Digital Electronic MCQ Set 1
1. If M and N are the orders of numerator and denominator of rational system function respectively, then how many multiplications are required in direct form-I realization of that IIR filter?
a) M+N-1
b) M+N
c) M+N+1
d) M+N+2
Answer
Answer: c [Reason:] From the direct form-I realization of the IIR filter, if M and N are the orders of numerator and denominator of rational system function respectively, then M+N+1 multiplications are required.
2. If M and N are the orders of numerator and denominator of rational system function respectively, then how many additions are required in direct form-I realization of that IIR filter?
a) M+N-1
b) M+N
c) M+N+1
d) M+N+2
Answer
Answer: b [Reason:] From the direct form-I realization of the IIR filter, if M and N are the orders of numerator and denominator of rational system function respectively, then M+N additions are required.
3. If M and N are the orders of numerator and denominator of rational system function respectively, then how many memory locations are required in direct form-I realization of that IIR filter?
a) M+N+1
b) M+N
c) M+N-1
d) M+N-2
Answer
Answer: a [Reason:] From the direct form-I realization of the IIR filter, if M and N are the orders of numerator and denominator of rational system function respectively, then M+N+1 memory locations are required.
4. In direct form-I realization, all-pole system is placed before the all-zero system.
a) True
b) False
Answer
Answer: b [Reason:] In direct form-I realization, all-zero system is placed before the all-pole system.
5. If M and N are the orders of numerator and denominator of rational system function respectively, then how many memory locations are required in direct form-II realization of that IIR filter?
a) M+N+1
b) M+N
c) Min [M,N].
d) Max [M,N].
Answer
Answer: d [Reason:] From the direct form-II realization of the IIR filter, if M and N are the orders of numerator and denominator of rational system function respectively, then Max[M,N] memory locations are required.
6. The basic elements of a flow graph are branches and nodes.
a) True
b) False
Answer
Answer: a [Reason:] A signal flow graph provides an alternative, but an equivalent graphical representation to a block diagram structure that we have been using to illustrate various system realization. The basic elements of a flow graph are branches and nodes.
7. Which of the following is true for the given signal flow graph?
a) Two pole system
b) Two zero system
c) Two pole and two zero system
d) None of the mentioned
Answer
Answer: c [Reason:] The equivalent filter structure of the given signal flow graph in the direct form-II is given by as
Thus from the above structure, the system has two zeros and two poles.
8. What are the nodes that replace the adders in the signal flow graphs?
a) Source node
b) Sink node
c) Branch node
d) Summing node
Answer
Answer: d [Reason:] Summing node is the node which is used in the signal flow graph which replaces the adder in the structure of a filter.
9. The output signal of a system is extracted at a sink node.
a) True
b) False
Answer
Answer: a [Reason:] The input to a system originates at a source node and the output signal is extracted at a sink node.
10. If we reverse the directions of all branch transmittances and interchange the input and output in the flow graph, then the resulting structure is called as:
a) Direct form-I
b) Transposed form
c) Direct form-II
d) None of the mentioned
Answer
Answer: b [Reason:] According to the transposition or flow-graph reversal theorem, if we reverse the directions of all branch transmittances and interchange the input and output in the flow graph, then the system remains unchanged. The resulting structure is known as transposed structure or transposed form.
11. What does the structure given below represents?
a) Direct form-I
b) Regular Direct form-II
c) Transposed direct form-II
d) None of the mentioned
Answer
Answer: c [Reason:] The structure given in the question is the transposed direct form-II structure of a two pole and two zero IIR system.
12. The structure shown below is known as:
a) Parallel form structure
b) Cascade structure
c) Direct form
d) None of the mentioned
Answer
Answer: a [Reason:] From the given figure, it consists of a parallel bank of single pole filters and thus it is called as parallel form structure.
Digital Electronic MCQ Set 2
1. The general linear constant coefficient difference equation characterizing an LTI discrete time system is:
Answer
Answer: a [Reason:] We know that, the general linear constant coefficient difference equation characterizing an LTI discrete time system is given by the expression.
2. Which of the following is the rational system function of an LTI system characterized by the difference equation 
Answer
Answer: c [Reason:] The difference equation of the LTI system is given as 
By applying the z-transform on both sides of the above equation and by rearranging the obtained equation, we get the rational system function as
3. We can view as the computational procedure (an algorithm) for determining the output sequence y(n) of the system from the input sequence x(n).
a) True
b) False
Answer
Answer: a [Reason:] The computations in the given equation can be arranged into equivalent sets of difference equations. Each set of equations defines a computational procedure or an algorithm for implementing the system.
4. Which of the following is used in the realization of a system?
a) Delay elements
b) Multipliers
c) Adders
d) All of the mentioned
Answer
Answer: d [Reason:] From each set of equations, we can construct a block diagram consisting of an interconnection of delay elements, multipliers and adders.
5. Computational complexity refers to the number of:
a) Additions
b) Arithmetic operations
c) Multiplications
d) None of the mentioned
Answer
Answer: b [Reason:] Computational complexity is one of the factor which is used in the implementation of the system. It refers to the numbers of Arithmetic operations (Additions, multiplications and divisions).
6. The number of times a fetch from memory is performed per output sample is one of the factor used in the implementation of the system.
a) True
b) False
Answer
Answer: a [Reason:] According to the recent developments in the design and fabrication of rather sophisticated programmable DSPs, other factors, such as the number of times a fetch from memory is performed or the number of times a comparison between two numbers is performed per output sample, have become important in assessing the computational complexity of a given realization of a system.
7. Which of the following refers the number of memory locations required to store the system parameters, past inputs, past outputs and any intermediate computed values?
a) Computational complexity
b) Finite world length effect
c) Memory requirements
d) None of the mentioned
Answer
Answer: c [Reason:] Memory requirements refers the number of memory locations required to store the system parameters, past inputs, past outputs and any intermediate computed values.
8. Finite word length effects refer to the quantization effects that are inherent in any digital implementation of the system, either in hardware or software.
a) True
b) False
Answer
Answer: a [Reason:] The parameters of the system must necessarily be represented with finite precision. The computations that are performed in the process of computing an output from the system must be rounded off or truncated to fit within the limited precision constraints of the computer or hardware used in the implementation. Thus, Finite word length effects refer to the quantization effects that are inherent in any digital implementation of the system, either in hardware or software.
9. Which of the following are called as finite word length effects?
a) Parameters of the system must be represented with finite precision
b) Computations are truncated to fit in the limited precision constraints
c) Whether the computations are performed in fixed point or floating point arithmetic
d) All of the mentioned
Answer
Answer: d [Reason:] All the three of the considerations given above are called as finite word length effects.
10. The factors Computational complexity, memory requirements and finite word length effects are the ONLY factors influencing our choice of the realization of the system.
a) True
b) False
Answer
Answer: b [Reason:] Apart from the three factors given in the question, other factors such as, whether the structure or the realization lends itself to parallel processing or whether the computations can be pipelined are also the factors which influence our choice of the realization of the system.
Digital Electronic MCQ Set 3
1. By impulse invariance method, the IIR filter will have a unit sample response h(n) that is the sampled version of the analog filter.
a) True
b) False
Answer
Answer: a [Reason:] In the impulse invariance method, our objective is to design an IIR filter having a unit sample response h(n) that is the sampled version of the impulse response of the analog filter. That is
h(n)=h(nT) ; n=0,1,2…
where T is the sampling interval.
2. If a continuous time signal x(t) with spectrum X(F) is sampled at a rate Fs=1/T samples per second, the spectrum of the sampled signal is:
a) Non periodic repetition
b) Non periodic non-repetition
c) Periodic repetition
d) None of the mentioned
Answer
Answer: c [Reason:] When a continuous time signal x(t) with spectrum X(F) is sampled at a rate Fs=1/T samples per second, the spectrum of the sampled signal is periodic repetition.
3. If a continuous time signal x(t) with spectrum X(F) is sampled at a rate Fs=1/T samples per second, then what is the scaled spectrum?
a) X(F)
b) Fs.X(F)
c) X(F)/ Fs
d) None of the mentioned
Answer
Answer: b [Reason:] When a continuous time signal x(t) with spectrum X(F) is sampled at a rate Fs=1/T samples per second, the spectrum of the sampled signal is periodic repetition of the scaled spectrum Fs.X(F).
4. When σ=0, then what is the condition on ‘r’?
a) 0<r<1
b) r=1
c) r>1
d) None of the mentioned
Answer
Answer: b [Reason:] We know that z=esT
Now substitute s=σ+jΩ and z=r.ejω, that is represent ‘z’ in the polar form
On equating both sides, we get
r=eσT
Thus when σ=0, the value of ‘r’ varies from r=1.
5. What is the equation for normalized frequency?
a) F/Fs
b) F.Fs
c) Fs/F
d) None of the mentioned
Answer
Answer: a [Reason:] In the impulse invariance method, the normalized frequency f is given by
f= F/Fs.
6. Aliasing occurs if the sampling rate Fs is more than twice the highest frequency contained in X(F).
a) True
b) False
Answer
Answer: b [Reason:] Aliasing occurs if the sampling rate Fs is less than twice the highest frequency contained in X(F).
7. Which of the filters have a frequency response as shown in the figure below?
a) Analog filter
b) Digital filter without aliasing
c) Digital filter with aliasing
d) None of the mentioned
Answer
Answer: c [Reason:] In the given diagram, the continuous line is the frequency response of analog filter and dotted line is the frequency response of the corresponding digital filter with aliasing.
8. The frequency response given in the above question is for a low pass digital filter.
a) True
b) False
Answer
Answer: a [Reason:] The above given frequency response depicts the frequency response of a low pass analog filter and the frequency response of the corresponding digital filter.
9. Sampling interval T is selected sufficiently large to completely avoid or at least minimize the effects of aliasing.
a) True
b) False
Answer
Answer: b [Reason:] The digital filter with frequency response H(ω) has the frequency response characteristics of the corresponding analog filter if the sampling interval T is selected sufficiently small to completely avoid or at least minimize the effects of aliasing.
10. Which of the following filters cannot be designed using impulse invariance method?
a) Low pass
b) Band pass
c) Low and band pass
d) High pass
Answer
Answer: d [Reason:] It is clear that the impulse invariance method is in -appropriate for designing high pass filter due to the spectrum aliasing that results from the sampling process.
11. Which of the following is the correct relation between ω and Ω?
a) Ω=ωT
b) T=Ωω
c) ω=ΩT
d) None of the mentioned
Answer
Answer: c [Reason:] We know that z=esT
Now substitute s=σ+jΩ and z=r.ejω, that is represent ‘z’ in the polar form
On equating both sides, we get
ω=ΩT.
12. When σ<0, then what is the condition on ‘r’?
a) 0<r<1
b) r=1
c) r>1
d) None of the mentioned
Answer
Answer: a [Reason:] We know that z=esT
Now substitute s=σ+jΩ and z=r.ejω, that is represent ‘z’ in the polar form
On equating both sides, we get
r=eσT
Thus when σ<0, the value of ‘r’ varies from 0<r<1.
13. When σ>0, then what is the condition on ‘r’?
a) 0<r<1
b) r=1
c) r>1
d) None of the mentioned
Answer
Answer: c [Reason:] We know that z=esT
Now substitute s=σ+jΩ and z=r.ejω, that is represent ‘z’ in the polar form
On equating both sides, we get
r=eσT
Thus when σ>0, the value of ‘r’ varies from r>1.
14. What is the period of the scaled spectrum Fs.X(F)?
a) 2Fs
b) Fs/2
c) 4Fs
d) Fs
Answer
Answer: d [Reason:] When a continuous time signal x(t) with spectrum X(F) is sampled at a rate Fs=1/T samples per second, the spectrum of the sampled signal is periodic repetition of the scaled spectrum Fs.X(F) with period Fs.
Digital Electronic MCQ Set 4
1. An analog filter can be converted into digital filter by approximating the differential equation by an equivalent difference equation.
a) True
b) False
Answer
Answer: a [Reason:] One of the simplest methods for converting an analog filter into digital filter is to approximate the differential equation by an equivalent difference equation.
2. Which of the following is the backward difference for the derivative of y(t) with respect to ‘t’ for t=nT?
a) [y(n)+y(n+1)]/T
b) [y(n)+y(n-1)]/T
c) [y(n)-y(n+1)]/T
d) [y(n)-y(n-1)]/T
Answer
Answer: d [Reason:] For the derivate dy(t)/dt at time t=nT, we substitute the backward difference [y(nT)-y(nT-T)]/T. Thus
dy(t)/dt =[y(nT)-y(nT-T)]/T
=[y(n)-y(n-1)]/T
where T represents the sampling interval and y(n)=y(nT).
3. Which of the following is true relation among s-domain and z-domain?
a) s=(1+z-1)/T
b) s=(1+z )/T
c) s=(1-z-1)/T
d) None of the mentioned
Answer
Answer: c [Reason:] The analog differentiator with output dy(t)/dt has the system function H(s)=s, while the digital system that produces the output [y(n)-y(n-1)]/T has the system function H(z) =(1-z-1)/T. Thus the relation between s-domain and z-domain is given as
s=(1-z-1)/T.
4. What is the second difference that is used to replace the second order derivate of y(t)?
a) [y(n)-2y(n-1)+y(n-2)]/T
b) [y(n)-2y(n-1)+y(n-2)]/T2
c) [y(n)+2y(n-1)+y(n-2)]/T
d) [y(n)+2y(n-1)+y(n-2)]/T2
Answer
Answer: b [Reason:] We know that dy(t)/dt =[ y(n)-y(n-1)]/T
Second order derivative of y(t) is d(dy(t)/dt)/dt=[y(n)-2y(n-1)+y(n-2)]/T2.
5. Which of the following in z-domain is equal to s-domain of second order derivate?
d) None of the mentioned
Answer
Answer: a [Reason:] We know that for a second order derivative
6. If s=jΩ and if Ω varies from -∞ to ∞, then what is the corresponding locus of points in z-plane?
a) Circle of radius 1 with centre at z=0
b) Circle of radius 1 with centre at z=1
c) Circle of radius 1/2 with centre at z=1/2
d) Circle of radius 1 with centre at z=1/2
Answer
Answer: c [Reason:] We know that
s=(1-z-1)/T
=> z=1/(1-sT)
Given s= jΩ => z = 1/(1- jΩT)
Thus from the above equation if Ω varies from -∞ to ∞, then the corresponding locus of points in z-plane is a circle of radius 1/2 with centre at z=1/2.
7. Which of the following mapping is true between s-plane and z-domain?
a) Points in LHP of the s-plane into points inside the circle in z-domain
b) Points in RHP of the s-plane into points outside the circle in z-domain
c) Points on imaginary axis of the s-plane into points onto the circle in z-domain
d) All of the mentioned
Answer
Answer: d [Reason:] The below diagram explains the given question
8. This mapping is restricted to the design of low pass filters and band pass filters having relatively small resonant frequencies.
a) True
b) False
Answer
Answer: a [Reason:] The possible location of poles of the digital filter are confined to relatively small frequencies and as a consequence, the mapping is restricted to the design of low pass filters and band pass filters having relatively small resonant frequencies.
9. Which of the following filter transformation is not possible?
a) High pass analog filter to low pass digital filter
b) High pass analog filter to high pass digital filter
c) Low pass analog filter to low pass digital filter
d) None of the mentioned
Answer
Answer: b [Reason:] We know that only low pass and band pass filters with low resonant frequencies in the digital can be designed. So, it is not possible to transform a high pass analog filter into corresponding high pass digital filter.
10. It is possible to map the jΩ-axis into the unit circle.
a) True
b) False
Answer
Answer: a [Reason:] By proper choice of the coefficients of {αk}, it is possible to map the jΩ-axis into the unit circle.
Digital Electronic MCQ Set 5
1. If the input analog signal is within the range of the quantizer, the quantization error e_q (n) is bounded in magnitude i.e.,
| e_q (n) | < ∆/2
and the resulting error is called?
a) Granular noise
b) Overload noise
c) Particulate noise
d) Heavy noise
Answer
Answer: a [Reason:] In the statistical approach, we assume that the quantization error is random in nature. We model this error as noise that is added to the original (unquantized) signal. If the input analog signal is within the range of the quantizer, the quantization error e_q (n) is bounded in magnitude
i.e.,
| e_q (n) | < ∆/2
and the resulting error is called Granular noise.
2. If the input analog signal falls outside the range of the quantizer (clipping), e_q (n) becomes unbounded and results in _______
a) Granular noise
b) Overload noise
c) Particulate noise
d) Heavy noise
Answer
Answer: b [Reason:] In the statistical approach, we assume that the quantization error is random in nature. We model this error as noise that is added to the original (unquantized) signal. If the input analog signal falls outside the range of the quantizer (clipping), e_q (n) becomes unbounded and results in overload noise.
3. In the mathematical model for the quantization error e_q (n), to carry out the analysis, what are the assumptions made about the statistical properties of e_q (n)?
1. The error e_q (n) is uniformly distributed over the range — ∆ /2 < e_q (n) < ∆ /2.
2. The error sequence is a stationary white noise sequence. In other words, the error e_q (m) and the error e_q (n) for m≠n are uncorrelated.
3. The error sequence {e_q (n)} is uncorrelated with the signal sequence x(n).
4. The signal sequence x(n) is zero mean and stationary.
a) 1, 2 & 3
b) 1,2,3,4
c) 1, 3
d) 2, 3, 4
Answer
Answer: b [Reason:] In the mathematical model for the quantization error e_q (n). To carry out the analysis, the following are the assumptions made about the statistical properties of e_q (n).
1. The error e_q (n) is uniformly distributed over the range — ∆ /2 < e_q (n) < ∆ /2.
2. The error sequence is a stationary white noise sequence. In other words, the error e_q (m)and the error e_q (n) for m≠n are uncorrelated.
3. The error sequence {e_q (n)} is uncorrelated with the signal sequence x(n).
4. The signal sequence x(n) is zero mean and stationary.
4. What is the abbreviation of SQNR?
a) Signal-to-Quantization Net Ratio
b) Signal-to-Quantization Noise Ratio
c) Signal-to-Quantization Noise Region
d) Signal-to-Quantization Net Region
Answer
Answer: b [Reason:] The effect of the additive noise e_q (n) on the desired signal can be quantified by evaluating the signal-to-quantization noise (power) ratio (SQNR).
5. What is the scale used for the measurement of SQNR?
a) DB
b) db
c) dB
d) All of the mentioned
Answer
Answer: c [Reason:] The effect of the additive noise e_q (n) on the desired signal can be quantified by evaluating the signal-to-quantization noise (power) ratio (SQNR), which can be expressed on a logarithmic scale (in decibels or dB).
6. What is the expression for SQNR which can be expressed in a logarithmic scale?
Answer
Answer: a [Reason:] The signal-to-quantization noise (power) ratio (SQNR), which can be expressed on a logarithmic scale (in decibels or dB) :
SQNR =
7. In the equation SQNR = what are the terms P_x and P_n are called ___ respectively?
a) Power of the Quantization noise and Signal power
b) Signal power and power of the quantization noise
c) None of the mentioned
d) All of the mentioned
Answer
Answer: b [Reason:] In the equation SQNR = then the terms P_x is the signal power and P_n is the power of the quantization noise
8. In the equation SQNR = what are the expressions of P_x and P_n ?
d) None of the mentioned
Answer
Answer: a [Reason:]
9. If the quantization error is uniformly distributed in the range (-∆ /2, ∆ /2) ,the mean value of the error is zero then the variance P_n is?
Answer
Answer: a [Reason:] 
10. By combining 
with P_n=σ_(e )^2= ∆^2/12 and substituting the result into SQNR = what is the final expression for SQNR = ?
Answer
Answer: b [Reason:] SQNR
11. In the equation SQNR = 
for R = 6σ_x the equation becomes?
a) SQNR = 6.02b-1.25 dB
b) SQNR = 6.87b-1.55 dB
c) SQNR = 6.02b+1.25 dB
d) SQNR = 6.87b+1.25 dB
Answer
Answer: c [Reason:] For example, if we assume that x(n) is Gaussian distributed and the range o f the quantizer extends from -3σ_x to 3σ_x (i.e., R = 6σ_x ), then less than 3 out o f every 1000 input signal amplitudes would result in an overload on the average. For R = 6σ_x , then the equation becomes
SQNR = 6.02b+1.25 dB.
