It is known that u(t) is a unit step signal and a Linear Time Invariant (LTI) system has an impulse response given by h(t) = (4t+1) u(t–2) + (-4t–1)u( t). The LTI system above is then evaluated by passing the input signal x(t) = 2u(t–1) –2u(t–2) into the system. a) Show mathematically whether the above system is a stable system or not and explain your answer completely and explain whether the system is a causal system! b) Draw the input signal for the system above and also describe the impulse response of the system! c) If y(t) is the output signal of the LTI system above, then determine the value of the y(t) signal for each t value!
It is known that u(t) is a unit step signal and a Linear Time Invariant (LTI) system has an impulse response given by h(t) = (4t+1) u(t–2) + (-4t–1)u( t). The LTI system above is then evaluated by passing the input signal x(t) = 2u(t–1) –2u(t–2) into the system. a) Show mathematically whether the above system is a stable system or not and explain your answer completely and explain whether the system is a causal system! b) Draw the input signal for the system above and also describe the impulse response of the system! c) If y(t) is the output signal of the LTI system above, then determine the value of the y(t) signal for each t value!
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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It is known that u(t) is a unit step signal and a Linear Time Invariant (LTI) system has an impulse response given by h(t) = (4t+1) u(t–2) + (-4t–1)u( t). The LTI system above is then evaluated by passing the input signal x(t) = 2u(t–1) –2u(t–2) into the system.
a) Show mathematically whether the above system is a stable system or not and explain your answer completely and explain whether the system is a causal system!
b) Draw the input signal for the system above and also describe the impulse response of the system!
c) If y(t) is the output signal of the LTI system above, then determine the value of the y(t) signal for each t value!
(use simple way)
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