Final answer:
To find the LTI system's output signal y(t), we convolve the input signal x1(t) = u(t) - u(t-2) with the impulse response h(t) = e⁻²ᵗu(t). The Matlab code provided plots the resulting y(t) over time.
Step-by-step explanation:
The student is asking how to determine the output signal y(t) of a linear time-invariant (LTI) system when the input signal x₁(t) = u(t) - u(t-2) and the impulse response h(t) = e⁻²ᵗu(t) are given. To find y(t), we need to perform the convolution of the input signal with the impulse response.
The convolution integral is defined by:
y(t) = ∫ x₁(τ)h(t-τ)dτ.
For Matlab plotting, the following code can be used:
syms t τ
h = exp(-2*t)*heaviside(t);
x1 = heaviside(t) - heaviside(t-2);
y = int(subs(h, t, t-τ)*x1, τ, -inf, inf);
fplot(y, [0, 10]);
xlabel('Time (t)');
ylabel('Output signal y(t)');
This will output the plot of y(t) against time in Matlab.