## Convolution Integral in Network Analysis

Convolution Integral in Network Analysis: The Convolution Integral in Network Analysis in Laplace transform states that where f1 (t) * f2 (t) = Convolution of f1 (t) and f2 (t) From the definition of system function, Taking inverse Laplace, From the convolution theorem, where Thus with the help of convolution of e(t) and h(t), the response of the network […]

## Inverse Laplace Transform

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 as, The F(s), in partial fraction method, is written in the form as, where N(s) = Numerator polynomial in s […]

## Convolution Theorem

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 (t) respectively. Then the product of F1 (s) and F2 (s) is the Laplace transform of f(t) which is obtained […]

## Laplace Transform of Periodic Function

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 by , where F1 (s) is the Laplace transform of the first cycle of the periodic function. Proof: Consider the […]

## Laplace Transform of Standard Functions

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 Laplace is given by A/s. If the unit step is delayed by T instants then, From the shifting theorem of […]