Convolution Integral in Network Analysis: The Convolution Integral in Network Analysis in Laplace transform states that where f1Â (t) * f2Â (t) = Convolution of f1Â (t) and f2Â (t) From the definition of system function, Taking inverse Laplace,…
Inverse Laplace Transform: As mentioned earlier, inverse Laplace transform is calculated by partial fraction method rather than complex integration evaluation. Let F(s) is the Laplace transform of f(t) then the inverse Laplace transform is denoted…
Convolution Theorem: The convolution theorem of Laplace transform states that, let f1 (t) and f2 (t) are the Laplace transformable functions and F1 (s), F2 (s) are the Laplace transforms of f1 (t) and f2…
Laplace Transform of Periodic Function: Consider a Laplace Transform of Periodic Function of time period T satisfying the condition, where n is positive or negative integer. The Laplace transform of such periodic function is given…
Laplace Transform of Standard Functions: The Laplace Transform of Standard Functions is given by Step Function: The unit step function is, If there is step of amplitude A i.e. f(t) = A u(t) then its…
Relationships Between Standard Time Function: The Relationships between Standard Time Function contains two parts, namely Relation Between Unit Step and Unit Ramp Relation Between Unit Step and Unit Impulse 1. Relation Between Unit Step and…
Laplace Transform of Impulse Function: The Laplace Transform of Impulse Function is a function which exists only at t = 0 and is zero, elsewhere. The impulse function is also called delta function. The unit…
Ramp Function: The ramp function is shown in the Fig. 2.10. Mathematically such a function is expressed as, Thus it is a straight line of slope A. This slope A is called amplitude or magnitude…
Laplace Transform of Unit Step Function: The step function is shown in the Fig. 2.2. Such a function has zero value for all t < 0, while has a value A for t ≥ 0.…
Laplace Transform Properties: The Laplace Transform Properties are namely, 1. Linearity: The transform of a finite sum of time functions is the sum of the Laplace transforms of the individual functions. So if F1(s), F2(s),........Fn(s)…