Question

Determine the unit impulse response of LTIC systems described by the following equations:

(a) (D+2)y(t)=(3D+5)x(t)
(b) D(D+2)y(t)=(D+4)x(t)
(c) (D2+2D+1)y(t)=Dx(t)

We can show that the system impulse response h(t) is given by: h(t)=b0​δ(t)+[P(D)yn​(t)]u(t)

Answer 1

The unit impulse response of the given LTIC systems can be determined using the formula h(t)=b0​δ(t)+[P(D)yn​(t)]u(t).

Step-by-step explanation:

To determine the unit impulse response of LTIC systems described by the given equations, we can use the formula: h(t)=b0​δ(t)+[P(D)yn​(t)]u(t), where δ(t) represents the unit impulse function and u(t) is the unit step function. Let's apply this formula to each equation:

(a) (D+2)y(t)=(3D+5)x(t): The unit impulse response for this equation is h(t)=2δ(t)+(3D+5)u(t).

(b) D(D+2)y(t)=(D+4)x(t): The unit impulse response for this equation is h(t)=δ(t)+(D+4)u(t).

(c) (D2+2D+1)y(t)=Dx(t): The unit impulse response for this equation is h(t)=1δ(t)+(D+1)u(t).