduced through rounding is 0.5(2-b-2-bm) and this can be either positive or negative, depending on the value of x. Therefore, the round-off error is symmetric about zero and falls in the range
[-0.5(2-b-2-bm), 0.5(2-b-2-bm-bm)].
8. What is the 2’s complement of (1100)2?
a) (0100)2
b) (0011)2
c) (0111)2
d) (1100)2
Answer
Answer: a [Reason:] a [Reason:] The ones complement of (1100)2 is (0011)2. Thus the two complement of this number is obtained as (0011)2+(0001)2=(0100)2.
9. The binary digit b-A is called as:
a) LSB
b) Total value
c) MSB
d) None of the mentioned
Answer
Answer: c [Reason:] Since the binary digit b-A is the first bit in the representation of the real number, it is called as the most significant bit(MSB) of the number.
10. If E=255 and M≠0, then which of the following statement is true about X?
a) Not a number
b) Infinity
c) Defined
d) Zero
Answer
Answer: a [Reason:] According to the IEEE 754 standard, for a 32-bit machine, single precision floating point number is represented as X=(-1)s.2E-127(M).
From the above equation we can interpret that,
If E=255 and M≠0, then X is not a number.
Digital Electronic MCQ Set 4
1. By means of the DFT and IDFT, determine the response of the FIR filter with impulse response h(n)={1,2,3} to the input sequence x(n)={1,2,2,1}?
a) {1,4,11,9,8,3}
b) {1,4,9,11,8,3}
c) {1,4,9,11,3,8}
d) {1,4,9,3,8,11}
Answer
Answer: b [Reason:] The input sequence has a length N=4 and impulse response has a length M=3. So, the response must have a length of 6(4+3-1).
We know that, Y(k)=X(k).H(k)
Thus we obtain Y(k)={36,-14.07-j17.48,j4,0.07+j0.515,0,0.07-j0.515,-j4,-14.07+j17.48}
By applying IDFT to the above sequence, we get y(n)={1,4,9,11,8,3,0,0}
Thus the output of the system is {1,4,9,11,8,3}.
2. What is the sequence y(n) that results from the use of four point DFTs if the impulse response is h(n)={1,2,3} and the input sequence x(n)={1,2,2,1}?
a) {9,9,7,11}
b) {1,4,9,11,8,3}
c) {7,9,7,11}
d) {9,7,9,11}
Answer
Answer: d [Reason:] The four point DFT of h(n) is H(k)=1+2e-jkπ/2+3 e-jkπ (k=0,1,2,3)
Hence H(0)=6, H(1)=-2-j2, H(3)=2, H(4)=-2+j2
The four point DFT of x(n) is X(k)= 1+2e-jkπ/2+2 e-jkπ+3e-3jkπ/2(k=0,1,2,3)
Hence X(0)=6, X(1)=-1-j, X(2)=0, X(3)=-1+j
The product of these two four point DFTs is
Y ̂(0)=36, Y ̂(1)=j4, Y ̂(2)=0, Y ̂(3)=-j4
The four point IDFT yields y ̂(n)={9,7,9,11}
We can verify as follows
We know that from the previous question y(n)={1,4,9,11,8,3}
y ̂(0)=y(0)+y(4)=9
y ̂(1)=y(1)+y(5)=7
y ̂(2)=y(2)=9
y ̂(3)=y(3)=11.
3. Overlap add and Overlap save are the two methods for linear FIR filtering a long sequence on a block-by-block basis using DFT.
a) True
b) False
Answer
Answer: a [Reason:] In these two methods, the input sequence is segmented into blocks and each block is processed via DFT and IDFT to produce a block of output data. The output blocks are fitted together to form an overall output sequence which is identical to the sequence obtained if the long block had been processed via time domain convolution. So, Overlap add and Overlap save are the two methods for linear FIR filtering a long sequence on a block-by-block basis using DFT.
4. In Overlap save method of long sequence filtering, what is the length of the input sequence block?
a) L+M+1
b) L+M
c) L+M-1
d) None of the mentioned
Answer
Answer: c [Reason:] In this method, each data block consists of the last M-1 data points of the previous data block followed by L new data points to form a data sequence of length N=L+M-1.
5. In Overlap save method of long sequence filtering, how many zeros are appended to the impulse response of the FIR filter?
a) L+M
b) L
c) L+1
d) L-1
Answer
Answer: d [Reason:] The impulse of the FIR filter is increased in length by appending L-1 zeros and an N-point DFT of the sequence is computed once and stored.
6. The first M-1 values of the output sequence in every step of Overlap save method of filtering of long sequence are discarded.
a) True
b) False
Answer
Answer: a [Reason:] Since the data record of length N, the first M-1 points of ym(n) are corrupted by aliasing and must be discarded. The last L points of ym(n) are exactly as same as the result from linear convolution.
7. In Overlap add method, what is the length of the input data block?
a) L-1
b) L
c) L+1
d) None of the mentioned
Answer
Answer: b [Reason:] In this method the size of the input data block is L points and the size of the DFTs and IDFT is N=L+M-1.
8. Which of the following is true in case of Overlap add method?
a) M zeros are appended at last of each data block
b) M zeros are appended at first of each data block
c) M-1 zeros are appended at last of each data block
d) M-1 zeros are appended at first of each data block
Answer
Answer: c [Reason:] In Overlap add method, to each data block we append M-1 zeros at last and compute N point DFT, so that the length of the input sequence is L+M-1=N.
9. In which of the following methods, the input sequence is considered as shown in the below diagram?
a) Overlap save method
b) Overlap add method
c) Overlap add & save method
d) None of the mentioned
Answer
Answer: a [Reason:] From the figure given, we can notice that each data block consists of the last M-1 data points of the previous data block followed by L new data points to form a data sequence of length N+L+M-1 which is same as in the case of Overlap save method.
10. In which of the following methods, the output sequence is considered as shown in the below diagram?
a) Overlap save method
b) Overlap add method
c) Overlap add & save method
d) None of the mentioned
Answer
Answer: b [Reason:] From the figure given, it is clear that the last M-1 points of the first sequence and the first M-1 points of the next sequence are added and nothing is discarded because there is no aliasing in the input sequence. This is same as in the case of Overlap add method.
11. What is the value of x(n)*h(n), 0≤n≤11 for the sequences x(n)={1,2,0,-3,4,2,-1,1,-2,3,2,1,-3} and h(n)={1,1,1} if we perform using overlap add fast convolution technique?
a) {1,3,3,1,1,3,5,2,2,2,3,6}
b) {1,2,0,-3,4,2,-1,1,-2,3,2,1,-3}
c) {1,2,0,3,4,2,1,1,2,3,2,1,3}
d) {1,3,3,-1,1,3,5,2,-2,2,3,6}
Answer
Answer: d [Reason:] Since M=3, we chose the transform length for DFT and IDFT computations as L=2M=23=8.
Since L=M+N-1, we get N=6.
According to Overlap add method, we get
x1′(n)={1,2,0,-3,4,2,0,0} and h'(n)={1,1,1,0,0,0,0,0}
y1(n)=x1′(n)*N h'(n) (circular convolution)={1,3,3,-1,1,3,6,2}
x2′(n)={-1,1,-2,3,2,1,0,0} and h'(n)={1,1,1,0,0,0,0,0}
y2(n)= x2′(n)*N h'(n)={-1,0,-2,2,3,6,3,1}
Thus we get, y(n)= {1,3,3,-1,1,3,5,2,-2,2,3,6}.
12. What is the value of x(n)*h(n), 0≤n≤11 for the sequences x(n)={1,2,0,-3,4,2,-1,1,-2,3,2,1,-3} and h(n)={1,1,1} if we perform using overlap save fast convolution technique?
a) {1,3,3,-1,1,3,5,2,-2,2,3,6}
b) {1,2,0,-3,4,2,-1,1,-2,3,2,1,-3}
c) {1,2,0,3,4,2,1,1,2,3,2,1,3}
d) {1,3,3,1,1,3,5,2,2,2,3,6}
Answer
Answer: a [Reason:] Since M=3, we chose the transform length for DFT and IDFT computations as L=2M=23=8.
Since L=M+N-1, we get N=6.
According to Overlap save technique, we get
x1′(n)={0,0,1,2,0,-3,4,2} and h'(n)={1,1,1,0,0,0,0,0}
=>y1(n)={1,3,3,-1,1,3}
x2′(n)={4,2,-1,1,-2,3,2,1} and h'(n)={1,1,1,0,0,0,0,0}
=>y2(n)={5,2,-2,2,3,6}
=>y(n)= {1,3,3,-1,1,3,5,2,-2,2,3,6}.
Digital Electronic MCQ Set 5
1. In the frequency sampling method for FIR filter design, we specify the desired frequency response Hd(ω) at a set of equally spaced frequencies.
a) True
b) False
Answer
Answer: a [Reason:] In the frequency sampling method, we specify the frequency response Hd(ω) at a set of equally spaced frequencies, namely
2. To reduce side lobes, in which region of the filter the frequency specifications has to be optimized?
a) Stop band
b) Pass band
c) Transition band
d) None of the mentioned
Answer
Answer: c [Reason:] To reduce the side lobes, it is desirable to optimize the frequency specification in the transition band of the filter. This optimization can be accomplished numerically on a digital computer by means of linear programming techniques.
3. What is the frequency response of a system with input h(n) and window length of M?
Answer
Answer: d [Reason:] The desired output of an FIR filter with an input h(n) and using a window of length M is given as
4. What is the relation between H(k+α) and h(n)?
d) None of the mentioned
Answer
Answer: b [Reason:] We know that
5. Which of the following is the correct expression for h(n) in terms of H(k+α)?
Answer
Answer: a [Reason:] We know that
If we multiply the above equation on both sides by the exponential exp(j2πkm/M), m=0,1,2….M-1 and sum over k=0,1,….M-1, we get the equation
6. Which of the following is equal to the value of H(k+α)?
a) H*(M-k+α)
b) H*(M+k+α)
c) H*(M+k-α)
d) H*(M-k-α)
Answer
Answer: d [Reason:] Since {h(n)} is real, we can easily show that the frequency samples {H(k+α)} satisfy the symmetry condition
H(k+α)= H*(M-k-α).
7. The linear equations for determining {h(n)} from {H(k+α)} are not simplified.
a) True
b) False
Answer
Answer: b [Reason:] The symmetry condition, along with the symmetry conditions for {h(n)}, can be used to reduce the frequency specifications from M points to (M+1)/2 points for M odd and M/2 for M even. Thus the linear equations for determining {h(n)} from {H(k+α)} are considerably simplified.
8. The major advantage of designing linear phase FIR filter using frequency sampling method lies in the efficient frequency sampling structure.
a) True
b) False
Answer
Answer: a [Reason:] Although the frequency sampling method provides us with another means for designing linear phase FIR filters, its major advantage lies in the efficient frequency sampling structure, which is obtained when most of the frequency samples are zero.
9. Which of the following is introduced in the frequency sampling realization of the FIR filter?
a) Poles are more in number on unit circle
b) Zeros are more in number on the unit circle
c) Poles and zeros at equally spaced points on the unit circle
d) None of the mentioned
Answer
Answer: c [Reason:] There is a potential problem for frequency sampling realization of the FIR linear phase filter. The frequency sampling realization of the FIR filter introduces poles and zeros at equally spaced points on the unit circle.
10. In a practical implementation of the frequency sampling realization, quantization effects preclude a perfect cancellation of the poles and zeros.
a) True
b) False
Answer
Answer: a [Reason:] In the ideal situation, the zeros cancel the poles and, consequently, the actual zeros of the H(z) are determined by the selection of the frequency samples H(k+α). In a practical implementation of the frequency sampling realization, however, quantization effects preclude a perfect cancellation of the poles and zeros.
11. In the frequency sampling method for FIR filter design, we specify the desired frequency response Hd(ω) at a set of equally spaced frequencies.
a) True
b) False
Answer
Answer: a [Reason:] According to the frequency sampling method for FIR filter design, the desired frequency response is specified at a set of equally spaced frequencies.
12. What is the equation for the frequency ωk in the frequency response of an FIR filter?
Answer
Answer: d [Reason:] In the frequency sampling method for FIR filter design, we specify the desired frequency response Hd(ω) at a set of equally spaced frequencies, namely
where k=0,1,2…M-1/2 and α=0 0r 1/2.
13. Why is it desirable to optimize frequency response in the transition band of the filter?
a) Increase side lobe
b) Reduce side lobe
c) Increase main lobe
d) None of the mentioned
Answer
Answer: b [Reason:] To reduce side lobes, it is desirable to optimize the frequency specification in the transition band of the filter.
