Digital Electronic MCQ Set 1
1. Which of the following justifies the linearity property of z-transform?[x(n)↔X(z)].
a) x(n)+y(n) ↔X(z)Y(z)
b) x(n)+y(n) ↔X(z)+Y(z)
c) x(n)y(n) ↔X(z)+Y(z)
d) x(n)y(n) ↔X(z)Y(z)
Answer
Answer: b [Reason:] According to the linearity property of z-transform, if X(z) and Y(z) are the z-transforms of x(n) and y(n) respectively then, the z-transform of x(n)+y(n) is X(z)+Y(z).
2. What is the z-transform of the signal x(n)=[3(2n)-4(3n)]u(n)?
a) 3/(1-2z-1)-4/(1-3z-1)
b) 3/(1+2z-1)-4/(1+3z-1)
c) 3/(1-2z)-4/(1-3z)
d) None of the mentioned
Answer
Answer: a [Reason:] Let us divide the given x(n) into x1(n)= 3(2n)u(n) and x2(n)= 4(3n)u(n)
and x(n)=x1(n)-x2(n)
From the definition of z-transform X1(z)= 3/(1-2z-1) and X2(z)= 4/(1-3z-1)
So, from the linearity property of z-transform
X(z)=X1(z)-X2(z)
=> X(z)= 3/(1-2z-1)-4/(1-3z-1).
3. What is the z-transform of the signal x(n)=sin(jω0n)u(n)?
Answer
Answer: d [Reason:] By Euler’s identity, the given signal x(n) can be written as
4. According to Time shifting property of z-transform, if X(z) is the z-transform of x(n) then what is the z-transform of x(n-k)?
a) zkX(z)
b) z-kX(z)
c) X(z-k)
d) X(z+k)
Answer
Answer: b [Reason:] According to the definition of Z-transform
5. What is the z-transform of the signal defined as x(n)=u(n)-u(n-N)?
Answer
Answer: d [Reason:]
6. If X(z) is the z-transform of the signal x(n) then what is the z-transform of anx(n)?
a) X(az)
b) X(az-1)
c) X(a-1z)
d) None of the mentioned
Answer
Answer: c [Reason:] We know that from the definition of z-transform
7. If the ROC of X(z) is r1<|z|<r2, then what is the ROC of X(a-1z)?
a) |a|r1<|z|<|a|r2
b) |a|r1>|z|>|a|r2
c) |a|r1<|z|>|a|r2
d) |a|r1>|z|<|a|r2
Answer
Answer: a [Reason:] Given ROC of X(z) is r1<|z|<r2
Then ROC of X(a-1z) will be given by r1<|a-1z |<r2=|a|r1<|z|<|a|r2
8. What is the z-transform of the signal x(n)=an(sinω0n)u(n)?
Answer
Answer: d [Reason:]
9. If X(z) is the z-transform of the signal x(n), then what is the z-transform of the signal x(-n)?
a) X(-z)
b) X(z-1)
c) X-1(z)
d) None of the mentioned
Answer
Answer: b [Reason:] From the definition of z-transform, we have
10. X(z) is the z-transform of the signal x(n), then what is the z-transform of the signal nx(n)?
a) -z(dX(z))/dz
b) zdX(z)/dz
c) -z-1dX(z)/dz
d) z-1(dX(z))/dz
Answer
Answer: a [Reason:]
From the definition of z-transform, we have
11. What is the z-transform of the signal x(n)=nanu(n)?
Answer
Answer: c [Reason:]
Digital Electronic MCQ Set 2
1. The basic task of the A/D converter is to convert a discrete set of digital code words into a continuous range of input amplitudes.
a) True
b) False
Answer
Answer: b [Reason:] The basic task of the A /D converter is to convert a continuous range of input amplitude into a discrete set of digital code words. This conversion involves the processes of Quantization and Coding.
2. What is the type of quantizer, if a Zero is assigned a quantization level?
a) Midrise type
b) Mid tread type
c) Mistreat type
d) None of the mentioned
Answer
Answer: b [Reason:] If a zero is assigned a quantization level, the quantizer is of the mid treat type.
3. What is the type of quantizer, if a Zero is assigned a decision level?
a) Midrise type
b) Mid tread type
c) Mistreat type
d) None of the mentioned
Answer
Answer: a [Reason:] If a zero is assigned a decision level, the quantizer is of the midrise type.
4. What is the term used to describe the range of an A/D converter for bipolar signals?
a) Full scale
b) FSR
c) Full-scale region
d) FS
Answer
Answer: b [Reason:] The term Full-scale range (FSR) is used to describe the range of an A /D converter for bipolar signals (i.e., signals with both positive and negative amplitudes).
5. What is the term used to describe the range of an A/D converter for uni-polar signals?
a) Full scale
b) FSR
c) Full-scale region
d) FSS
Answer
Answer: a [Reason:] The term Full scale (FS) is used for uni-polar signals
6. What is the fixed range of the quantization error eq(n)?
a) – ∆/6 < eq(n) ≤ ∆/6
b) – ∆/4 < eq(n) ≤ ∆/4
c) – ∆/2 <eq(n) ≤ ∆/2
d) – ∆/16 <eq(n) ≤ ∆/16
Answer
Answer: c [Reason:] The quantization error eq(n) is always in the range – ∆/2 < eq(n) ≤ ∆/2 , where ∆ is quantizer step size.
7. If the dynamic range of the signal is smaller than the range of quantizer, the samples that exceed the quantizer are clipped, resulting in large quantization error.
a) True
b) False
Answer
Answer: b [Reason:] If the dynamic range o f the signal, defined as xmax-xmin, is larger than the range of the quantizer, the samples that exceed the quantizer range are clipped, resulting in a large (greater than ∆/2) quantization error.
8. What is the relation defined by the operation of quantizer?
a) xq(n) ≡ Q[x(n)]= xk
b) xq(n) = Q[x(n)]= xk , if x(n) ∈ I_k
c) xq(k) ≡ Q[x(k)]= xk
d) None of the mentioned
Answer
Answer: b [Reason:] The possible outputs of the quantizer (i.e., the quantization levels) are denoted as x1,x 2,…xL . The operation of the quantizer is defined by the relation, xq(n) ≡ Q[x(n) ]= xk,if x(n) ∈ Ik.
9. What is the step size or the resolution of an A/D converter?
a) ∆ = (R)/2(b+1)
b) ∆ = (R )/2(b-1)
c) ∆ = (R )/3(b+1)
d) ∆ = (R )/2
Answer
Answer: a [Reason:] The coding process in an A /D converter assigns a unique binary number to each quantization level. If we have L levels, we need at least L different binary numbers. With a word length of b + 1 bits we can represent 2^(b+1) distinct binary numbers. Hence we should have 2^(b+1) > L or, equivalently, b + 1 > log2 L. Then the step size or the resolution of the A /D converter is given by
∆ = (R )/2(b+1), where R is the range of the quantizer.
10. In the practical A/D converters, if the first transition may not occur at exactly + 1/2 LSB ,then such kind of error is known as ______
a) Scale-factor error
b) Offset error
c) Linearity error
d) All of the mentioned
Answer
Answer: b [Reason:] We note that practical A /D converters may have offset error (the first transition may not occur at exactly +1/2 LSB).
11. In the practical A/D converters, if the difference between the values at which the first transition and the last transition occur is not equal to FS – 2LSB, then such error is known as ___
a) Scale-factor error
b) Offset error
c) Linearity error
d) All of the mentioned
Answer
Answer: a [Reason:] We note that practical A /D converters scale-factor (or gain) error (the difference between the values at which the first transition and the last transition occur is not equal to FS — 2LSB ).
12. In the practical A/D converters, if the differences between transition values are not all equal or uniformly changing, then such error is known as ?
a) Scale-factor error
b) Offset error
c) Linearity error
d) All of the mentioned
Answer
Answer: c [Reason:] We note that practical A /D converters, linearity error (the differences between transition values are not all equal or uniformly changing).
Digital Electronic MCQ Set 3
1. What are the values of z for which the value of X(z)=0?
a) Poles
b) Zeros
c) Solutions
d) None of the mentioned
Answer
Answer: b [Reason:] For a rational z-transform X(z) to be zero, the numerator of X(z) is zero and the solutions of the numerator are called as ‘zeros’ of X(z).
2. What are the values of z for which the value of X(z)=∞?
a) Poles
b) Zeros
c) Solutions
d) None of the mentioned
Answer
Answer: a [Reason:] For a rational z-transform X(z) to be infinity, the denominator of X(z) is zero and the solutions of the denominator are called as ‘poles’ of X(z).
3. If X(z) has M finite zeros and N finite poles, then which of the following condition is true?
a) |N-M| poles at origin(if N>M)
b) |N+M| zeros at origin(if N>M)
c) |N+M| poles at origin(if N>M)
d) |N-M| zeros at origin(if N>M)
Answer
Answer: d [Reason:] If X(z) has M finite zeros and N finite poles, then X(z) can be rewritten as X(z)=z -M+N.X'(z).
So, if N>M then z has a positive power. So, it has |N-M| zeros at origin.
4. If X(z) has M finite zeros and N finite poles, then which of the following condition is true?
a) |N-M| poles at origin(if N < M)
b) |N+M| zeros at origin(if N < M)
c) |N+M| poles at origin(if N < M)
d) |N-M| zeros at origin(if N < M)
Answer
Answer: a [Reason:] If X(z) has M finite zeros and N finite poles, then X(z) can be rewritten as X(z)=z-M+N.X'(z).
So, if N < M then z has a negative power. So, it has |N-M| poles at origin.
5. Which of the following signals have a pole-zero plot as shown below?
a) a.u(n)
b) u(an)
c) anu(n)
d) none of the mentioned
Answer
Answer: c [Reason:] From the given pole-zero plot, the z-transform of the signal has one zero at z=0 and one pole at z=a.
So, we obtain X(z)=z/(z-a)
By applying inverse z-transform for X(z), we get
x(n)= anu(n).
6. Which of the following signals have a pole-zero plot as shown below?(Let M=8 in the figure)
Answer
Answer: b [Reason:] From the figure given, the z-transform of the signal has 8 zeros on circle of radius ‘a’ and 7 poles at origin.
7. The z-transform X(z) of the signal x(n)=anu(n) has:
a) One pole at z=0 and one zero at z=a
b) One pole at z=0 and one zero at z=0
c) One pole at z=a and one zero at z=a
d) One pole at z=a and one zero at z=0
Answer
Answer: d [Reason:] The z-transform of the given signal is X(z)= z/(z-a)
So, it has one pole at z=a and one zero at z=0.
8. What is the nature of the signal whose pole-zero plot is as shown?
a) Rising signal
b) Constant signal
c) Decaying signal
d) None of the mentioned
Answer
Answer: c [Reason:] From the pole-zero plot, it is shown that r < 1, so the signal is a decaying signal.
9. What are the values of z for which the value of X(z)=0?
a) Poles
b) Zeros
c) Solutions
d) None of the mentioned
Answer
Answer: b [Reason:] For a rational z-transform X(z) to be zero, the numerator of X(z) is zero and the solutions of the numerator are called as ‘zeros’ of X(z).
10. If Y(z) is the z-transform of the output function, X(z) is the z-transform of the input function and H(z) is the z-transform of system function of the LTI system, then H(z)=?
a) (Y(z))/(X(z))
b) (X(z))/(Y(z))
c) Y(z).X(z)
d) None of the mentioned
Answer
Answer: a [Reason:] We know that for an LTI system, y(n)=h(n)*x(n)
On applying z-transform on both sides we get, Y(z)=H(z).X(z)=>H(z)= ( Y(z))/(X(z) ).
11. What is the system function of the system described by the difference equation y(n)=0.5y(n-1)+2x(n)?
Answer
Answer: d [Reason:] Given difference equation of the system is y(n)=0.5y(n-1)+2x(n)
On applying z-transform on both sides we get, Y(z)=0.5z-1Y(z)+2X(z)
12. What is the unit sample response of the system described by the difference equation y(n)=0.5y(n-1)+2x(n)?
a) 0.5(2)nu(n)
b) 2(0.5)nu(n)
c) 0.5(2)nu(-n)
d) 2(0.5)nu(-n)
Answer
Answer: b [Reason:] By applying the z-transform on both sides of the difference equation given in the question we obtain,
By applying the inverse z-transform we get h(n)= 2(0.5)nu(n).
Digital Electronic MCQ Set 4
1. Which of the following is the right way of representation of equation that contains only the positive frequencies in a given x(t) signal?
a) X+(F)=4V(F)X(F)
b) X+(F)=V(F)X(F)
c) X+(F)=2V(F)X(F)
d) X+(F)=8V(F)X(F)
Answer
Answer: c [Reason:] In a real valued signal x(t), has a frequency content concentrated in a narrow band of frequencies in the vicinity of a frequency Fc. Such a signal which has only positive frequencies can be expressed as X+(F)=2V(F)X(F)
Where X+(F) is a Fourier transform of x(t) and V(F) is unit step function.
2. What is the equivalent time –domain expression of X+(F)=2V(F)X(F)?
a) F(+1)2V(F)*F(+1)X(F)
b) F(-1)4V(F)*F(-1)X(F)
c) F(-1)V(F)*F(-1)X(F)
d) F(-1)2V(F)*F(-1)X(F)
Answer
Answer: d [Reason:] Given Expression , X+(F)=2V(F)X(F).It can be calculated as follows
3. In time-domain expression, 
The signal x+(t) is known as
a) Systematic signal
b) Analytic signal
c) Pre-envelope of x(t)
d) Both Analytic signal & Pre-envelope of x(t)
Answer
Answer: d [Reason:] From the given expression,
4. In equation 
Then the value of ẋ(t) is ?
Answer
Answer: b [Reason:]
5. If the signal ẋ(t) can be viewed as the output of the filter with impulse response h(t) = 1/πt , -∞ < t < ∞
when excited by the input signal x(t) then such a filter is called as___
a) Analytic transformer
b) Hilbert transformer
c) Both Analytic & Hilbert transformer
d) None of the mentioned
Answer
Answer: B [Reason:] The signal ẋ(t) can be viewed as the output of the filter with impulse response h(t) = 1/πt ,
-∞ < t < ∞ when excited by the input signal x(t) then such a filter is called as Hilbert transformer.
6. What is the frequency response of a Hilbert transform H(F)=?
Answer
Answer: a [Reason:] 
We Observe that │H (F) │=1 and the phase response ʘ(F) = -1/2π for F > 0 and ʘ(F) = 1/2π for F < 0.
7. What is the equivalent lowpass representation obtained by performing a frequency translation of X+(F) to Xl(F)= ?
a) X+(F+Fc)
b) X+(F-Fc)
c) X+(F*Fc)
d) X+(Fc-F)
Answer
Answer: a [Reason:] The analytic signal x+(t) is a bandpass signal. We obtain an equivalent lowpass representation by performing a frequency translation of X+(F).
8. What is the equivalent time domain relation of xl(t) i.e., lowpass signal?
Answer
Answer: c
9. If we substitute the equation 
in equation x (t) +j ẋ (t) = xl(t) e(j2πFct) and equate real and imaginary parts on side, then what are the relations that we obtain?
Answer
Answer: b [Reason:] If we substitute the given equation in other, then we get the required result
10. In the relation, 
the low frequency components uc and us are called __ of the bandpass signal x(t).
a) Quadratic components
b) Quadrature components
c) Triplet components
d) None of the mentioned
Answer
Answer: b [Reason:] The low -frequency signal components uc(t) and us(t) can be viewed as amplitude modulations impressed on the carrier components cos2πFct and sin2πFct , respectively. Since these carrier components are in phase quadrature, uc(t) and us(t) are called the Quadrature components of the bandpass signal x (t).
11. What is the other way of representation of bandpass signal x(t)?
Answer
Answer: a [Reason:] The above signal is formed from quadrature components, 
where Re denotes the real part of complex valued quantity.
12. In the equation 
What is the lowpass signal xl (t) is usually called the ___ of the real signal x(t) ?
a) Mediature envelope
b) Complex envelope
c) Equivalent envelope
D) All of the mentioned
Answer
Answer: b [Reason:] In the equation x(t) = Re[xl(t)e(j2πFct)],Re denotes the real part of the complex valued quantity in the brackets following. The lowpass signal x_l (t) is usually called the Complex envelope of the real signal x(t) , and is basically the equivalent low pass signal.
13. If a possible representation of a band pass signal is obtained by expressing xl (t) as 
then what are the equations of a(t) and θ(t) ?
Answer
Answer: a [Reason:] A third possible representation of a band pass signal is obtained by expressing 
14. What is the possible representation of x(t) if xl(t)=a(t)e(jθ(t)) ?
a) x(t) = a(t) cos(2pFct – ?(t))
b) x(t) = a(t) cos(2pFct + ?(t))
c) x(t) = a(t) sin(2pFct + ?(t))
d) x(t) = a(t) sin(2pFct – ?(t))
Answer
Answer: b [Reason:] 
Hence proved.
15. In the equation x(t) = a(t)cos[2πFct+θ(t) ], Which of the following relations between a(t) and x(t), θ(t) and x(t) are true?
a) a(t), θ(t) are called the Phases of x(t)
b) a(t) is the Phase of x(t), θ(t) is called the Envelope of x(t)
c) a(t) is the Envelope of x(t), θ(t) is called the Phase of x(t)
d) None of the mentioned
Answer
Answer: c [Reason:] In the equation x(t) = a(t) cos[2πFct+θ(t) ], the signal a(t) is called the Envelope of x(t), and θ(t) is called the phase of x(t)
Digital Electronic MCQ Set 5
1. What is the main function of (A/D) or ADC converter?
a) Converts Digital to Analog Signal
b) Converts Analog to Digital signal
c) All of the mentioned
d) None of the mentioned
Answer
Answer: b [Reason:] The electronic device that performs this conversion from an analog signal to a digital sequence is called an analog-to-digital (A /D ) converter (ADC ).
2. What is the main function of (D/A) or DAC converter?
a) Converts Digital to Analog Signal
b) Converts Analog to Digital signal
c) All of the mentioned
d) None of the mentioned
Answer
Answer: a [Reason:] A digital-to-analog ( D /A ) converter (DAC ) takes a digital sequence and produces at its output a voltage or current proportional to the size o f the digital word applied to its input.
3. T he S/H is a digitally controlled analog circuit that tracks the analog input signal during the sample mode, and then holds it fixed during the hold mode to the instantaneous value of the signal at the time the system is switched from the sample to the hold mode.
a) True
b) False
Answer
Answer: a [Reason:] The sampling of an analog signal is performed by a sample-and-hold (S/H ) circuit. The sampled signal is then quantized and converted to digital form. Usually, the S/H is integrated into the (A/D) converter. T he S/H is a digitally controlled analog circuit that tracks the analog input signal during the sample mode, and then holds it fixed during the hold mode to the instantaneous value o f the signal at the time the system is switched from the sample mode to the hold mode.
4. The time required to complete the conversion of Analog to Digital is ________ the duration of the hold mode of S/H.
a) Greater than
b) Equals to
c) Less than
d) Greater than or Equals to
Answer
Answer: c [Reason:] The A /D converter begins the conversion after it receives a convert command. The time required to complete the conversion should be less than the duration of the hold mode of S/H.
5. In A/D converter, what is the time relation between sampling period T and the duration of the sample mode and the hold mode?
a) Should be larger than the duration of sample mode and hold mode
b) Should be smaller than the duration of sample mode and hold mode
c) Should be equal to the duration of sample mode and hold mode
d) Should be larger than or equals to the duration of sample mode and hold mode
Answer
Answer: a [Reason:] The A /D converter begins the conversion after it receives a convert command. The sampling period T should be larger than the duration of the sample mode and the hold mode.
6. In the practical A/D converters, what are the distortions and time- related degradations occur during the conversion process?
a) Jitter errors
b) Droops
c) Nonlinear variations in the duration of the sampling aperture
d) All of the mentioned
Answer
Answer: d [Reason:] An ideal S/H introduces no distortion in the conversion process and is accurately modeled as an ideal sampler. However, time-related degradations such as errors in the periodicity of the sampling process ( “jitter”), nonlinear variations in the duration o f the sampling aperture, and changes in the voltage held during conversion ( “droop”) do occur in practical devices.
7. In the absence of an S/H, the input signal must change by more than one-half of the quantization step during the conversion, which may be an impractical constraint.
a) True
b) False
Answer
Answer: b [Reason:] The use of an S/H allows the A /D converter to operate more slowly compared to the time actually used to acquire the sample. In the absence of an S/H, the input signal must not change by more than one-half of the quantization step during the conversion, which may be an impractical constraint.
8. The noise power σn2 can be reduced by increasing the sampling rate to spread the quantization noise power over a larger frequency band (-Fs/2,Fs/2).
a) True
b) False
Answer
Answer: a [Reason:] The noise power σn2 can be reduced by increasing the sampling rate to spread the quantization noise power over a larger frequency band (-Fs/2,Fs/2), and then shaping the noise power spectral density by means o f an appropriate filter.
9. What is the process of down sampling called?
a) Decimation
b) Fornication
c) Both Decimation & Fornication
d) None of the mentioned
Answer
Answer: a [Reason:] To avoid aliasing, w e first filter out the out-of-band (fl, F2) noise by processing the wideband signal. The signal is then passed through the low pass filter and re-sampled (down sampled) at the lower rate. The down sampling process is called decimation.
10. If the interpolation factor is I = 256, the A /D converter output can be obtained by averaging successive non-overlapping blocks of 128 bits.
a) True
b) False
Answer
Answer: a [Reason:] If the interpolation factor is I = 256, the A /D converter output can be obtained by averaging successive non-overlapping blocks o f 128 bits. This averaging would result in a digital signal with a range of values from zero to 256(b as 8 bits) at the Nyquist rate. The averaging process also provides the required anti-aliasing filtering.
11. The crosshatched areas gives two types of Quantization error in DM ,They are ?
a) Slope-overload distortion
b) Granular noise
c) Slope-overload distortion & Granular noise
d) None of the mentioned
Answer
Answer: c [Reason:] The crosshatched areas illustrate two types of quantization error in DM , slope-overload distortion and granular noise.
12. The slope-overload distortion is avoided, if which of the following conditions satisfy?
a) Min| dx(t)/d(t) | ≤ ∆/T
b) Max| dx(t)/d(t) | ≤ ∆/T
c) |dx(t)/d(t) | ≤∆/T
d) None of the mentioned
Answer
Answer: b [Reason:] The crosshatched areas illustrate two types of quantization error in DM , slope-overload distortion and granular noise. types of quantization error in DM , slope-overload distortion and granular noise. Since the maximum slope A (T in x ( n ) is limited by the step size, slope-overload distortion can be avoided if max| dx(t)/d(t) | ≤∆/T .
13. In DM, By increasing∆, reduces the overload distortion but increases the granular noise, and vice versa
a) True
b) False
Answer
Answer: a [Reason:] The granular noise occurs w hen the DM tracks a relatively flat (slowly changing) input signal. We note that increasing ∆ reduces overload distortion but increases the granular noise, and vice versa.
14. Which of the following is the right way to reduce distortion in the DM?
a) By setting up an integrator in front of DM
b) By setting up an integrator behind the DM
c) By setting up an integrator in the middle of DM
d) None of the mentioned
Answer
Answer: a [Reason:] We note that increasing ∆ reduces overload distortion but increases the granular noise, and vice versa. One way to reduce these two types of distortion is to use an integrator in front of the DM.
15. What are the effects produced by Dm by setting up an integrator at the front of DM?
a) Simplifies the DM decoder
b) Increases correlation of the signal into the DM input
c) Emphasizes the low frequencies of x(t)
d) All of the mentioned
Answer
Answer: d [Reason:] One way to reduce these two types of distortion is to use an integrator in front of the DM. This has two effects. First, it emphasizes the low frequencies of x (t) and increases the correlation of the signal into the DM input. Second, it simplifies the DM decoder because the differentiator (inverse system) required at the decoder is canceled by the DM integrator.
Digital Electronic MCQ Set 6
1. The frequency shift can be achieved by multiplying the band pass signal as given in equation
by the quadrature carriers cos[2πFct] and sin[2πFct] and lowpass filtering the products to eliminate the signal components of 2Fc.
a) True
b) False
Answer
Answer: a [Reason:] It is certainly be advantageous to perform a frequency shift of the band pass signal by and sampling the equivalent low pass signal. Such a frequency shift can be achieved by multiplying the band pass signal as given in the above equation by the quadrature carriers cos[2πFct] and sin[2πFct] and low pass filtering the products to eliminate the signal components at 2Fc. Clearly, the multiplication and the subsequent filtering are first performed in the analog domain and then the outputs o f the filters are sampled.
2. What is the final result obtained by substituting Fc=kB-B/2 , T= 1/2B and say n = 2m i.e., for even and n=2m-1 for odd in equation
Answer
Answer: d [Reason:]
3. Which low pass signal component occurs at the rate of B samples per second with even numbered samples of x(t)?
a) uc– lowpass signal component
b) us– lowpass signal component
c) uc & us – lowpass signal component
d) None of the mentioned
Answer
Answer: a [Reason:] With the even-numbered samples o f x(t), which occur at the rate o f B samples per second, produce samples of the low pass signal component uc.
4. Which low pass signal component occurs at the rate of B samples per second with odd numbered samples of x(t)?
a) uc– lowpass signal component
b) us– lowpass signal component
c) uc & us – lowpass signal component
d) None of the mentioned
Answer
Answer: b [Reason:] : With the odd-numbered samples o f x(t), which occur at the rate o f B samples per second, produce samples of the low pass signal component us.
5. What is the reconstruction formula for the bandpass signal x(t) with samples taken at the rate of 2B samples per second?
Answer
Answer: a [Reason:]
, where T=1/2B
6. What is the new centre frequency for the increased bandwidth signal ?
a) Fc‘= Fc+B/2+B’/2
b) Fc‘= Fc+B/2-B’/2
c) Fc‘= Fc-B/2-B’/2
d) None of the mentioned
Answer
Answer: b [Reason:] A new centre frequency for the increased bandwidth signal is Fc‘= Fc+B/2-B’/2
7. According to the sampling theorem for low pass signals with T1=1/B, then what is the expression for uc(t) = ?
Answer
Answer: a [Reason:] To reconstruct the equivalent low pass signals. Thus, according to the sampling
theorem for low pass signals with T1= 1 / B .
8. According to the sampling theorem for low pass signals with T1=1/B, then what is the expression for us(t) = ?
Answer
Answer: b [Reason:] To reconstruct the equivalent low pass signals. Thus, according to the sampling
theorem for low pass signals with T1= 1 / B .
9. What is the expression for low pass signal component uc(t) that can be expressed in terms of samples of the bandpass signal ?
Answer
Answer: b [Reason:] The low pass signal components uc(t) can be expressed in terms of samples of the
band pass signal as follows:
10. What is the expression for low pass signal component us(t) that can be expressed in terms of samples of the bandpass signal ?
Answer
Answer: a [Reason:] The low pass signal components us(t) can be expressed in terms of samples of the
band pass signal as follows:
11. What is the Fourier transform of x(t) ?
Answer
Answer: d [Reason:]
12. What is the basic relationship between the spectrum o f the real band pass signal x( t ) and the spectrum of the equivalent low pass signal xl(t) ?
Answer
Answer: d [Reason:]
, where Xl(F) is the Fourier transform of xl(t). This is the basic relationship between the spectrum o f the real band pass signal x ( t ) and the spectrum of the equivalent low pass signal xl(t).
Digital Electronic MCQ Set 7
1. The Z-Transform X(z) of a discrete time signal x(n) is defined as:
Answer
Answer: b [Reason:] The z-transform of a real discrete time sequence x(n) is defined as a power of ‘z’ which is equal to 
, where ‘z’ is a complex variable.
2. What is the set of all values of z for which X(z) attains a finite value?
a) Radius of convergence
b) Radius of divergence
c) Feasible solution
d) None of the mentioned
Answer
Answer: a [Reason:] Since X(z) is a infinite power series, it is defined only at few values of z. The set of all values of z where X(z) converges to a finite value is called as Radius of Convergence(ROC).
3. What is the z-transform of the finite duration signal
a) 2 + 4z + 5z2 + 7z3 + z4
b) 2 + 4z + 5z2 + 7z3 + z5
c) 2 + 4z-1 + 5z-2 + 7z-3 + z-5
d) 2z2 + 4z + 5 +7z-1 + z-3
Answer
Answer: d [Reason:] We know that, for a given signal x(n) the z-transform is defined as
Substitute the values of n from -2 to 3 and the corresponding signal values in the above formula
We get, X(z) = 2z2 + 4z + 5 +7z-1 + z-3.
4. What is the ROC of the signal x(n)=δ(n-k),k>0?
a) z=0
b) z=∞
c) Entire z-plane, except at z=0
d) Entire z-plane, except at z=∞
Answer
Answer: c [Reason:] We know that, the z-transform of a signal x(n) is
Given x(n)= δ(n-k)=1 at n=k
=> X(z)=z-k
From the above equation, X(z) is defined at all values of z except at z=0 for k>0.
So ROC is defined as Entire z-plane, except at z=0.
5. What is the z-transform of the signal x(n)=(0.5)nu(n)?
Answer
Answer: a [Reason:] For a given signal x(n), its z-transform
6. Which of the following series has an ROC as mentioned below?
a) α-nu(n)
b) αnu(n)
c) α-nu(-n)
d) αnu(n)
Answer
Answer: b [Reason:]
Let x(n)= αnu(n)
7. What is the z-transform of the signal x(n)= -αnu(-n-1)?
Answer
Answer: d [Reason:]
8. What is the ROC of the z-transform of the signal x(n)= anu(n)+bnu(-n-1)?
a) |a|<|z|<|b| b) |a|>|z|>|b| c) |a|>|z|<|b| d) |a|<|z|>|b|
Answer
Answer: a [Reason:] We know that,
ROC of z-transform of a<sup>n</sup>u(n) is |z|>|a|. ROC of z-transform of b<sup>n</sup>u(-n-1) is |z|<|b|. By combining both the ROC's we get the ROC of z-transform of the signal x(n) as |a|<|z|<|b|.
9. What is the ROC of z-transform of finite duration anti-causal sequence?
a) z=0
b) z=∞
c) Entire z-plane, except at z=0
d) Entire z-plane, except at z=∞
Answer
Answer: d [Reason:] Let us an example of anti causal sequence whose z-transform will be in the form X(z)=1+z+z2 which has a finite value at all values of ‘z’ except at z=∞.So, ROC of an anti-causal sequence is entire z-plane except at z=∞.
10. What is the ROC of z-transform of an two sided infinite sequence?
a) |z|>r1 b) |z|<r1 c) r2<|z|<r1 d) None of the mentioned
Answer
Answer: c [Reason:] Let us plot the graph of z-transform of any two sided sequence which looks as follows.
From the above graph, we can state that the ROC of a two sided sequence will be of the form r2 < |z| < r1.
11. The z-transform of a sequence x(n) which is given as is known as:
a) Uni-lateral Z-transform
b) Bi-lateral Z-transform
c) Tri-lateral Z-transform
d) None of the mentioned
Answer
Answer: b [Reason:] The entire timing sequence is divided into two parts n=0 to ∞ and n=-∞ to 0.
Since the z-transform of the signal given in the questions contains both the parts, it is called as Bi-lateral z-transform.
12. What is the ROC of the system function H(z) if the discrete time LTI system is BIBO stable?
a) Entire z-plane, except at z=0
b) Entire z-plane, except at z=∞
c) Contain unit circle
d) None of the mentioned
Answer
Answer: c [Reason:] A discrete time LTI is BIBO stable, if and only if its impulse response h(n) is absolutely summable. That is,
13. The ROC of z-transform of any signal cannot contain poles.
a) True
b) False
Answer
Answer: a [Reason:] Since the value of z-transform tends to infinity, the ROC of the z-transform does not contain poles.
14. Is the discrete time LTI system with impulse response h(n)=an(n) (|a| < 1) BIBO stable?
a) True
b) False
Answer
Answer: a [Reason:]
Given h(n)= a<sup>n</sup>(n) (|a|<1) The z-transform of h(n) is H(z)=z/(z-a),ROC is |z|>|a| If |a|<1, then the ROC contains the unit circle. So, the system is BIBO stable.
15. What is the ROC of a causal infinite length sequence?
a) |z|<r1 b) |z|>r1 c) r2<|z|<r1 d) None of the mentioned
Answer
Answer: b [Reason:] The ROC of causal infinite sequence is of form |z|>r1 where r1 is largest magnitude of poles.
