Signal & System UNIT I MCQ PDF

Preview

Summary

Organisational Behavior Multiple Choice Questions...

Description

1. The type of systems which are characterized by input and the output quantized at certain levels are called as a) analog b) discrete c) continuous d) digital View Answer Answer: b Explanation: Discrete systems have their input and output values restricted to enter some quantised/discretized levels. 2. The type of systems which are characterized by input and the output capable of taking any value in a particular set of values are called as a) analog b) discrete c) digital d) continuous View Answer Answer: d Explanation: Continuous systems have a restriction on the basis of the upper bound and lower bound, but within this set, the input and output can assume any value. Thus, there are infinite values attainable in this system 3. An example of a discrete set of information/system is a) the trajectory of the Sun b) data on a CD c) universe time scale d) movement of water through a pipe View Answer Answer: b Explanation: The rest of the parameters are continuous in nature. Data is stored in the form of discretized bits on CDs.

4. A system which is linear is said to obey the rules of a) scaling b) additivity c) both scaling and additivity d) homogeneity View Answer 5. A time invariant system is a system whose output a) increases with a delay in input b) decreases with a delay in input c) remains same with a delay in input d) vanishes with a delay in input View Answer Answer: c Explanation: A time invariant system’s output should be directly related to the time of the output. There should be no scaling, i.e. y(t) = f(x(t)). 6. Should real time instruments like oscilloscopes be time invariant? a) Yes b) Sometimes c) Never d) They have no relation with time variance View Answer Answer: a Explanation: Oscilloscopes should be time invariant, i.e they should work the same way everyday, and the output should not change with the time at which it is operated. 7. All real time systems concerned with the concept of causality are a) non causal b) causal c) neither causal nor non causal

d) memoryless View Answer Answer: b Explanation: All real time systems are causal, since they cannot have perception of the future, and only depend on their memory. 8. A system is said to be defined as non causal, when a) the output at the present depends on the input at an earlier time b) the output at the present does not depend on the factor of time at all c) the output at the present depends on the input at the current time d) the output at the present depends on the input at a time instant in the future View Answer Answer: d Explanation: A non causal system’s output is said to depend on the input at a time in the future. 9. When we take up design of systems, ideally how do we define the stability of a system? a) A system is stable, if a bounded input gives a bounded output, for some values of the input b) A system is unstable, if a bounded input gives a bounded output, for all values of the input c) A system is stable, if a bounded input gives a bounded output, for all values of the input d) A system is unstable, if a bounded input gives a bounded output, for some values of the input View Answer Answer: c Explanation: For designing a system, it should be kept in mind that the system does not blow out for a finite input. Thus, every finite input should give a finite output.

10. All causal systems must have the component of a) memory b) time invariance c) stability d) linearity View Answer Answer: a Explanation: Causal systems depend on the functional value at an earlier time, compelling the system to possess memory.

11. Amplifiers, motors, filters etc. are examples for which type of system? a) Distributed parameter systems b) Unstable systems c) Discrete time systems d) Continuous time systems View Answer Answer: d Explanation: Amplifiers, motors, filters etc. are examples of continuous time systems as these systems operate on a continuous time input signal and produce a continuous time output signal. Whereas discrete time systems operate on discrete time signals, distributed parameter systems have signals which are functions of space as well as time and unstable systems produce unbounded output from bounded or unbounded input. 12. Which among the following systems are described by partial differential functions? a) Causal Systems and Dynamic systems b) Distributed parameter systems and linear systems c) Distributed parameter systems and Dynamic systems d) Causal systems and linear systems View Answer

Answer: c Explanation: In distributed parameter systems, signals are functions of space as well as time. In dynamic systems the output depends on past, present and future values of input, hence, both of these systems are described by differential functions. 13. Which one of the following systems is causal? a) y(t)=x(t)+x(t-3)+x(t2) b) y(n)=x(n+2) c) y(t)=x(t-1)+x(t-2) d) y(n)=x(2n2) View Answer Answer: c Explanation: A causal system is one in which the output depends on the present or past values of the input, not future. If it depends on future values then it is noncausal. For y(t)=x(t)+x(t-3)+x(t2), y(n)=x(n+2), and y(n)=x(2n2), the output depends on future values i.e., x (t2), x (n + 2) and x (2n2) respectively. Whereas in y(t)=x(t1)+x(t-2), the output y(t) depends on past values only i.e., x(t – 1) and x(t – 2). 14. Which among the following is not a linear system?

View Answer

Answer: a Explanation: Here is the Explanation.

15. a) Static, linear, causal and time variant b) Dynamic, non – linear, causal and time invariant c) Static, non – linear, causal and time variant d) Dynamic, non – linear, causal and time variant View Answer

Answer: b Explanation: Here is the Explanation.

16. Which one of the following is an example of a bounded signal? a) et coswt b) et sinw(-t) c) e-t coswt d) et cosw(-t) View Answer Answer: c Explanation: A bounded signal is the one which satisfies the condition |x(t)|< M < ∞ for all t. Clearly, the signals et coswt, et sinw(-t) and et cosw(-t) are exponentially growing signals as the power of the function is positive i.e., the signals will grow beyond infinity. Whereas the signal e-t coswt is an exponentially decaying signal, hence it will decay to zero and will always be less than infinity. Therefore, it is bounded. 17. A system produces zero output for one input and same gives the same output for several other inputs. What is the system called? a) Non – invertible System b) Invertible system c) Non – causal system

d) Causal system View Answer Answer: a Explanation: A system is said to be invertible if the input fed to the system can be retrieved from the output of the system. Otherwise the system is non-invertible. Also, if a system gives zero output for any input and gives the same output for many inputs, then the system is non-invertible. 18. Which among the following is a LTI system? a) dy(t)/dt+ty(t)=x(t) b) y(t)=x(t)cosπt c) y(n)=x(n)+nx(n-1) d) y(n)=x3 (n+1) View Answer Answer: d Explanation: A system is said to be linear time invariant (LTI) if the input-output characteristics do not change with time. This expression has a coefficient which is a function of time. ∴ the system is time variant. Output when input is delayed by T, y(t,T)=x(t-T)cosπt If the output is delayed by T, y(t-T)=x(t-T)cosπ(t-T) Clearly, both expressions are not equal ∴ The system is time variant. Output when input is delayed by N, y(n,N)=x(n-N)+nx(n-1-N) If the output is delayed by N, y(n-N)=x(n-N)+(n-N)x(n-1-N) Clearly, both expressions are not equal ∴ The system is time variant. Output when input is delayed by N, y(n,N)=x3 (n+1-N) If the output is delayed by N, y(n-N)= x3 (n+1-N) Clearly, both expressions are equal. ∴ The system is time invariant.

19. What is single-valued function? a) Single value for all instants of time b) Unique value for every instant of time c) A single pattern is followed by after ‘t’ intervals d) Different pattern of values is followed by after ‘t’ intervals of time View Answer Answer: b Explanation: Single-valued function means “for every instant of time there exists unique value of the function”. 20. In real valued function and complex valued function, time is _______________ a) Real b) Complex c) Imaginary d) Not predictable View Answer Answer: a Explanation: Time is an independent variable and it is real valued irrespective of real valued or complex valued function. And time is always real. 21. Discrete time signal is derived from continuous time signal by _____________ process. a) Addition b) Multiplying c) Sampling d) Addition and multiplication View Answer Answer: c Explanation: Sampling is a process wherein continuous time signal is converted to its equivalent discrete time signal. It is given by t = N*t.

22. Even signals are symmetric about the vertical axis. a) True b) False View Answer Answer: a Explanation: Signals are classified as even if it has symmetry about its vertical axis. It is given by the equation x (-t) = x (t). 23. If x (-t) = -x (t) then the signal is said to be _____________ a) Even signal b) Odd signal c) Periodic signal d) Non periodic signal View Answer Answer: a Explanation: Signals is said to be odd if it is anti- symmetry over the time origin. And it is given by the equation x (-t) = -x (t). 24. Which of the following is true for complex-valued function? a) X (-t) = x*(t) b) X (-t) = x(t) c) X (-t) = – x(t) d) X (-t) = x*(-t) View Answer Answer: a Explanation: Complex-valued function is said to be conjugate symmetry if its real part is even and imaginary part is odd and it is shown by the equation x(-t) = x*(t). 25. When x(t ) is said to be non periodic signal? a) If the equation x (t) = x (t + T) is satisfied for all values of T b) If the equation x (t) = x (t + T) is satisfied for only one value of T c) If the equation x (t) = x (t + T) is satisfied for no values of T

d) If the equation x (t) = x (t + T) is satisfied for only odd values of T View Answer 26. Fundamental frequency x[n] is given by ___________ a) Omega = 2*pi /N b) Omega = 2*pi*N c) Omega = 4*pi *2N d) Omega = pi / N View Answer Answer: a Explanation: Fundamental frequency is the smallest value of N which satisfies the equation Omega = 2*pi/ N, Where N is a positive integer. 27. Noise generated by an amplifier of radio is an example for? a) Discrete signal b) Deterministic signal c) Random signal d) Periodic signal View Answer Answer: c Explanation: Random signal is the one which there is uncertainty before its actual occurrence. Noise is a best example for random signal.

28. What is the fundamental frequency of discrete –time wave shown in fig a? a) π/6 b) π/3 c) 2π/8 d) π View Answer

Answer: b Explanation: Omega = 2* π / N. In the given example the number of samples in one period is N = 6. By substituting the value of N =6 in the above equation then we get fundamental frequency as π/3.

29. Which one of the following is an example of a system with memory? a) Identity System b) Resistor c) y(n)=x(n)-2x(n) d) Accumulator View Answer Answer: d Explanation: An identity system gives the output same as input hence it totally depends on the present state of the input. Therefore, it is memory less. Similarly, a resistor and the expression in option c are memory less systems as they depend upon the present state of the input. An accumulator sums up the values of all past and present states of input. Therefore, it is a system with memory. 30.. Which among the following is a memory less system? a) Delay b) Summer c) Resistor d) Capacitor View Answer Answer: c Explanation: Options Delay, Summer and Capacitor are all systems with memory as they depend upon past, past and present, past and present values of input respectively. Whereas, a resistor is a memory less system as its relationship with output always depends upon the current or present state of the input.

31. In a continuous-time physical system, memory is directly associated with _____________ a) Storage registers b) Time c) Storage of energy d) Number of components in the system View Answer Answer: c Explanation: Memory is directly associated with storage of energy such as electric charge in the capacitor or kinetic energy in an automobile. Storage registers are for discrete time systems such as microprocessor etc. Time and number of components of a system have got nothing to do with memory. 32.. A system with memory which anticipates future values of input is called _________ a) Non-causal System b) Non-anticipative System c) Causal System d) Static System View Answer Answer: a Explanation: A system which anticipates the future values of input is called a noncausal system. A causal depends only on the past and present values of input. Nonanticipative is another name for the causal system. A static system is memory less system. 33.. Determine the nature of the system: y(n)=x(-n). a) Causal b) Non-causal c) Causal for all positive values of n d) Non-causal for negative values of n View Answer

Answer: b Explanation: The given system gives negative values of input i.e., past values of input when we feed positive integers to LHS. However, it gives positive values for negative values of n i.e., future values. Therefore, the system depends upon past values for some integers and future values for some other. A system cannot be called partially causal or non-causal, therefore, the system is non-causal. 34.. Which among the following is an application of non-causal system? a) Image processing b) RC circuit c) Stock market Analysis d) Automobile View Answer Answer: c Explanation: Image processing, RC circuit, and an automobile are all causal systems as they do not anticipate the future values of an image, RC circuit and future actions of a driver respectively. Instead, they function upon either the stored information or on the current values of the input. Whereas, in the stock market, analysts try to figure out a trend in the future based upon the stored information. Therefore, it is noncausal. 35.. Determine the nature of the given system: y(t)=x(sint) a) Causal, Non-linear b) Causal, Linear c) Non-Causal, Non-linear d) Non-causal, Linear View Answer Answer: d Explanation: The system is non-causal as it gives future values for some inputs. E.g. y (- π) = x (sin (-π)) = x (0) For linearity, it needs to satisfy superposition principle, ⇒ y1 (t) = x1 (sint) ⇒ y2 (t) = x2 (sint)

⇒ ay1 (t) + by2 (t) = ax1 (sint) + bx1 (sint) Equation 1 Now, y3 (t) = x3 (sint) = (ax1 + bx2)(sint) = ax1 (sint) + bx1 (sint) Equation 2 Clearly, Equation 1 and 2 are equal, hence the system is linear. 36.. Is the system y[n]=2x[n]+2 linear? a) YES b) NO View Answer Answer: b Explanation: The system needs to satisfy superposition principle for linearity: For input x1[n], y1 [n] = 2x1 [n] + 2 For input x2[n], y2 [n] = 2x2 [n] + 2 ⇒ ay1 [n]+ by2 [n] = 2(ax1 [n]+ bx2 [n]) + 2(a+b) Equation 1 For, x3[n], y3 [n]=2x3 [n]+2 = 2(ax1 [n]+ bx2 [n]) + 2 Equation 2 Clearly, Equation 1 is not equal to equation ∴ The system does not satisfy superposition principle ⇒ The system is not linear. 37.. An inverse system with the original system gives an output equal to the input. How is the inverse system connected to the original system? a) Series b) Cascaded c) parallel d) No connection View Answer Answer: c Explanation: An inverse system when cascaded with the original system gives an output equal to the input. 38. Which among the following is an invertible system? a) y[n] = 0 b) y[n] = 2x[n] c) y(t) = x2(t)

d) y(t) = dx(t)/dt View Answer Answer: b Explanation: A system is said to be invertible if it’s input can be found out from its output. Implying, if a system has same outputs for several inputs then it is impossible to find the correct input as output is same for many. Therefore, a system is invertible if it gives distinct outputs to distinct inputs. It is non-invertible if it gives same outputs for many inputs. Option a produces 0 output for any input → Non-invertible Option b produces different outputs for different inputs and also it’s inverse system is (1/2)y[n] → Invertible Option c, we get same output for both positive and negative values → Non-invertible Option d, we get 0 for all constant input values → Non-invertible. 39.. Is the system time invariant: y(t) = x(4t)? a) YES b) NO View Answer Answer: b Explanation: A system is said to be time invariant if a change input causes the same change in output. For change in input by T ⇒ y(t, T) = x(4(t – T)) = x(4t – 4T) Equation 1 For the same change in output ⇒ y(t – T) = x(4t – T) Equation 2 Equation 1 is not equal to equation 2. ∴ The system is not time invariant or is time variant. 40.. Determine the nature of the system: y[n] = x[n]x[n – 1] with unit impulse function as an input. a) Dynamic, output always zero, non-invertible b) Static, output always zero, non-invertible c) Dynamic, output always 1, invertible

d) Dynamic, output always 1, invertible View Answer Answer: a Explanation: Since the system depends on present and past values, therefore, it is not memory less(dynamic). Now, input is a unit impulse function. Unit impulse function = 1 at n = 0, otherwise it is equal to 0. For, y[0] = x[0]x[-1] = 1 × 0 = 0 For, y[1] = x[1]x[0] = 0 × 1 = 0 For, y[2] = x[2]x[1] = 0 × 0 = 0 ∴ For any time, output is always zero. Since, the output is always same, the system is non-invertible. 41.. Determine the nature of the system: y(t)= t2 x(t-1) a) Linear, time invariant b) Linear, time variant c) Non-linear, time invariant d) Non-linear, time variant View Answer Answer: b Explanation: For linearity: For input x1(t): y1 (t)= t2 x1 (t-1) For input x2(t): y2 (t)= t2 x2 (t-1) ⇒ ay1 (t)+by2 (t)= t2 [x1 (t-1)+ bx2 (t-1)] Equation 1 For input x3(t): y3 (t)= t2 x3 (t-1) = t2 [ax1 (t-1)+ bx2 (t-1)] Equation 2 ∴ The system is linear. For time invariancy: Shift in input: ⇒y(t,T)= t2 x(t-1-T) Shift in output: y(t- T)= (t-T)2 x(t-1-T) ∵ The shift in output is not equal to the shift in input, therefore, the system is time variant.

42.. y[n]=rn x[n] is ________ system. a) LTI b) Time varying c) Linear and time invariant d) Causal and time invariant View Answer Answer: b Explanation: The input-output relationship of the given system shows it does not satisfy the condition of time-invariant system. Hence it is time varying system. 43.. A system is said to be linear if _______ a) It satisfies only the principle of superposition theorem b) It satisfies only amplitude scaling c) It satisfies both amplitude scaling and principle of superposition theorem d) It satisfies amplitude scaling but not the principle of superposition theorem View Answer Answer: c Explanation: By the definition of linearity a system is said to be linear if it satisfies the condition y1(t) + y2(t) = ax1(t) + bx2(t). 44. If the input-output relationship is given by y(t) = 2x(t) d⁄dx x(t). What kind of system it represents? a) Linear system b) Non linear system c) LTI system d) Linear but time-invariant system View Answer Answer: b Explanation: The given input-output relationship of the system does not satisfy the principle of superposition theorem hence it is an example for non linear system....