Digital Electronic MCQ Set 1
1. The quantization inherent in the finite precision arithmetic operations render the system linear.
a) True
b) False
Answer
Answer: b [Reason:] In the realization of a digital filter, either in digital hardware or in software on a digital computer, the quantization inherent in the finite precision arithmetic operations render the system linear.
2. In recursive systems, which of the following is caused because of the nonlinearities due to the finite-precision arithmetic operations?
a) Periodic oscillations in the input
b) Non-Periodic oscillations in the input
c) Non-Periodic oscillations in the output
d) Periodic oscillations in the output
Answer
Answer: d [Reason:] In the recursive systems, the nonlinearities due to the finite-precision arithmetic operations often cause periodic oscillations to occur in the output even when the input sequence is zero or some non zero constant value.
3. The oscillations in the output of the recursive system are called as ‘limit cycles’.
a) True
b) False
Answer
Answer: a [Reason:] In the recursive systems, the nonlinearities due to the finite-precision arithmetic operations often cause periodic oscillations to occur in the output even when the input sequence is zero or some non zero constant value. The oscillations thus produced in the output are known as ‘limit cycles’.
4. Limit cycles in the recursive are directly attributable to which of the following?
a) Round-off errors in multiplication
b) Overflow errors in addition
c) Both of the mentioned
d) None of the mentioned
Answer
Answer: c [Reason:] The oscillations in the output of the recursive system are called as limit cycles and are directly attributable to round-off errors in multiplication and overflow errors in addition.
5. What is the range of values called as to which the amplitudes of the output during a limit cycle ae confined to?
a) Stop band
b) Pass band
c) Live band
d) Dead band
Answer
Answer: d [Reason:] The amplitudes of the output during a limit circle are confined to a range of values that is called the ‘dead band’ of the filter.
6. Zero input limit cycles occur from non-zero initial conditions with the input x(n)=0.
a) True
b) False
Answer
Answer: a [Reason:] When the input sequence x(n) to the filter becomes zero, the output of the filter then, after a number of iterations, enters into the limit cycle. The output remains in the limit cycle until another input of sufficient size is applied that drives the system out of the limit cycle. Similarly, zero input limit cycles occur from non-zero initial conditions with the input x(n)=0.
7. Which of the following is true when the response of the single pole filter is in the limit cycle?
a) Actual non-linear system acts as an equivalent non-linear system
b) Actual non-linear system acts as an equivalent linear system
c) Actual linear system acts as an equivalent non-linear system
d) Actual linear system acts as an equivalent linear system
Answer
Answer: b [Reason:] We note that when the response of the single pole filter is in the limit cycle, the actual non-linear system acts as an equivalent linear system with a pole at z=1 when the pole is positive and z=-1 when the poles is negative.
8. Which of the following expressions define the dead band for a single-pole filter?
Answer
Answer: c [Reason:] Since the quantization product av(n-1) is obtained by rounding, it follows that the quantization error is bounded as
9. What is the dead band of a single pole filter with a pole at 1/2 and represented by 4 bits?
a) (-1/2,1/2)
b) (-1/4,1/4)
c) (-1/8,1/8)
d) (-1/16,1/16)
Answer
Answer: d [Reason:] We know that
Given |a|=1/2 and b=4 => |v(n-1)| ≤ 1/16=> The dead band is (-1/16,1/16).
10. The limit cycle mode with zero input, which occurs as a result of rounding the multiplications, corresponds to an equivalent second order system with poles at z=±1.
a) True
b) False
Answer
Answer: a [Reason:] There is an possible limit cycle mode with zero input, which occurs as a result of rounding the multiplications, corresponds to an equivalent second order system with poles at z=±1. In this case the two pole filter exhibits oscillations with an amplitude that falls in the dead band bounded by 2-b/(1-|a1|-a2).
11. What is the necessary and sufficient condition for a second order filter that no zero-input overflow limit cycles occur?
a) |a1|+|a2|=1
b) |a1|+|a2|>1
c) |a1|+|a2|<1
d) None of the mentioned
Answer
Answer: c [Reason:] It can be easily shown that a necessary and sufficient condition for ensuring that no zero-input overflow limit cycles occur is |a1|+|a2|<1
which is extremely restrictive and hence an unreasonable constraint to impose on any second order section.
12. An effective remedy for curing the problem of overflow oscillations is to modify the adder characteristic.
a) True
b) False
Answer
Answer: a [Reason:] An effective remedy for curing the problem of overflow oscillations is to modify the adder characteristic, so that it performs saturation arithmetic. Thus when an overflow is sensed, the output of the adder will be the full scale value of ±1.
13. What is the dead band of a single pole filter with a pole at 3/4 and represented by 4 bits?
a) (-1/2,1/2)
b) (-1/8,1/8)
c) (-1/4,1/4)
d) (-1/16,1/16)
Answer
Answer: b [Reason:] We know that
Given |a|=3/4 and b=4 => |v(n-1)| ≤ 1/8=> The dead band is (-1/8,1/8).
Digital Electronic MCQ Set 2
1. Which of the following is common independent variable for speech signal, EEG and ECG?
a) Time
b) Spatial coordinates
c) Pressure
d) None of the mentioned
Answer
Answer: a [Reason:] Speech, EEG and ECG signals are the examples of information-bearing signals that evolve as functions of a single independent variable, namely, time.
2. Which of the following conditions made digital signal processing more advantageous over analog signal processing?
a) Flexibility
b) Accuracy
c) Storage
d) All of the mentioned
Answer
Answer: d [Reason:] Digital programmable system allows flexibility in reconfiguring the DSP operations by just changing the program, as the digital signal is in the form of 1 and 0’s it is more accurate and it can be stored in magnetic tapes.
3. Which property does y(t)=x(1-t) exhibit?
a) Time scaling
b) Time shifting
c) Reflecting
d) Time shifting and reflecting
Answer
Answer: d [Reason:] First the signal x(t) is shifted by 1 to get x(1+t) and it is reflected to get x(1-t). So, it exhibits both time shifting and reflecting properties.
4. If x(n)=(0,1,2,3,3,0,0,0) then x(2n) is:
a) (0,2,4,6,6,0,0,0)
b) (0,1,2,3,3,0,0,0)
c) (0,2,3,0,0,0,0,0)
d) None of the mentioned
Answer
Answer: c [Reason:] Substitute n=0,1,2… in x(2n) and obtain the values from the given x(n).
5. If x(n)=(0,0,1,2,3,4,0,0) then x(n-2) is:
a) (0,0,2,4,6,8,0,0)
b) (0,0,1,2,3,4,0,0)
c) (1,2,3,4,0,0,0,0)
d) (0,0,0,0,1,2,3,4)
Answer
Answer: d [Reason:] The signal x(n) is shifted right by 2.
6. If x(n)=(0,0,1,1,1,1,1,0) then x(3n+1) is:
a) (0,1,0,0,0,0,0,0)
b) (0,0,1,1,1,1,0,0)
c) (1,1,0,0,0,0,0,0)
d) None of the mentioned
Answer
Answer: a [Reason:] First shift the given signal left by 1 and then time scale the obtained signal by 3.
7. If a signal x(t) is processed through a system to obtain the signal (x(t)2), then the system is said to be:
a) Linear
b) Non-linear
c) Exponential
d) None of the mentioned
Answer
Answer: b [Reason:] Let the input signal be ‘t’. Then the output signal after passing through the system is y=t2 which is the equation of a parabola. So, the system is non-linear.
8. What are the important block(s) required to process an input analog signal to get an output analog signal?
a) A/D converter
b) Digital signal processor
c) D/A converter
d) All of the mentioned
Answer
Answer: d [Reason:] The input analog signal is converted into digital using A/D converter and passed through DSP and then converted back to analog using D/A converter.
9. Which of the following block is not required in digital processing of an RADAR signal?
a) A/D converter
b) D/A converter
c) DSP
d) All of the mentioned
Answer
Answer: b [Reason:] In the digital processing of the radar signal, the information extracted from the radar signal, such as the position of the aircraft and its speed, may simply be printed on a paper. So, there is no need of an D/A converter in this case.
10. Which of the following wave is known as “amplitude modulated wave” of x(t)?
a) C.x(t) (where C is a constant)
b) x(t)+y(t)
c) x(t).y(t)
d) dx(t)/dt
Answer
Answer: c [Reason:] The multiplicative operation is often encountered in analog communication, where an audio frequency signal is multiplied by a high frequency sinusoid known as carrier. The resulting signal is known as “amplitude modulated wave”.
11. What is the physical device that performs an operation on the signal?
a) Signal source
b) System
c) Medium
d) None of the mentioned
Answer
Answer: b [Reason:] A system is a physical device which performs the operation on the signal and modifies the input signal.
Digital Electronic MCQ Set 3
1. What is the region between origin and the pass band frequency in the magnitude frequency response of a low pass filter?
a) Stop band
b) Pass band
c) Transition band
d) None of the mentioned
Answer
Answer: b [Reason:] From the magnitude frequency response of a low pass filter, we can state that the region before pass band frequency is known as ‘pass band’ where the signal is passed without huge losses.
2. What is the region between stop band and the pass band frequencies in the magnitude frequency response of a low pass filter?
a) Stop band
b) Pass band
c) Transition band
d) None of the mentioned
Answer
Answer: c [Reason:] From the magnitude frequency response of a low pass filter, we can state that the region between pass band and stop band frequencies is known as ‘transition band’ where no specifications are provided.
3. What is the region after the stop band frequency in the magnitude frequency response of a low pass filter?
a) Stop band
b) Pass band
c) Transition band
d) None of the mentioned
Answer
Answer: a [Reason:] 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.
4. If δP is the forbidden magnitude value in the pass band and δS is the forbidden magnitude value in th stop band, then which of the following is true in the pass band region?
a) 1- δS≤|H(jΩ)|≤1
b) δP≤|H(jΩ)|≤1
c) 0≤|H(jΩ)|≤ δS
d) 1- δP≤|H(jΩ)|≤1
Answer
Answer: d [Reason:] From the magnitude frequency response of the low pass filter, the hatched region in the pass band indicate forbidden magnitude value whose value is given as
1- δP≤|H(jΩ)|≤1.
5. If δPis the forbidden magnitude value in the pass band and δS is the forbidden magnitude value in th stop band, then which of the following is true in the stop band region?
a) 1- δP≤|H(jΩ)|≤1
b) δP≤|H(jΩ)|≤1
c) 0≤|H(jΩ)|≤ δS
d) 1- δP≤|H(jΩ)|≤1
Answer
Answer: c [Reason:] From the magnitude frequency response of the low pass filter, the hatched region in the stop band indicate forbidden magnitude value whose value is given as
0≤|H(jΩ)|≤ δS.
6. What is the value of pass band ripple in dB?
a) -20log(1- δP)
b) -20log(δP)
c) 20log(1- δP)
d) None of the mentioned
Answer
Answer: a [Reason:] 1- δP is known as the pass band ripple or the pass band attenuation, and its value in dB is given as -20log(1- δP).
7. What is the value of stop band ripple in dB?
a) -20log(1- δS)
b) -20log(δS)
c) 20log(1- δS)
d) None of the mentioned
Answer
Answer: b [Reason:] δS is known as the stop band attenuation, and its value in dB is given as -20log(δS).
8. What is the pass band gain of a low pass filter with 1- δP as the pass band attenuation?
a) -20log(1- δP)
b) -20log(δP)
c) 20log(δP)
d) 20log(1- δP)
Answer
Answer: d [Reason:] If 1- δP is the pass band attenuation, then the pass band gain is given by the formula 20log(1- δP).
9. What is the stop band gain of a low pass filter with δS as the pass band attenuation?
a) -20log(1- δS)
b) -20log(δS)
c) 20log(δS)
d) 20log(1- δS)
Answer
Answer: c [Reason:] If δS is the stop band attenuation, then the stop band gain is given by the formula 20log(δS).
10. 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
Answer: b [Reason:] A filter is said to be normalized if the cutoff frequency of the filter, Ωc is 1 rad/sec.
11. The low pass, high pass, band pass and band stop filters can be designed by applying a specific transformation to a normalized low pass filter.
a) True
b) False
Answer
Answer: a [Reason:] It is known that the low pass, high pass, band pass and band stop filters can be designed by applying a specific transformation to a normalized low pass filter. Therefore, a lot of importance is given to the design of normalized low pass analog filter.
Digital Electronic MCQ Set 4
1. The state space or the internal description of the system still involves a relationship between the input and output signals, what are the additional set of variables it also involves?
a) System variables
b) Location variables
c) State variables
d) None of the mentioned
Answer
Answer: c [Reason:] Although the state space or the internal description of the system still involves a relationship between the input and output signals, it also involves an additional set of variables, called State variables.
2. State variables provide information about all the internal signals in the system.
a) True
b) False
Answer
Answer: a [Reason:] The state variables provide information about all the internal signals in the system. As a result, the state-space description provides a more detailed description of the system than the input-output description.
3. Which of the following gives the complete definition of the state of a system at time n0?
a) Amount of information at n0 determines output signal for n≥n0
b) Input signal x(n) for n≥n0 determines output signal for n≥n0
c) Input signal x(n) for n≥0 determines output signal for n≥n0
d) Amount of information at n0+input signal x(n) for n≥n0 determines output signal for n≥n0
Answer
Answer: d [Reason:] We define the state of a system at time n0 as the amount of information that must be provided at time n0, which, together with the input signal x(n) for n≥n0 determines output signal for n≥n0.
4. From the definition of state of a system ,the system consists of only one component called memory less component.
a) True
b) False
Answer
Answer: b [Reason:] According to the definition of state of a system, the system consists of two components called memory component and memory less component.
5. If we interchange the rows and columns of the matrix F, then the system is called as:
a) Identity system
b) Diagonal system
c) Transposed system
d) None of the mentioned
Answer
Answer: c [Reason:] The transpose of the matrix F is obtained by interchanging its rows and columns, and it is denoted by FT. The system thus obtained is known as Transposed system.
6. A single input-single output system and its transpose have identical impulse responses and hence the same input-output relationship.
a) True
b) False
Answer
Answer: a [Reason:] If h(n) is the impulse response of the single input-single output system, and h1(n) is the impulse response of the transposed system, then we know that h(n)=h1(n). Thus, a single input-single output system and its transpose have identical impulse responses and hence the same input-output relationship.
7. A closed form solution of the state space equations is easily obtained when the system matrix F is:
a) Transpose
b) Symmetric
c) Identity
d) Diagonal
Answer
Answer: d [Reason:] A closed form solution of the state space equations is easily obtained when the system matrix F is diagonal. Hence, by finding a matrix P so that F1=PFP-1 is diagonal, the solution of the state equations is simplified considerably.
8. What is the condition to call a number λ is an Eigen value of F and a nonzero vector U is the associated Eigen vector?
a) (F+ λI)U=0
b) (F- λI)U=0
c) F- λI=0
d) None of the mentioned
Answer
Answer: b [Reason:] A number λ is an Eigen value of F and a nonzero vector U is the associated Eigen vector if
FU= λU
Thus, we obtain (F- λI)U=0.
9. The determinant |F- λI|=0 yields the characteristic polynomial of the matrix F.
a) True
b) False
Answer
Answer: a [Reason:] We know that (F- λI)U=0
The above equation has a nonzero solution U if the matrix F- λI is singular, which is the case if the determinant of (F- λI) is zero. That is, |F- λI|=0.
This determinant yields the characteristic polynomial of the matrix F.
10. The parallel form realization is also known as normal form representation.
a) True
b) False
Answer
Answer: a [Reason:] The parallel form realization is also known as normal form representation, because the matrix F is diagonal, and hence the state variables are uncoupled.
Digital Electronic MCQ Set 5
1. In general, an FIR system is described by the difference equation 
a) True
b) False
Answer
Answer: a [Reason:] The difference equation describes the FIR system.
2. What is the general system function of an FIR system?
Answer
Answer: c [Reason:] We know that the difference equation of an FIR system is given by 
3. Which of the following is an method for implementing an FIR system?
a) Direct form
b) Cascade form
c) Lattice structure
d) All of the mentioned
Answer
Answer: d [Reason:] There are several structures for implementing an FIR system, beginning with the simplest structure, called the direct form. There are several other methods like cascade form realization, frequency sampling realization and lattice realization which are used for implementing and FIR system.
4. How many memory locations are used for storage of the output point of a sequence of length M in direct form realization?
a) M+1
b) M
c) M-1
d) None of the mentioned
Answer
Answer: c [Reason:] The direct form realization follows immediately from the non-recursive difference equation given by
We observe that this structure requires M-1 memory locations for storing the M-1 previous inputs.
5. The direct form realization is often called a transversal or tapped-delay-line filter.
a) True
b) False
Answer
Answer: a [Reason:] The structure of the direct form realization, resembles a tapped delay line or a transversal system.
6. What is the condition of M, if the structure according to the direct form is as follows?
a) M even
b) M odd
c) All values of M
d) Doesn’t depend on value of M
Answer
Answer: b [Reason:] When the FIR system has linear phase, the unit sample response of the system satisfies either the symmetry or asymmetry condition, h(n)= ±h(M-1-n)
For such a system the number of multiplications is reduced from M to M/2 for M even and to (M-1)/2 for M odd. Thus for the structure given in the question, M is odd.
7. By combining two pairs of poles to form a fourth order filter section, by what factor we have reduced the number of multiplications?
a) 25%
b) 30%
c) 40%
d) 50%
Answer
Answer: d [Reason:] We have to do 3 multiplications for every second order equation. So, we have to do 6 multiplications if we combine two second order equations and we have to perform 3 multiplications by directly calculating the fourth order equation. Thus the number of multiplications are reduced by a factor of 50%.
8. The desired frequency response is specified at a set of equally spaced frequencies defined by the equation:
a) π/2M(k+α)
b) π/M(k+α)
c) 2π/M(k+α)
d) None of the mentioned
Answer
Answer: c [Reason:] To derive the frequency sampling structure, we specify the desired frequency response at a set of equally spaced frequencies, namely ωk=2π/M(k+α) ,k=0,1…(M-1)/2 for M odd
k=0,1….(M/2)-1 for M even
α=0 or 0.5.
9. The realization of FIR filter by frequency sampling realization can be viewed as cascade of how many filters?
a) Two
b) Three
c) Four
d) None of the mentioned
Answer
Answer: a [Reason:] In frequency sampling realization, the system function H(z) is characterized by the set of frequency samples {H(k+ α)} instead of {h(n)}. We view this FIR filter realization as a cascade of two filters. One is an all-zero or a comb filter and the other consists of parallel bank of single pole filters with resonant frequencies.
10. What is the system function of all-zero filter or comb filter?
Answer
Answer: d [Reason:] The system function H(z) which is characterized by the set of frequency samples is obtained as
11. The zeros of the system function of comb filter are located:
a) Inside unit circle
b) On unit circle
c) Outside unit circle
d) None of the mentioned
Answer
Answer: b [Reason:] The system function of the comb filter is given by the equation
12. What is the system function of the second filter other than comb filter in the realization of FIR filter?
Answer
Answer: c [Reason:] The system function H(z) which is characterized by the set of frequency samples is obtained as
13. Where does the poles of the system function of the second filter locate?
Answer
Answer: b [Reason:] The system function of the second filter in the cascade of an FIR realization by frequency sampling method is given by
14. When the desired frequency response characteristic of the FIR filter is narrowband, most of the gain parameters {H(k+α)} are zero.
a) True
b) False
Answer
Answer: a [Reason:] When the desired frequency response characteristic of the FIR filter is narrowband, most of the gain parameters {H(k+α)} are zero. Consequently, the corresponding resonant filters can be eliminated and only the filters with nonzero gains need be retained.
15. Which of the following filters have a cascade realization as shown below?
a) IIR filter
b) Comb filter
c) High pass filter
d) FIR filter
Answer
Answer: d [Reason:] The system function of the FIR filter according to the frequency sampling realization is given by the equation
The above system function can be represented in the cascade form as shown in the above block diagram.
