Assertion (A): The z-transform of the output of the sampler is given by the series.Reason (R): The relationship is the result of the application of z = e-sT, where T stands for the time gap between the samples.

Both A and R are true and R is correct explanation of A

Both A and R are true but R is not correct explanation of A

The signal is reconstructed back with the help of

Signal is reconstructed with zero order holds and extrapolations

Assertion (A): An LTI discrete system represented by the difference equation. y (n+2)-5y(n+1)+6y(n) =x(n) is unstable.Reason (R): A system is unstable if the roots of the characteristic equation lie outside the unit circle.

Both A and R are true but R is NOT the correct explanation of A

Both A and R are true and R is the correct explanation of A

Both A and R are true but R is NOT the correct explanation of A

First column elements of the Routh's tabulation are 3, 5, -3/4, ½, 2. It means that there are:

Is one root in the right half of s-plane

Is one root in the left half of s-plane

Are two roots in the left half of s-plane

Are two roots in the right half of the s-plane

Is one root in the right half of s-plane

An LTI system having transfer function s2+1/s2+2s+1 and input x(t) =sin(t+1) is in steady state. The output is sampled at ws rad/s to obtain the final output {y (k)}. Which of the following is true?

Y is non zero for all sampling frequencies ws

Y is zero for all sampling frequencies ws

Y is non zero for all sampling frequencies ws

Y is non zero for ws>2 but zero for ws

Y is zero for ws>2 but non zero for ws

Assertion (A): The discrete time system described by y[n] =2x[n] +4x[n-1] is unstableReason (R): It has an impulse response with a finite number of non-zero samples

Both A and R are true and R is correct explanation of A

Both A and R are true but R is not correct explanation of A

For the successful reconstruction of signals :

Sampling frequency must be equal to the message signal

Sampling frequency must be greater to the message signal

Sampling frequency must be less to the message signal

Sampling frequency must be greater than or equal to the message signal

Assertion (A): For the rational transfer function H(z) to be causal, stable and causally invertible, both the zeroes and the poles should lie within the unit circle in the z-plane.Reason (R): For a rational system, ROC is bounded by poles

Both A and R are true and R is the correct explanation of A

Both A and R are true bit R is NOT the correct explanation of A

The continuous time system described by 2 y(t) = x (t2) is

Causal, linear and time varying

Causal, non-linear and time varying

Non causal, non-linear and time-invariant

Non causal, linear and time-invariant

H (z) is discrete rational transfer function. To ensure that both H(z) and its inverse are stable:

Poles and zeroes must be outside the unit circle

Poles must be inside the unit circle and zeros must be outside the unit circle

Poles and zeroes must be inside the unit circle

Poles and zeroes must be outside the unit circle

Poles must be outside the unit circle and zeros must be inside the unit circle

Assertion (A): The signals anu(n) and anu(-n-1) have the same Z transform, z/(z-

Reason (R): the region of convergence of anu(n) is |z|>|a|, whereas the ROC for anu(-n-1) is |z|

Both A and R are true but R is not correct explanation of A

Assertion (A): The system functionH(z) = z3-2z2+z/z2+1/4z+1/s is not causalReason (R): If the numerator of H (z) is of lower order than the denominator, the system may be causal.

Both A and R are true and R is not correct Explanation of A

Both A and R are true and R is correct explanation of A

Both A and R are true and R is not correct Explanation of A

Assertion (A): The stability of the system is assured if the ROC includes the unit circle in z-plane.Reason (R): For a causal stable system all the poles should be outside the unit circle in the z-plane.

Both A and R are true and R is the correct explanation of A

Both A and R are true bit R is NOT the correct explanation of A

Assertion (A): Feedback control system offer more accurate control over open-loop systems.Reason (R): The feedback path establishes a link for input and output comparison and subsequent error correction.

Both A and R are true and R is not correct Explanation of A

Both A and R are true and R is correct explanation of A

Both A and R are true and R is not correct Explanation of A

Aliasing is caused when:

Sampling frequency must be greater than or equal to the message signal

Sampling frequency must be equal to the message signal

Sampling frequency must be greater to the message signal

Sampling frequency must be less to the message signal

Sampling frequency must be greater than or equal to the message signal

Statement (I): Aliasing occurs when the sampling frequency is less than twice the maximum frequency in the signal.Statement (II): Aliasing is a reversible process.

Statement (I) is False but Statement (II) is true

Both statement (I) and Statement (II) are individually true and Statement (II) is the correct explanation of Statement (I).

Both Statement (I) and Statement (II) are individually true but Statement (II) is not correct explanation of Statement (I)

Statement (I) is true but Statement (II) is false

Statement (I) is False but Statement (II) is true

The given characteristic equation s4+s3+2s2+2s+3=0 has:

Three root in the RHS of s-plane

If a periodic function f(t) of period T satisfies f(t) = −f (t + T/2) , then in its Fourier series expansion

There will be no even harmonics

Assertion (A): Z-transform is used to analyze discrete time systems and it is also called pulsed transfer function approach.Reason(R): The sampled signal is assumed to be a train of impulses whose strengths, or areas, are equal to the continuous time signal at the sampling instants.

Both A and R are true and R is not correct Explanation of A

Both A and R are true and R is correct explanation of A

Both A and R are true and R is not correct Explanation of A

Assertion (A): Practical systems must be closed loop system.Reason (R): This is due to the fact that closed loop systems are least affected by parameter variations, stable, higher bandwidth, linear and more speed of response.

Both A and R are true but R is not the correct explanation of A.

Both A and R are true and R is the correct explanation of A.

Both A and R are true but R is not the correct explanation of A.

Assertion (A): The closed loop stability can be determined from the poles of an open loop system and the polar plot of the frequency response.Reason (R): Unstable system has right half poles.

Both A and R are true and R is correct explanation of A

Both A and R are true and R is not correct Explanation of A

59 + Mcqs in Digital Control Systems in Control Systems Page 1 McqOptions

1.	Unit step response of the system described by the equation y(n) +y(n-1) =x(n) is:
A.	z2/(z+1)(z-1)
B.	z/(z+1)(z-1)
C.	z+1/z-1
D.	z(z-1)/z+1
Answer» B. z/(z+1)(z-1)

Discussion

2.	The Fourier Transform of a rectangular pulse is
A.	Another rectangular pulse
B.	Triangular pulse
C.	Sinc function
D.	Impulse
Answer» D. Impulse

Discussion

3.	The following characteristic equation results in stable operation of the feedback system s3+4s2+10s+11=0
A.	True
B.	False
Answer» B. False

Discussion

4.	Assertion (A): The z-transform of the output of the sampler is given by the series.Reason (R): The relationship is the result of the application of z = e-sT, where T stands for the time gap between the samples.
A.	Both A and R are true and R is correct explanation of A
B.	Both A and R are true but R is not correct explanation of A
C.	A is true but R is false
D.	A is false but R is true
Answer» D. A is false but R is true

Discussion

5.	The signal is reconstructed back with the help of
A.	Zero order hold circuits
B.	Extrapolations
C.	Signal is reconstructed with zero order holds and extrapolations
D.	Signal is not reconstructed
Answer» D. Signal is not reconstructed

Discussion

6.	Assertion (A): An LTI discrete system represented by the difference equation. y (n+2)-5y(n+1)+6y(n) =x(n) is unstable.Reason (R): A system is unstable if the roots of the characteristic equation lie outside the unit circle.
A.	Both A and R are true and R is the correct explanation of A
B.	Both A and R are true but R is NOT the correct explanation of A
C.	A is true but R is false
D.	A is false but R is false
Answer» B. Both A and R are true but R is NOT the correct explanation of A

Discussion

7.	First column elements of the Routh's tabulation are 3, 5, -3/4, ½, 2. It means that there are:
A.	Is one root in the left half of s-plane
B.	Are two roots in the left half of s-plane
C.	Are two roots in the right half of the s-plane
D.	Is one root in the right half of s-plane
Answer» D. Is one root in the right half of s-plane

Discussion

8.	An LTI system having transfer function s2+1/s2+2s+1 and input x(t) =sin(t+1) is in steady state. The output is sampled at ws rad/s to obtain the final output {y (k)}. Which of the following is true?
A.	Y is zero for all sampling frequencies ws
B.	Y is non zero for all sampling frequencies ws
C.	Y is non zero for ws>2 but zero for ws<2
D.	Y is zero for ws>2 but non zero for ws<2
Answer» B. Y is non zero for all sampling frequencies ws

Discussion

9.	Assertion (A): The discrete time system described by y[n] =2x[n] +4x[n-1] is unstableReason (R): It has an impulse response with a finite number of non-zero samples
A.	Both A and R are true and R is correct explanation of A
B.	Both A and R are true but R is not correct explanation of A
C.	A is true but R is false
D.	A is false but R is true
Answer» E.

Discussion

10.	For the successful reconstruction of signals :
A.	Sampling frequency must be equal to the message signal
B.	Sampling frequency must be greater to the message signal
C.	Sampling frequency must be less to the message signal
D.	Sampling frequency must be greater than or equal to the message signal
Answer» E.

Discussion

11.	A sequence x (n) with the z-transform X (z) = Z4 + Z2 – 2z + 2 – 3Z-4 is applied to an input to a linear time invariant system with the impulse response h (n) = 2δ (n-3). The output at n = 4 will be:
A.	-6
B.	Zero
C.	2
D.	-4
Answer» C. 2

Discussion

12.	For what values of K does the polynomial s4+8s3+24s2+32s+K=0 have roots with zero real parts?
A.	10
B.	20
C.	40
D.	80
Answer» E.

Discussion

13.	How many roots with positive real parts do the equation s3+s2-s+1=0 have?
A.	0
B.	1
C.	2
D.	3
Answer» D. 3

Discussion

14.	Assertion (A): For the rational transfer function H(z) to be causal, stable and causally invertible, both the zeroes and the poles should lie within the unit circle in the z-plane.Reason (R): For a rational system, ROC is bounded by poles
A.	Both A and R are true and R is the correct explanation of A
B.	Both A and R are true bit R is NOT the correct explanation of A
C.	A is true but R is false
D.	A is false but R is true
Answer» C. A is true but R is false

Discussion

15.	The continuous time system described by 2 y(t) = x (t2) is
A.	Causal, linear and time varying
B.	Causal, non-linear and time varying
C.	Non causal, non-linear and time-invariant
D.	Non causal, linear and time-invariant
Answer» E.

Discussion

16.	A system can be represented in the form of state equations as:S (n+1) =A S (n) +B x (n)Y (n) = C S (n) +D x (n)Where, A, B, C, D are the matrices , S(n) is the state vector , x(n) is the input and y(n) is the output . The transfer function of the system.H (z) =Y (z)/X (z) is given by:
A.	A(ZI – B)-1 C + D
B.	B(ZI – C)-1 D + A
C.	C(ZI – A)-1 B + D
D.	D(ZI – A)-1 C + B
Answer» D. D(ZI – A)-1 C + B

Discussion

17.	H (z) is discrete rational transfer function. To ensure that both H(z) and its inverse are stable:
A.	Poles must be inside the unit circle and zeros must be outside the unit circle
B.	Poles and zeroes must be inside the unit circle
C.	Poles and zeroes must be outside the unit circle
D.	Poles must be outside the unit circle and zeros must be inside the unit circle
Answer» C. Poles and zeroes must be outside the unit circle

Discussion

18.	Assertion (A): The signals anu(n) and anu(-n-1) have the same Z transform, z/(z-
A.	Reason (R): the region of convergence of anu(n) is \|z\|>\|a\|, whereas the ROC for anu(-n-1) is \|z\|<\|a\|.a) Both A and R are true and R is correct explanation of A
B.	Both A and R are true but R is not correct explanation of A
C.	A is true but R is false
D.	A is false but R is true
Answer» E.

Discussion

19.	Two sequences x1 (n) and x2 (n) are related by x2 (n) = x1 (- n). In the z- domain, their ROC's are
A.	The same
B.	Reciprocal of each other
C.	Negative of each other
D.	Complements of each other
Answer» C. Negative of each other

Discussion

20.	The open loop control transfer function of a unity feedback system is given by :G(s) =K/(s+2)(s+4)(s^2+6s+25)Which is the value of K which causes sustained oscillations in the closed loop system?
A.	590
B.	790
C.	990
D.	1190
Answer» B. 790

Discussion

21.	The characteristic equation of a control system is given by s6+2s5+8s4+12s3+20s2+16s+16=0 . The number of the roots of the equation which lie on the imaginary axis of s-plane:
A.	0
B.	2
C.	4
D.	6
Answer» D. 6

Discussion

22.	Assertion (A): The system functionH(z) = z3-2z2+z/z2+1/4z+1/s is not causalReason (R): If the numerator of H (z) is of lower order than the denominator, the system may be causal.
A.	Both A and R are true and R is correct explanation of A
B.	Both A and R are true and R is not correct Explanation of A
C.	A is True and R is false
D.	A is False and R is true
Answer» B. Both A and R are true and R is not correct Explanation of A

Discussion

23.	Assertion (A): The stability of the system is assured if the ROC includes the unit circle in z-plane.Reason (R): For a causal stable system all the poles should be outside the unit circle in the z-plane.
A.	Both A and R are true and R is the correct explanation of A
B.	Both A and R are true bit R is NOT the correct explanation of A
C.	A is true but R is false
D.	A is false but R is true
Answer» D. A is false but R is true

Discussion

24.	The probability cumulative distribution function must be monotone and
A.	Increasing
B.	Decreasing
C.	Non-increasing
D.	Non-decreasing
Answer» E.

Discussion

25.	Assertion (A): Feedback control system offer more accurate control over open-loop systems.Reason (R): The feedback path establishes a link for input and output comparison and subsequent error correction.
A.	Both A and R are true and R is correct explanation of A
B.	Both A and R are true and R is not correct Explanation of A
C.	A is True and R is false
D.	A is False and R is true
Answer» B. Both A and R are true and R is not correct Explanation of A

Discussion

26.	A signal represented by x(t) =5cos 400πt is sampled at a rate 300 samples/sec. The resulting samples are passed through an ideal low pass filter of cut-off frequency 150 Hz. Which of the following will be contained in the output of the LPF?
A.	100 Hz
B.	100 Hz, 150 Hz
C.	50 Hz, 100 Hz
D.	50 Hz, 100 Hz, 150 Hz
Answer» B. 100 Hz, 150 Hz

Discussion

27.	Aliasing is caused when:
A.	Sampling frequency must be equal to the message signal
B.	Sampling frequency must be greater to the message signal
C.	Sampling frequency must be less to the message signal
D.	Sampling frequency must be greater than or equal to the message signal
Answer» D. Sampling frequency must be greater than or equal to the message signal

Discussion

28.	Convolution of two sequences X1[n] and X2[n] are represented by:
A.	X1(z)*X2(z)
B.	X1(z)X2(z)
C.	X1(z)+X2(z)
D.	X1(z)/X2(z)
Answer» B. X1(z)X2(z)

Discussion

29.	Statement (I): Aliasing occurs when the sampling frequency is less than twice the maximum frequency in the signal.Statement (II): Aliasing is a reversible process.
A.	Both statement (I) and Statement (II) are individually true and Statement (II) is the correct explanation of Statement (I).
B.	Both Statement (I) and Statement (II) are individually true but Statement (II) is not correct explanation of Statement (I)
C.	Statement (I) is true but Statement (II) is false
D.	Statement (I) is False but Statement (II) is true
Answer» D. Statement (I) is False but Statement (II) is true

Discussion

30.	Consider the following statements regarding a linear discrete-time system:H (z) = z2+1/(z+0.5)(z-0.5)1. The system is stable2. The initial value of h(0) of the impulse response is -43. The steady-state output is zero for a sinusoidal discrete time input of frequency equal to one-fourth the sampling frequencyWhich of these statements are correct?
A.	1,2 and 3
B.	1 and 2
C.	1 and 3
D.	2 and 3
Answer» D. 2 and 3

Discussion

31.	What is the number of roots of the polynomial F(z) = 4z3-8z2-z+2, lying outside the unit circle?
A.	0
B.	1
C.	2
D.	3
Answer» C. 2

Discussion

32.	In closed loop control system, what is the sensitivity of the gain of the overall system, M to the variation in G?
A.	1/1+GH
B.	1/1+G
C.	G/1GH
D.	G/1+G
Answer» B. 1/1+G

Discussion

33.	What is the z-transform of the signal x[n] = anu(n)?
A.	X(z) =1/z-1
B.	X(z) = 1/1-z
C.	X(z) = z/z-a
D.	X(z) = 1/z-a
Answer» D. X(z) = 1/z-a

Discussion

34.	Region of convergence of a causal LTI system
A.	Is the entire s-plane
B.	Is the right-half of s-plane
C.	Is the left-half of s-plane
D.	Does not exist
Answer» C. Is the left-half of s-plane

Discussion

35.	Z and Laplace transform are related by:
A.	s = ln z
B.	s =ln z/T
C.	s =z
D.	s= T/ln z
Answer» C. s =z

Discussion

36.	The characteristic equation of the control system is s5+15s4+85s3+225s2+274s+120=0 . What are the number of roots of the equation which lie to the left of the line s+1 = 0?
A.	2
B.	3
C.	4
D.	5
Answer» D. 5

Discussion

37.	The frequency of a continuous time signal x (t) changes on transformation from x (t) to x (α t), α > 0 by a factor
A.	α
B.	1/α
C.	α2
D.	α
Answer» B. 1/α

Discussion

38.	A digital measuring instrument employs a sampling rate of 100 samples/second. The sampled input x(n) is averaged using the difference equation:Y (n) =[x (n)+x (n-1)+x(n-2)+x(n-4)/4]For a step input, the maximum time taken for the output to reach the final value after the input transition is
A.	20 ms
B.	40 ms
C.	80 ms
D.	∞
Answer» C. 80 ms

Discussion

39.	The FT of a rectangular pulse existing between t = − T 2/ to t = T / 2 is a
A.	Sinc squared function
B.	Sinc function
C.	Sine squared function
D.	Sine function
Answer» C. Sine squared function

Discussion

40.	The minimum number of delay elements required realizing a digital filter with transfer functionH (z) =
A.	2
B.	3
C.	4
D.	5
Answer» C. 4

Discussion

41.	The given characteristic equation s4+s3+2s2+2s+3=0 has:
A.	Zero root in the s-plane
B.	One root in the RHS of s-plane
C.	Two root in the RHS of s-plane
D.	Three root in the RHS of s-plane
Answer» D. Three root in the RHS of s-plane

Discussion

42.	If a periodic function f(t) of period T satisfies f(t) = −f (t + T/2) , then in its Fourier series expansion
A.	The constant term will be zero
B.	There will be no cosine terms
C.	There will be no sine terms
D.	There will be no even harmonics
Answer» C. There will be no sine terms

Discussion

43.	Consider the following statements:Routh-Hurwitz criterion gives:1. Absolute stability2. The number of roots lying on the right half of the s-plane3. The gain margin and the phase margin
A.	1,2 and3
B.	1 and 2
C.	2 and 3
D.	1 and 3
Answer» C. 2 and 3

Discussion

44.	Assertion (A): Z-transform is used to analyze discrete time systems and it is also called pulsed transfer function approach.Reason(R): The sampled signal is assumed to be a train of impulses whose strengths, or areas, are equal to the continuous time signal at the sampling instants.
A.	Both A and R are true and R is correct explanation of A
B.	Both A and R are true and R is not correct Explanation of A
C.	A is True and R is false
D.	A is False and R is true
Answer» B. Both A and R are true and R is not correct Explanation of A

Discussion

45.	Regenerative feedback implies feedback with
A.	Oscillations
B.	Step input
C.	Negative sign
D.	Positive sign
Answer» E.

Discussion

46.	The discrete-time signal x (n) = (-1)n is periodic with fundamental period
A.	6
B.	4
C.	2
D.	0
Answer» D. 0

Discussion

47.	Assertion (A): Practical systems must be closed loop system.Reason (R): This is due to the fact that closed loop systems are least affected by parameter variations, stable, higher bandwidth, linear and more speed of response.
A.	Both A and R are true and R is the correct explanation of A.
B.	Both A and R are true but R is not the correct explanation of A.
C.	A is true but R is false.
D.	A is false but R is true.
Answer» B. Both A and R are true but R is not the correct explanation of A.

Discussion

48.	Assertion (A): The closed loop stability can be determined from the poles of an open loop system and the polar plot of the frequency response.Reason (R): Unstable system has right half poles.
A.	Both A and R are true and R is correct explanation of A
B.	Both A and R are true and R is not correct Explanation of A
C.	A is True and R is false
D.	A is False and R is true
Answer» C. A is True and R is false

Discussion

49.	Phase margin is always positive for stable feedback system?
A.	True
B.	False
Answer» B. False

Discussion

50.	Z-transform converts convolution of time-signals to
A.	Addition
B.	Subtraction
C.	Multiplication
D.	Division
Answer» D. Division

Discussion

Explore topic-wise MCQs in Control Systems.

Unit step response of the system described by the equation y(n) +y(n-1) =x(n) is:

The Fourier Transform of a rectangular pulse is

The following characteristic equation results in stable operation of the feedback system s3+4s2+10s+11=0

Assertion (A): The z-transform of the output of the sampler is given by the series.Reason (R): The relationship is the result of the application of z = e-sT, where T stands for the time gap between the samples.

The signal is reconstructed back with the help of

Assertion (A): An LTI discrete system represented by the difference equation. y (n+2)-5y(n+1)+6y(n) =x(n) is unstable.Reason (R): A system is unstable if the roots of the characteristic equation lie outside the unit circle.

First column elements of the Routh's tabulation are 3, 5, -3/4, ½, 2. It means that there are:

An LTI system having transfer function s2+1/s2+2s+1 and input x(t) =sin(t+1) is in steady state. The output is sampled at ws rad/s to obtain the final output {y (k)}. Which of the following is true?

Assertion (A): The discrete time system described by y[n] =2x[n] +4x[n-1] is unstableReason (R): It has an impulse response with a finite number of non-zero samples

For the successful reconstruction of signals :

A sequence x (n) with the z-transform X (z) = Z4 + Z2 – 2z + 2 – 3Z-4 is applied to an input to a linear time invariant system with the impulse response h (n) = 2δ (n-3). The output at n = 4 will be:

For what values of K does the polynomial s4+8s3+24s2+32s+K=0 have roots with zero real parts?

How many roots with positive real parts do the equation s3+s2-s+1=0 have?

Assertion (A): For the rational transfer function H(z) to be causal, stable and causally invertible, both the zeroes and the poles should lie within the unit circle in the z-plane.Reason (R): For a rational system, ROC is bounded by poles

The continuous time system described by 2 y(t) = x (t2) is

A system can be represented in the form of state equations as:S (n+1) =A S (n) +B x (n)Y (n) = C S (n) +D x (n)Where, A, B, C, D are the matrices , S(n) is the state vector , x(n) is the input and y(n) is the output . The transfer function of the system.H (z) =Y (z)/X (z) is given by:

H (z) is discrete rational transfer function. To ensure that both H(z) and its inverse are stable:

Assertion (A): The signals anu(n) and anu(-n-1) have the same Z transform, z/(z-

Two sequences x1 (n) and x2 (n) are related by x2 (n) = x1 (- n). In the z- domain, their ROC's are

The open loop control transfer function of a unity feedback system is given by :G(s) =K/(s+2)(s+4)(s^2+6s+25)Which is the value of K which causes sustained oscillations in the closed loop system?

The characteristic equation of a control system is given by s6+2s5+8s4+12s3+20s2+16s+16=0 . The number of the roots of the equation which lie on the imaginary axis of s-plane:

Assertion (A): The system functionH(z) = z3-2z2+z/z2+1/4z+1/s is not causalReason (R): If the numerator of H (z) is of lower order than the denominator, the system may be causal.

Assertion (A): The stability of the system is assured if the ROC includes the unit circle in z-plane.Reason (R): For a causal stable system all the poles should be outside the unit circle in the z-plane.

The probability cumulative distribution function must be monotone and

Assertion (A): Feedback control system offer more accurate control over open-loop systems.Reason (R): The feedback path establishes a link for input and output comparison and subsequent error correction.

A signal represented by x(t) =5cos 400πt is sampled at a rate 300 samples/sec. The resulting samples are passed through an ideal low pass filter of cut-off frequency 150 Hz. Which of the following will be contained in the output of the LPF?

Aliasing is caused when:

Convolution of two sequences X1[n] and X2[n] are represented by:

Statement (I): Aliasing occurs when the sampling frequency is less than twice the maximum frequency in the signal.Statement (II): Aliasing is a reversible process.

What is the number of roots of the polynomial F(z) = 4z3-8z2-z+2, lying outside the unit circle?

In closed loop control system, what is the sensitivity of the gain of the overall system, M to the variation in G?

What is the z-transform of the signal x[n] = anu(n)?

Region of convergence of a causal LTI system

Z and Laplace transform are related by:

The characteristic equation of the control system is s5+15s4+85s3+225s2+274s+120=0 . What are the number of roots of the equation which lie to the left of the line s+1 = 0?

The frequency of a continuous time signal x (t) changes on transformation from x (t) to x (α t), α > 0 by a factor

A digital measuring instrument employs a sampling rate of 100 samples/second. The sampled input x(n) is averaged using the difference equation:Y (n) =[x (n)+x (n-1)+x(n-2)+x(n-4)/4]For a step input, the maximum time taken for the output to reach the final value after the input transition is

The FT of a rectangular pulse existing between t = − T 2/ to t = T / 2 is a

The minimum number of delay elements required realizing a digital filter with transfer functionH (z) =

The given characteristic equation s4+s3+2s2+2s+3=0 has:

If a periodic function f(t) of period T satisfies f(t) = −f (t + T/2) , then in its Fourier series expansion

Consider the following statements:Routh-Hurwitz criterion gives:1. Absolute stability2. The number of roots lying on the right half of the s-plane3. The gain margin and the phase margin

Assertion (A): Z-transform is used to analyze discrete time systems and it is also called pulsed transfer function approach.Reason(R): The sampled signal is assumed to be a train of impulses whose strengths, or areas, are equal to the continuous time signal at the sampling instants.

Regenerative feedback implies feedback with

The discrete-time signal x (n) = (-1)n is periodic with fundamental period

Assertion (A): Practical systems must be closed loop system.Reason (R): This is due to the fact that closed loop systems are least affected by parameter variations, stable, higher bandwidth, linear and more speed of response.

Assertion (A): The closed loop stability can be determined from the poles of an open loop system and the polar plot of the frequency response.Reason (R): Unstable system has right half poles.

Phase margin is always positive for stable feedback system?

Z-transform converts convolution of time-signals to