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Which of the following options is true for a linear time-invariant discrete time system that obeys the difference equation:
y [n] – ay [n – 1] = b0x[n] – b1x[n – 1]
  • a)
    When x[n] = 0, n < 0, the function y[n ]; n > 0 is solely determined by the function x[n].
  • b)
    The system is necessarily causal.
  • c)
    y[n] is unaffected by the values of x[n – k ]; k > 2.
  • d)
    The system impulse response is non-zero at infinitely many instants.
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Which of the following options is true for a linear time-invariant dis...
y (n) – ay (n – 1) = b0x(n) – b1x(n – 2)
By applying ZT,
Y (z) – az–1 Y (z)= b0X (z) – b1z–1 X (z)
⇒ 
By taking right-sided inverse ZT,
h(n)= b0an u(n) – b1an – 1u (n – 1)
By taking left-sided inverse ZT,
h(n)= –b0an u (–n – 1) + b1an – 1u (–n )
Thus system is not necessarily causal.
The impulse response is non-zero at infinitely many instants.
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Which of the following options is true for a linear time-invariant dis...
The options provided are not visible, so I am unable to determine which option is true for the given difference equation. Please provide the options for further assistance.
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Which of the following options is true for a linear time-invariant discrete time system that obeys the difference equation:y [n] – ay [n – 1] = b0x[n] – b1x[n – 1]a)When x[n] = 0, n < 0, the function y[n ]; n > 0 is solely determined by the function x[n].b)The system is necessarily causal.c)y[n] is unaffected by the values of x[n – k ]; k > 2.d)The system impulse response is non-zero at infinitely many instants.Correct answer is option 'D'. Can you explain this answer?
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Which of the following options is true for a linear time-invariant discrete time system that obeys the difference equation:y [n] – ay [n – 1] = b0x[n] – b1x[n – 1]a)When x[n] = 0, n < 0, the function y[n ]; n > 0 is solely determined by the function x[n].b)The system is necessarily causal.c)y[n] is unaffected by the values of x[n – k ]; k > 2.d)The system impulse response is non-zero at infinitely many instants.Correct answer is option 'D'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Which of the following options is true for a linear time-invariant discrete time system that obeys the difference equation:y [n] – ay [n – 1] = b0x[n] – b1x[n – 1]a)When x[n] = 0, n < 0, the function y[n ]; n > 0 is solely determined by the function x[n].b)The system is necessarily causal.c)y[n] is unaffected by the values of x[n – k ]; k > 2.d)The system impulse response is non-zero at infinitely many instants.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following options is true for a linear time-invariant discrete time system that obeys the difference equation:y [n] – ay [n – 1] = b0x[n] – b1x[n – 1]a)When x[n] = 0, n < 0, the function y[n ]; n > 0 is solely determined by the function x[n].b)The system is necessarily causal.c)y[n] is unaffected by the values of x[n – k ]; k > 2.d)The system impulse response is non-zero at infinitely many instants.Correct answer is option 'D'. Can you explain this answer?.
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