engineering recuitment GATE EE 2023-24 Test Series Signals and Systems Laplace Transform Initial Value Theorem
We have information about an LTI system as given below.
1. The system is causal
2. The system function is rational and has only two poles, at s = -2 and s = 4
3. If x(t) = 1, then y(t) = 0
4. The value of the impulse response at t = 0+ is 4.
The system function of this system is
1
\(H\left( s \right) = \frac{{4\left( {s + 2} \right)}}{{\left( {s + 2} \right)\left( {s - 4} \right)}}\)
2
\(H\left( s \right) = \frac{{4s}}{{\left( {s + 2} \right)\left( {s - 4} \right)}}\)
3
\(H\left( s \right) = \frac{{4\left( {s + 1} \right)}}{{\left( {s + 2} \right)\left( {s - 4} \right)}}\)
4
\(H\left( s \right) = \frac{{4\left( {s + 4} \right)}}{{\left( {s + 2} \right)\left( {s - 4} \right)}}\)