Lti analysis signal system presentation by vijay ,vishal ,rahul upadhyay ,satyaprakash
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The document provides an analysis of LTI (Linear Time-Invariant) systems, focusing on the role of complex exponential signals in both continuous and discrete time frameworks. It explains that LTI systems respond to complex exponential inputs with an output that is a scaled version of the input, highlighting key properties such as step response and eigenfunctions. The relationship between input signals and their corresponding outputs is described using complex variables, emphasizing the importance of understanding these concepts for effective LTI system analysis.
Lti analysis signal system presentation by vijay ,vishal ,rahul upadhyay ,satyaprakash
- 1. LTI SYSTEM Analysis By: Vijay Singh Munda Vishal Yadav Rahul Upadhyay Satyaprakash
- 2. LTI SYSTEM Analysis By:- Complex Exponential Differential Equation and Difference Equation Step Response
- 3. 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.
- 4. 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 𝑒 𝑠𝑡 in continuous time • And 𝑧 𝑛 in discrete time where s and z are complex numbers or variables
- 5. 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:- 𝑒 𝑠𝑡 → 𝐻(𝑠) 𝑒 𝑠𝑡 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
- 6. • 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.