1. The impulse response h(t) of an LTI system is given by h(t) = u(t + 2) ? u(t

ID: 1814216 • Letter: 1

Question

1. The impulse response h(t) of an LTI system is given by h(t) = u(t + 2) ? u(t ? 1).

What is the output y(t) when the input x(t) = u(t) ? u(t ? 2). What is the output z(t)

when the input x(t) = u(t ? 2) ? u(t ? 4)? (Derive z(t) from y(t).)

2. The impulse response h(t) of an LTI system is given by h(t) = e^(-at)u(t)

What is the output y(t) when the input x(t) = e^(-bt)u(t), a, b > 0 and (i) a does not = b, (ii) a = b.

3. The impulse response h[n] of an LTI system is given by h[n] = u[n + 1] ? u[n ? 1].

What is the output y[n] when the input x[n] = u[n + 2] ? u[n ? 2]. What is the output z[n]

when the input x[n] = u[n + 2] ? u[n ? 2] + u[n ? 4] ? u[n ? 8]?

y(t) = h(t)*x(t) => (u(t+2)-u(t-1))*(u(t)-u(t-2))

as it is time invariant system , and linear sysetm z(t) = y(t-2);

i.y(t)=h(t)*x(t) = (u(t)^2)*e^(-at-bt)

ii.y(t)=h(t)*x(t) = (u(t)^2)*e^(-(a+b)t)

3.y[n] = h[n]*x[n] = (u[n+1]-u[n-1])*(u[n+2]-u[n-2]);

z[n] = h[n]*x[n] = (u[n+1]-u[n-1])*(u[n+2]-u[n-2]+u[n-4]-u[n-8]);

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