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51.

If the system is initially relaxed at time n=0 and memory equals to zero, then the response of such state is called as ____________(a) Zero-state response(b) Zero-input response(c) Zero-condition response(d) None of the mentionedI got this question by my school teacher while I was bunking the class.This intriguing question originated from Discrete Time Systems Described by Difference Equations topic in portion Discrete Time Signals and Systems of Digital Signal Processing

Answer» CORRECT choice is (a) Zero-state RESPONSE

The EXPLANATION is: The memory of the system, describes, in some case, the ‘state’ of the system, the OUTPUT of the system is CALLED as ‘zero-state response’.
52.

The solution obtained by assuming the input x(n) of the system is zero is ____________(a) General solution(b) Particular solution(c) Complete solution(d) Homogenous solutionThe question was asked by my college director while I was bunking the class.I need to ask this question from Discrete Time Systems Described by Difference Equations in division Discrete Time Signals and Systems of Digital Signal Processing

Answer»

Right choice is (d) Homogenous solution

To elaborate: By making the input X(n)=0 we will GET a homogeneous DIFFERENCE equation and the solution of that difference equation is KNOWN as Homogenous or Complementary solution.

53.

Zero-state response is also known as ____________(a) Free response(b) Forced response(c) Natural response(d) None of the mentionedThe question was asked in an interview for job.The question is from Discrete Time Systems Described by Difference Equations topic in division Discrete Time Signals and Systems of Digital Signal Processing

Answer»

Right choice is (B) FORCED response

The EXPLANATION is: The zero-state response depends on the nature of the system and the input SIGNAL. Since this OUTPUT is a response forced upon it by the input signal, it is also known as ‘Forced response’.

54.

Zero-input response is also known as Natural or Free response.(a) True(b) FalseI got this question in an international level competition.This is a very interesting question from Discrete Time Systems Described by Difference Equations in chapter Discrete Time Signals and Systems of Digital Signal Processing

Answer» RIGHT option is (a) True

The best EXPLANATION: For a zero-input response, the input is zero and the output of the system is INDEPENDENT of the input of the system. So, the response if such system is also known as Natural or FREE response.
55.

The system described by the equation y(n)=ay(n+1)+b x(n) is a recursive system.(a) True(b) FalseThis question was addressed to me in an online quiz.Question is from Implementation of Discrete Time Systems topic in chapter Discrete Time Signals and Systems of Digital Signal Processing

Answer»

Right choice is (b) False

Explanation: SINCE the present output depends on the VALUE of the FUTURE output, the system is not called a Recursive system.

56.

Which of the following is a recursive form of a non-recursive system described by the equation y(n)=\(\frac{1}{M+1} \sum_{k=0}^Mx(n-k)\)?(a) y(n)=y(n-1)+\(\frac{1}{M+1}\)[x(n)+x(n-1-M)](b) y(n)=y(n-1)+\(\frac{1}{M+1}\)[x(n)+x(n-1+M)](c) y(n)=y(n-1)+\(\frac{1}{M+1}\)[x(n)-x(n-1+M)](d) y(n)=y(n-1)+\(\frac{1}{M+1}\)[x(n)-x(n-1-M)]This question was posed to me in an international level competition.This interesting question is from Implementation of Discrete Time Systems topic in division Discrete Time Signals and Systems of Digital Signal Processing

Answer»

The correct OPTION is (d) y(N)=y(n-1)+\(\frac{1}{M+1}\)[x(n)-x(n-1-M)]

The explanation: The given system equation is y(n)=\(\frac{1}{M+1} \sum_{k=0}^M x(n-k)\)

It can be expressed as FOLLOWS

\(y(n)=\frac{1}{M+1} \sum_{k=0}^M x(n-1-k)+\frac{1}{M+1}[x(n)-x(n-1-M)]\)

=\(y(n-1)+\frac{1}{M+1}[x(n)-x(n-1-M)]\)

57.

An FIR system is also called as “recursive system”.(a) True(b) FalseI got this question in an interview for job.My question is from Implementation of Discrete Time Systems topic in section Discrete Time Signals and Systems of Digital Signal Processing

Answer»

The correct choice is (B) False

The best explanation: For a system to be recursive, the output of the system MUST be DEPENDENT only on the past values of the output. For an FIR system the output of the system must be depending only on the present and past values of the input. So, FIR system is not an recursive system.

58.

What is the form of the FIR system to compute the moving average of the signal x(n)?(a) y(n)=\(\frac{1}{M+1} \sum_{k=0}^M x(n-k)\)(b) y(n)=\(\frac{1}{M+1} \sum_{k=0}^M x(n+k)\)(c) y(n)=\(\frac{1}{M+1} \sum_{k=0}^{\infty} x(n-k)\)(d) None of the mentionedI got this question by my college professor while I was bunking the class.This interesting question is from Implementation of Discrete Time Systems topic in portion Discrete Time Signals and Systems of Digital Signal Processing

Answer»

The correct answer is (a) y(N)=\(\frac{1}{M+1} \sum_{k=0}^M x(n-k)\)

For explanation: A normal FIR non-recursive system with the impulse response h(n)=\(\frac{1}{M+1}\) is the system which is USED to compute the moving AVERAGE of a signal x(n).

59.

The system represented by the following direct form structure is:(a) General second order system(b) Purely recursive system(c) Partial recursive system(d) FIR systemThe question was asked during an online interview.The origin of the question is Implementation of Discrete Time Systems in section Discrete Time Signals and Systems of Digital Signal Processing

Answer»

Right choice is (d) FIR system

To EXPLAIN: The OUTPUT of the system according to the direct form given is

y(n)= b0x(n)+b1x(n-1)+b2x(n-2)

SINCE the output of the system is purely dependent on the present and past values of the input, the system is called as FIR system.

60.

Which of the following linear time invariant system is a purely recursive system?(a) y(n) = \(-\sum_{k=1}^{N} a_k y(n-k)+\sum_{k=0}^{M} b_k x(n-k)\)(b) y(n) = \(\sum_{k=1}^{N} a_k y(n-k)+\sum_{k=0}^{M} b_k x(n-k)\)(c) y(n) = \(-\sum_{k=1}^{N} a_k y(n-k)-\sum_{k=0}^{M} b_k x(n-k)\)(d) y(n) = \(-\sum_{k=1}^{N} a_k y(n-k)+b_0x(n)\)I had been asked this question in an online quiz.My question comes from Implementation of Discrete Time Systems topic in division Discrete Time Signals and Systems of Digital Signal Processing

Answer»

Correct answer is (d) y(n) = \(-\sum_{k=1}^{N} a_k y(n-k)+b_0x(n)\)

The explanation is: Since the output of the SYSTEM depend only on the past values of output and the PRESENT VALUE of the input, the system is called as “purely recursive” system.

61.

Which of the following is the difference equation of a special case ofFIR system?(a) y(n) = \(\sum_{k=0}^{M} b_k x(n-k)\)(b) y(n) = \(a_0y(n)-\sum_{k=1}^{N} a_k y(n-k)\)(c) y(n) = \(-\sum_{k=1}^{N} a_k y(n-k)\)(d) None of the mentionedI have been asked this question during an interview.My doubt is from Implementation of Discrete Time Systems in chapter Discrete Time Signals and Systems of Digital Signal Processing

Answer» CORRECT choice is (a) y(n) = \(\sum_{k=0}^{M} b_k x(n-k)\)

The BEST explanation: If the coefficients of the past values of the output in the difference EQUATION of the SYSTEM, then the system is said to be FIR system.
62.

The system described by the equation y(n)=ay(n-1)+b x(n) is a recursive system.(a) True(b) FalseThe question was asked by my college professor while I was bunking the class.This is a very interesting question from Implementation of Discrete Time Systems in section Discrete Time Signals and Systems of Digital Signal Processing

Answer»

Correct answer is (a) True

To explain: SINCE the present OUTPUT depends on the VALUE of the previous output, the system is called a Recursive system.

63.

To implement the linear time invariant recursive system described by the difference equation y(n)=\(-\sum_{k=1}^N a_k y(n-k)+\sum_{k=0}^M b_k x(n-k)\) in Direct form-I, how many number of delay elements and multipliers are required respectively?(a) M+N+1, M+N(b) M+N-1, M+N(c) M+N, M+N+1(d) None of the mentionedI had been asked this question in an interview for job.My question is from Implementation of Discrete Time Systems in portion Discrete Time Signals and Systems of Digital Signal Processing

Answer»

Right answer is (c) M+N, M+N+1

The EXPLANATION is: From the GIVEN equation, there are M+N delays, so it requires M+N number of DELAY elements and it has to PERFORM M+N+1 multiplications, so it require that many number of MULTIPLIERS.