Consider the causal discrete-time LTI system described by the following constant coefficient difference equation: y(n) = 1.4y(n − 1) −0.48y(n − 2) + 2x(n − 1) + x(n − 2) - (a) Determine the system function H(z) and the impulse response h(n). Is the system BIBO stable? Is the system FIR or IIR? Is the system an-all pole system? (b) Suppose the system is initially relaxed, i.e., y(−1) = 0, y(−2) = 0, and the input x(n) = n()u(n) is applied to the relaxed system. Determine the zero-state response y(n). Deter- mine the system natural response Ynr (n) and the system forced response yfr(n). Simplify your answers as much as possible.
Consider the causal discrete-time LTI system described by the following constant coefficient difference equation: y(n) = 1.4y(n − 1) −0.48y(n − 2) + 2x(n − 1) + x(n − 2) - (a) Determine the system function H(z) and the impulse response h(n). Is the system BIBO stable? Is the system FIR or IIR? Is the system an-all pole system? (b) Suppose the system is initially relaxed, i.e., y(−1) = 0, y(−2) = 0, and the input x(n) = n()u(n) is applied to the relaxed system. Determine the zero-state response y(n). Deter- mine the system natural response Ynr (n) and the system forced response yfr(n). Simplify your answers as much as possible.
Introductory Circuit Analysis (13th Edition)
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Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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Question
![Consider the causal discrete-time LTI system described by the following constant
coefficient difference equation:
y(n) = 1.4y(n − 1) – 0.48y(n − 2) + 2x(n − 1) + x(n − 2)
(a) Determine the system function H(z) and the impulse response h(n). Is the system BIBO
stable? Is the system FIR or IIR? Is the system an-all pole system?
(b) Suppose the system is initially relaxed, i.e., y(-1) = 0, y(-2) = 0, and the input x(n)
n()u(n) is applied to the relaxed system. Determine the zero-state response y(n). Deter-
mine the system natural response ynr (n) and the system forced response yfr(n). Simplify your
answers as much as possible.
=](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcb23cde1-d29d-434b-98b1-3e624e29f5ef%2Fd566fe8f-8ebb-4aad-a16d-58ca350c459f%2Fnkzq1ay_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the causal discrete-time LTI system described by the following constant
coefficient difference equation:
y(n) = 1.4y(n − 1) – 0.48y(n − 2) + 2x(n − 1) + x(n − 2)
(a) Determine the system function H(z) and the impulse response h(n). Is the system BIBO
stable? Is the system FIR or IIR? Is the system an-all pole system?
(b) Suppose the system is initially relaxed, i.e., y(-1) = 0, y(-2) = 0, and the input x(n)
n()u(n) is applied to the relaxed system. Determine the zero-state response y(n). Deter-
mine the system natural response ynr (n) and the system forced response yfr(n). Simplify your
answers as much as possible.
=
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