LTI SYSTEM Analysis

By:

Vijay Singh MundaVishal YadavRahul UpadhyaySatyaprakash

LTI SYSTEM Analysis

By:-

Complex ExponentialDifferential Equation and Difference EquationStep Response

Properties necessary for LTI system

• The set of basic signal can be used to construct a broad class of equal signal.

• The response of LTI system to each signal should be simple enough to provide an easy representation.

Complex Exponential

Complex exponential signals play an important and unique role in analysis of LTI systems both in continuous and discrete time

• The two properties are provided by complex exponential signals in both continuous and discrete domain

i.e.• Signals of the form in continuous time• And in discrete timewhere s and z are complex numbers or variables

complex exponentials are important in study LTI systems as the response of an LTI system to a complex exponential input is the same complex exponential with only a change in amplitude

In continuous time:-

In discrete time:-zⁿ→H(z)zⁿ

where the complex amplitude factor H(s)and H(z) are function of the complex variable s and z

• A signal for which the system output is constant times the input is referred as an EIGENfunction of the LTI system

• and the amplitude factor is referred to as system’s eigenvalue.