A continuous Linear Time-Invariant (LTI) system is modelled in differentiation equation as follows: day(t) dy(t) +2 dt² dt dx(t) dt +y(t)=4- + 2x(t) Using Fourier Transform, determine the system function, H(a) and the impulse response, h(t) of the system. Figure Q7 (b) shows an LTI system with the impulse response, h(t) and the input signal, x(t) using Fourier Transform. e-2tu(t) te-u(t). Determine output of the LTI system y(t) =

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07 (a) A continuous Linear Time-Invariant (LTI) system is modelled in differentiation
equation as follows:
d²y(t)
dt²
BEJ 20203
+2-
2 dy(t)
+ y(t) = dx(t)
dt
+ 2x(t)
Using Fourier Transform, determine the system function, H() and the impulse
response, h(t) of the system.
Figure Q7 (b) shows an LTI system with the impulse response, h(t) = e-²¹u(t)
and the input signal, x(t) = te-u(t). Determine output of the LTI system y(t)
using Fourier Transform.
Transcribed Image Text:07 (a) A continuous Linear Time-Invariant (LTI) system is modelled in differentiation equation as follows: d²y(t) dt² BEJ 20203 +2- 2 dy(t) + y(t) = dx(t) dt + 2x(t) Using Fourier Transform, determine the system function, H() and the impulse response, h(t) of the system. Figure Q7 (b) shows an LTI system with the impulse response, h(t) = e-²¹u(t) and the input signal, x(t) = te-u(t). Determine output of the LTI system y(t) using Fourier Transform.
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