An input signal x (t) = u(t-1)-u(t-3) is applied to an LTI system h (t) =...

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An input signal x (t) = u(t-1)-u(t-3) is applied to an LTI system h₁ (t) = 8(t-2) to give the output y₁ (t). a) (2) Sketch x(t) and h₁ (t). Show important values. b) (2) Use convolution integral to express the output y₁ (t) in terms of h₁ (t) only. c) (2) Write down the output expression and sketch the output y₁ (t). Show important values. The output y₁ (t) is then applied to a differentiator to give z₁ (t). d) (2) Write down the expression of z₁ (t) and sketch z₁ (t). Show important values. The input signal x (t) is applied to an LTI system h₂(t) = u(t-2) - u(t-6) to give the output y₂ (t). e) (2) Sketch the output y₂ (t). Show important values. The input signal x (t) is applied to an LTI system h3 (t) = -1 h₁ (t-2k) to give the output y3 (t). f) (2) Sketch the output y3 (t). Show important values. The output y(t) is then applied to an integrator to give z3(t). g) (2) Sketch Z3 (t). Show important values. The block diagram of an LTI system ho(t) is given below. x(t) h₁ (t) d dt h₂ (t) y(t) ho(t) h) (2) Write down the impulse response of the overall LTI system in terms of h₁ (t) and h₂ (t). The input signal x (t) is applied to the LTI system h, (t) shown above to give the output y(t). i) (2) Sketch the output y(t). Show important values. j) (2) Write down the expression of y(t). An input signal x (t) = u(t-1)-u(t-3) is applied to an LTI system h₁ (t) = 8(t-2) to give the output y₁ (t). a) (2) Sketch x(t) and h₁ (t). Show important values. b) (2) Use convolution integral to express the output y₁ (t) in terms of h₁ (t) only. c) (2) Write down the output expression and sketch the output y₁ (t). Show important values. The output y₁ (t) is then applied to a differentiator to give z₁ (t). d) (2) Write down the expression of z₁ (t) and sketch z₁ (t). Show important values. The input signal x (t) is applied to an LTI system h₂(t) = u(t-2) - u(t-6) to give the output y₂ (t). e) (2) Sketch the output y₂ (t). Show important values. The input signal x (t) is applied to an LTI system h3 (t) = -1 h₁ (t-2k) to give the output y3 (t). f) (2) Sketch the output y3 (t). Show important values. The output y(t) is then applied to an integrator to give z3(t). g) (2) Sketch Z3 (t). Show important values. The block diagram of an LTI system ho(t) is given below. x(t) h₁ (t) d dt h₂ (t) y(t) ho(t) h) (2) Write down the impulse response of the overall LTI system in terms of h₁ (t) and h₂ (t). The input signal x (t) is applied to the LTI system h, (t) shown above to give the output y(t). i) (2) Sketch the output y(t). Show important values. j) (2) Write down the expression of y(t).

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Solving the mathematical difficulties associated with the LTI Linear TimeInvariant system shown in the image I will break down each step and provide h... View the full answer