Digital Electronic MCQ Set 1
1. The equation for Heq(s) is 
a) True
b) False
Answer
Answer: a [Reason:] The analog filter in the time domain is governed by the following difference equation,
2. What is the first backward difference of y(n)?
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:] A simple approximation to the first order derivative is given by the first backward difference. The first backward difference is defined by
[y(n)-y(n-1)]/T.
3. Which of the following is the correct relation between ‘s’ and ‘z’?
a) z=1/(1+sT)
b) s=1/(1+zT)
c) z=1/(1-sT)
d) None of the mentioned
Answer
Answer: c [Reason:] We know that s=(1-z-1)/T=> z=1/(1-sT).
4. What is the center of the circle represented by the image of jΩ axis of the s-domain?
a) z=0
b) z=0.5
c) z=1
d) None of the mentioned
Answer
Answer: b [Reason:] Letting s=σ+jΩ in the equation z=1/(1-sT) and by letting σ=0, we get
|z-0.5|=0.5
Thus the image of the jΩ axis of the s-domain is a circle with centre at z=0.5 in z-domain.
5. What is the radius of the circle represented by the image of jΩ axis of the s-domain?
a) 0.75
b) 0.25
c) 1
d) 0.5
Answer
Answer: d [Reason:] Letting s=σ+jΩ in the equation z=1/(1-sT) and by letting σ=0, we get
|z-0.5|=0.5
Thus the image of the jΩ axis of the s-domain is a circle of radius 0.5 centered at z=0.5 in z-domain.
6. The frequency response H(ω) will be considerably distorted with respect to H(jΩ).
a) True
b) False
Answer
Answer: a [Reason:] Since jΩ axis is not mapped to the circle |z|=1, we can expect that the frequency response H(ω) will be considerably distorted with respect to H(jΩ).
7. The left half of the s-plane is mapped to which of the following in the z-domain?
a) Outside the circle |z-0.5|=0.5
b) Outside the circle |z+0.5|=0.5
c) Inside the circle |z-0.5|=0.5
d) Inside the circle |z+0.5|=0.5
Answer
Answer: c [Reason:] The left half of the s-plane is mapped inside the circle of |z-0.5|=0.5 in the z-plane, which completely lies in the right half z-plane.
8. An analog high pass filter can be mapped to a digital high pass filter.
a) True
b) False
Answer
Answer: b [Reason:] An analog high pass filter cannot be mapped to a digital high pass filter because the poles of the digital filter cannot lie in the correct region, which is the left-half of the z-plane(z < 0) in this case.
9. Which of the following is the correct relation between ‘s’ and ‘z’?
a) s=(1-z-1)/T
b) s=1/(1+zT)
c) s=(1+z-1)/T
d) None of the mentioned
Answer
Answer: a [Reason:] We know that z=1/(1-sT)=> s=(1-z-1)/T.
10. What is the z-transform of the first backward difference equation of y(n)?
d) None of the mentioned
Answer
Answer: b [Reason:] The first backward difference of y(n) is given by the equation
[y(n)-y(n-1)]/T
Thus the z-transform of the first backward difference of y(n) is given as
.
Digital Electronic MCQ Set 2
1. Bilinear Transformation is used for transforming an analog filter to a digital filter.
a) True
b) False
Answer
Answer: a [Reason:] The bilinear transformation can be regarded as a correction of the backward difference method. The bilinear transformation is used for transforming an analog filter to a digital filter.
2. Which of the following rule is used in the bilinear transformation?
a) Simpson’s rule
b) Backward difference
c) Forward difference
d) Trapezoidal rule
Answer
Answer: d [Reason:] Bilinear transformation uses trapezoidal rule for integrating a continuous time function.
3. Which of the following substitution is done in Bilinear transformations?
d) None of the mentioned
Answer
Answer: c [Reason:] In bilinear transformation of an analog filter to digital filter, using the trapezoidal rule, the substitution for ‘s’ is given as
.
4. What is the value of
according to trapezoidal rule?
Answer
Answer: b [Reason:] The given integral is approximated by the trapezoidal rule. This rule states that if T is small, the area (integral) can be approximated by the mean height of x(t) between the two limits and then multiplying by the width. That is
.
5. What is the value of y(n)-y(n-1) in terms of input x(n)?
Answer
Answer: a [Reason:] We know that the derivate equation is
dy(t)/dt=x(t)
6. What is the expression for system function in z-domain?
Answer
Answer: c [Reason:] We know that
y(n)-y(n-1)= [(x(n)+x(n-1))/2]T
Taking z-transform of the above equation gives
=>Y(z)[1-z-1]=([1+z-1]/2).TX(z)
=>H(z)=Y(z)/X(z)= T/2[(1+z-1)/(1-z1 )].
7. In bilinear transformation, the left-half s-plane is mapped to which of the following in the z-domain?
a) Entirely outside the unit circle |z|=1
b) Partially outside the unit circle |z|=1
c) Partially inside the unit circle |z|=1
d) Entirely inside the unit circle |z|=1
Answer
Answer: d [Reason:] In bilinear transformation, the z to s transformation is given by the expression
z=[1+(T/2)s]/[1-(T/2)s].
Thus unlike the backward difference method, the left-half s-plane is now mapped entirely inside the unit circle, |z|=1, rather than to a part of it.
8. The equation is a true frequency-to-frequency transformation.
a) True
b) False
Answer
Answer: a [Reason:] Unlike the backward difference method, the left-half s-plane is now mapped entirely inside the unit circle, |z|=1, rather than to a part of it. Also, the imaginary axis is mapped to the unit circle. Therefore, equation is a true frequency-to-frequency transformation.
9. If s=σ+jΩ and z=rejω, then what is the condition on σ if r<1?
a) σ > 0
b) σ < 0
c) σ > 1
d) σ < 1
Answer
Answer: b [Reason:] We know that if =σ+jΩ and z=rejω, then by substituting the values in the below expression
When r<1 => σ < 0.
10. If s=σ+jΩ and z=rejω and r=1, then which of the following inference is correct?
a) LHS of the s-plane is mapped inside the circle, |z|=1
b) RHS of the s-plane is mapped outside the circle, |z|=1
c) Imaginary axis in the s-plane is mapped to the circle, |z|=1
d) None of the mentioned
Answer
Answer: c [Reason:] We know that if =σ+jΩ and z=rejω, then by substituting the values in the below expression
=>σ = 2/T[(r2-1)/(r2+1+2rcosω)]
When r=1 => σ = 0.
This shows that the imaginary axis in the s-domain is mapped to the circle of unit radius centered at z=0 in the z-domain.
11. If s=σ+jΩ and z=rejω, then what is the condition on σ if r>1?
a) σ > 0
b) σ < 0
c) σ > 1
d) σ < 1
Answer
Answer: a [Reason:] We know that if =σ+jΩ and z=rejω, then by substituting the values in the below expression
s = 2/T[(1-z-1)/(1+z-1)]
=>σ = 2/T[(r2-1)/(r2+1+2rcosω)]
When r>1 => σ > 0.
12. What is the expression for the digital frequency when r=1?
Answer
Answer: d [Reason:] When r=1, we get σ=0 and
13. What is the kind of relationship between Ω and ω?
a) Many-to-one
b) One-to-many
c) One-to-one
d) Many-to-many
Answer
Answer: c [Reason:] The analog frequencies Ω=±∞ are mapped to digital frequencies ω=±π. The frequency mapping is not aliased; that is, the relationship between Ω and ω is one-to-one. As a consequence of this, there are no major restrictions on the use of bilinear transformation.
Digital Electronic MCQ Set 3
1. Which of the following defines a chebyshev polynomial of order N, TN(x)?
a) cos(Ncos-1x) for all x
b) cosh(Ncosh-1x) for all x
c) cos(Ncos-1x), |x|≤1
cosh(Ncosh-1x), |x|>1
d) None of the mentioned
Answer
Answer: c [Reason:] In order to understand the frequency-domain behavior of chebyshev filters, it is utmost important to define a chebyshev polynomial and then its properties. A chebyshev polynomial of degree N is defined as
TN(x) = cos(Ncos-1x), |x|≤1
cosh(Ncosh-1x), |x|>1.
2. What is the formula for chebyshev polynomial TN(x) in recursive form?
a) 2TN-1(x)- TN-2(x)
b) 2TN-1(x)+ TN-2(x)
c) 2xTN-1(x)+ TN-2(x)
d) 2xTN-1(x)- TN-2(x)
Answer
Answer: d [Reason:] We know that a chebyshev polynomial of degree N is defined as
TN(x) = cos(Ncos-1x), |x|≤1
cosh(Ncosh-1x), |x|>1
From the above formula, it is possible to generate chebyshev polynomial using the following recursive formula
TN(x)= 2xTN-1(x)- TN-2(x), N ≥ 2.
3. What is the value of chebyshev polynomial of degree 0?
a) 1
b) 0
c) -1
d) 2
Answer
Answer: a [Reason:] We know that a chebyshev polynomial of degree N is defined as
TN(x) = cos(Ncos-1x), |x|≤1
cosh(Ncosh-1x), |x|>1
For a degree 0 chebyshev filter, the polynomial is obtained as
T0(x)=cos(0)=1.
4. What is the value of chebyshev polynomial of degree 1?
a) 1
b) x
c) -1
d) -x
Answer
Answer: b [Reason:] We know that a chebyshev polynomial of degree N is defined as
TN(x) = cos(Ncos-1x), |x|≤1
cosh(Ncosh-1x), |x|>1
For a degree 1 chebyshev filter, the polynomial is obtained as
T0(x)=cos(cos-1x)=x.
5. What is the value of chebyshev polynomial of degree 3?
a) 3x3+4x
b) 3x3-4x
c) 4x3+3x
d) 4x3-3x
Answer
Answer: d [Reason:] We know that a chebyshev polynomial of degree N is defined as
TN(x) = cos(Ncos-1x), |x|≤1 cosh(Ncosh-1x), |x|>1
And the recursive formula for the chebyshev polynomial of order N is given as
TN(x)= 2xTN-1(x)- TN-2(x)
Thus for a chebyshev filter of order 3, we obtain
T3(x)=2xT2(x)-T1(x)=2x(2x2-1)-x= 4x3-3x.
6. What is the value of chebyshev polynomial of degree 5?
a) 16x5+20x3-5x
b) 16x5+20x3+5x
c) 16x5-20x3+5x
d) 16x5-20x3-5x
Answer
Answer: c [Reason:] We know that a chebyshev polynomial of degree N is defined as
TN(x) = cos(Ncos-1x), |x|≤1
cosh(Ncosh-1x), |x|>1
And the recursive formula for the chebyshev polynomial of order N is given as
TN(x)= 2xTN-1(x)- TN-2(x)
Thus for a chebyshev filter of order 5, we obtain
T5(x)=2xT4(x)-T3(x)=2x(8x4-8x2+1)-( 4x3-3x )= 16x5-20x3+5x.
7. For |x|≤1, |TN(x)|≤1, and it oscillates between -1 and +1 a number of times proportional to N.
a) True
b) False
Answer
Answer: a [Reason:] For |x|≤1, |TN(x)|≤1, and it oscillates between -1 and +1 a number of times proportional to N.
The above is evident from the equation,
TN(x) = cos(Ncos-1x), |x|≤1.
8. Chebyshev polynomials of odd orders are:
a) Even functions
b) Odd functions
c) Exponential functions
d) Logarithmic functions
Answer
Answer: b [Reason:] Chebyshev polynomials of odd orders are odd functions because they contain only odd powers of x.
9. What is the value of TN(0) for even degree N?
a) -1
b) +1
c) 0
d) ±1
Answer
Answer: d [Reason:] We know that a chebyshev polynomial of degree N is defined as
TN(x) = cos(Ncos-1x), |x|≤1
cosh(Ncosh-1x), |x|>1
For x=0, we have TN(0)=cos(Ncos-10)=cos(N.π/2)=±1 for N even.
10. TN(-x)=(-1)NTN(x)
a) True
b) False
Answer
Answer: a [Reason:] We know that a chebyshev polynomial of degree N is defined as
TN(x) = cos(Ncos-1x), |x|≤1
cosh(Ncosh-1x), |x|>1
=> TN(-x)= cos(Ncos-1(-x))= cos(N(π-cos-1x))= cos(Nπ-Ncos-1x)= (-1)N cos(Ncos-1x)= (-1)NTN(x)
Thus we get, TN(-x)=(-1)NTN(x).
Digital Electronic MCQ Set 4
1. Which of the following is done to convert a continuous time signal into discrete time signal?
a) Modulating
b) Sampling
c) Differentiating
d) Integrating
Answer
Answer: b [Reason:] A discrete time signal can be obtained from a continuous time signal by replacing t by nT, where T is the reciprocal of the sampling rate or time interval between the adjacent values. This procedure is known as sampling.
2. The deflection voltage of an oscilloscope is a ‘deterministic’
signal. True or False?
a) True
b) False
Answer
Answer: a [Reason:] The behavior of the signal is known and can be represented by a saw tooth wave form. So, the signal is deterministic.
3. The even part of a signal x(t) is:
a) x(t)+x(-t)
b) x(t)-x(-t)
c) (1/2)*(x(t)+x(-t))
d) (1/2)*(x(t)-x(-t))
Answer
Answer: c [Reason:] Let x(t)=xe(t)+xo(t)
=>x(-t)=xe(-t)-xo(-t)
By adding the above two equations, we get
xe(t)=(1/2)*(x(t)+x(-t)).
4. Which of the following is the odd component of the signal x(t)=e(jt)?
a) cost
b) j*sint
c) j*cost
d) sint
Answer
Answer: b [Reason:] Let x(t)=e(jt)
Now, xo(t)=(1/2)*(x(t)-x(-t))
=(1/2)*(e(jt) – e(-jt))
=(1/2)*(cost+jsint-cost+jsint)
=(1/2)*(2jsint)
=j*sint.
5. For a continuous time signal x(t) to be periodic with a period T, then x(t+mT) should be equal to:
a) x(-t)
b) x(mT)
c) x(mt)
d) x(t)
Answer
Answer: d [Reason:] If a signal x(t) is said to be periodic with period T, then x(t+mT)=x(t) for all t and any integer m.
6. Let x1(t) and x2(t) be periodic signals with fundamental periods T1 and T2 respectively. Which of the following must be a rational number for x(t)=x1(t)+x2(t) to be periodic?
a) T1+T2
b) T1-T2
c) T1/T2
d) T1*T2
Answer
Answer: c [Reason:] Let T be the period of the signal x(t)
=>x(t+T)=x1(t+mT1)+x2(t+nT2)
Thus, we must have
mT1=nT2=T
=>(T1/T2)=(k/m)= a rational number.
7. Let x1(t) and x2(t) be periodic signals with fundamental periods T1 and T2 respectively. Then the fundamental period of x(t)=x1(t)+x2(t) is:
a) LCM of T1 and T2
b) HCF of T1and T2
c) Product of T1 and T2
d) Ratio of T1 to T2
Answer
Answer: a [Reason:] For the sum of x1(t) and x2(t) to be periodic the ratio of their periods should be a rational number, then the fundamental period is the LCM of T1 and T2.
8. All energy signals will have an average power of:
a) Infinite
b) Zero
c) Positive
d) Cannot be calculated
Answer
Answer: b [Reason:] For any energy signal, the average power should be equal to 0 i.e., P=0.
9. x(t) or x(n) is defined to be an energy signal, if and only if the total energy content of the signal is a:
a) Finite quantity
b) Infinite
c) Zero
d) None of the mentioned
Answer
Answer: a [Reason:] The energy signal should have total energy value that lies between 0 and infinity.
10. What is the period of cos2t+sin3t?
a) pi
b) 2*pi
c) 3*pi
d) 4*pi
Answer
Answer: b [Reason:] Period of cos2t=(2*pi)/2=pi
Period of sin3t=(2*pi)/3
LCM of pi and (2*pi)/3 is 2*pi.
Digital Electronic MCQ Set 5
1. Which of the following parameters are required to calculate the correlation between the signals x(n) and y(n)?
a) Time delay
b) Attenuation factor
c) Noise signal
d) All of the mentioned
Answer
Answer: d [Reason:] Let us consider x(n) be the input reference signal and y(n) be the reflected signal.
Now, the relation between the two signals is given as y(n)=αx(n-D)+w(n)
Where α-attenuation factor representing the signal loss in the round-trip transmission of the signal x(n)
D-time delay between the time of projection of signal and the reflected back signal
w(n)-noise signal generated in the electronic parts in the front end of the receiver.
2. The cross correlation of two real finite energy sequences x(n) and y(n) is given as:
d) None of the mentioned
Answer
Answer: a [Reason:] If any two signals x(n) and y(n) are real and finite energy signals, then the correlation between the two signals is known as cross correlation and its equation is given as
3. Which of the following relation is true?
a) rxy(l)= rxy(-l)
b) rxy(l)= ryx(l)
c) rxy(l)= ryx(-l)
d) None of the mentioned
Answer
Answer: c [Reason:] we know that, the correlation of two signals x(n) and y(n) is 
4. What is the cross correlation sequence of the following sequences?
x(n)={….0,0,2,-1,3,7,1,2,-3,0,0….}
y(n)={….0,0,1,-1,2,-2,4,1,-2,5,0,0….}
a) {10,9,19,36,-14,33,0,7,13,-18,16,7,5,-3}
b) {10,-9,19,36,-14,33,0,7,13,-18,16,-7,5,-3}
c) {10,9,19,36,14,33,0,-7,13,-18,16,-7,5,-3}
d) {10,-9,19,36,-14,33,0,-7,13,18,16,7,5,-3}
Answer
Answer: b [Reason:]
5. Which of the following is the auto correlation of x(n)?
a) rxy(l)=x(l)*x(-l)
b) rxy(l)=x(l)*x(l)
c) rxy(l)=x(l)+x(-l)
d) None of the mentioned
Answer
Answer: a [Reason:] We know that, the correlation of two signals x(n) and y(n) is
Let x(n)=y(n)=> 
6. What is the energy sequence of the signal ax(n)+by(n-l) in terms of cross correlation and auto correlation sequences?
a) a2rxx(0)+b2ryy(0)+2abrxy(0)
b) a2rxx(0)+b2ryy(0)-2abrxy(0)
c) a2rxx(0)+b2ryy(0)+2abrxy(1)
d) a2rxx(0)+b2ryy(0)-2abrxy(1)
Answer
Answer: c [Reason:]
The energy signal of the signal ax(n)+by(n-l) is
7. What is the relation between cross correlation and auto correlation?
a) |rxy(l)|=√(rxx(0).ryy(0))
b) |rxy(l)|≥√(rxx(0).ryy(0))
c) |rxy(l)|≠√(rxx(0).ryy(0))
d) |rxy(l)|≤√(rxx(0).ryy(0))
Answer
Answer: d [Reason:]
We know that, a2rxx(0)+b2ryy(0)+2abrxy(l) ≥0
=> (a/b)2rxx(0)+ryy(0)+2(a/b)rxy(l) ≥0
Since the quadratic is nonnegative, it follows that the discriminate of this quadratic must be non positive, that is 4[r2xy(l)- rxx(0) ryy(0)] ≤0 =>|rxy(l)|≤√(rxx(0).ryy(0)).
8. The normalized auto correlation ρxx(l) is defined as:
a) (rxx (l))/(rxx (0))
b) -(rxx (l))/(rxx (0))
c) (rxx (l))/(rxy (0))
d) None of the mentioned
Answer
Answer: a [Reason:] If the signal involved in auto correlation is scaled, the shape of auto correlation does not change, only the amplitudes of auto correlation sequence are scaled accordingly. Since scaling is unimportant, it is often desirable, in practice, to normalize the auto correlation sequence to the range from -1 to 1. In the case of auto correlation sequence, we can simply divide by rxx (0). Thus the normalized auto correlation sequence is defined as ρxx(l)= (rxx (l))/(rxx (0)).
9. Auto correlation sequence is an even function.
a) True
b) False
Answer
Answer: a [Reason:] Let us consider a signal x(n) whose auto correlation is defined as rxx (l).
We know that, for auto correlation sequence rxx (l)=rxx (-l).
So, auto correlation sequence is an even sequence.
10. What is the auto correlation of the sequence x(n)=anu(n), 0<a<l?
a) 1/(1-a2 )al (l≥0)
b) 1/(1-a2 )a-l (l<0)
c) 1/(1-a2 )a|l|(-∞<l<∞)
d) All of the mentioned
Answer
Answer: d [Reason:]
11. Which of the following relation is true?
a) ryx(l)=h(l)*ryy(l)
b) rxy(l)=h(l)*rxx(l)
c) ryx(l)=h(l)*rxx(l)
d) None of the mentioned
Answer
Answer: c [Reason:] Let x(n) be the input signal and y(n) be the output signal with impulse response h(n).
We know that 
The cross correlation between the input signal and output signal is
ryx(l)=y(l)*x(-l)=h(l)*[x(l)*x(-l)]= h(l)*rxx(l).
12. If x(n) is the input signal of a system with impulse response h(n) and y(n) is the output signal, then the auto correlation of the signal y(n) is:
a) rxx(l)*rhh(l)
b) rhh(l)*rxx(l)
c) rxy(l)*rhh(l)
d) ryx(l)*rhh(l)
Answer
Answer: b [Reason:] ryy(l)=y(l)*y(-l)
=[h(l)*x(l)]*[h(-l)*x(-l)]
=[h(l)*h(-l)]*[x(l)*x(-l)]
=rhh(l)*rxx(l).
