The document discusses time domain analysis of linear time-invariant (LTI) systems. It explains that LTI systems can be analyzed using tools like superposition, where the input is broken into parts and the output of each part is determined individually then combined. It also discusses convolution, which is a mathematical operation used to find the output of an LTI system for a given input by performing shifting, multiplying and summing. Finally, it provides an example tutorial problem on finding the convolution sum of two sequences.

1. Date : 30-7-2020
Time Domain Analysis of Signals and Systems
ECEN341 Signals and Systems
Chapter-2 – Convolution Sum and Convolution Integral
Chapter-2 Time Domain Analysis of systems

2. Date : 30-7-2020
LTI – Systems Analysis
LTI stands for Linear Time Invariant
Why Linear Time-Invariant (LTI) Systems?
• Very powerful mathematical tools have been developed for analyzing LTI
systems
• LTI systems are much easier to analyze than systems that are not LTI
• In practice, systems that are not LTI can be well approximated using LTI
models.
Chapter-2 Time Domain Analysis of systems

3. Date : 30-7-2020
How LTI – Systems Analyzed
LTI stands for Linear Time Invariant
• Break the input into small parts and find the output for every small part.
• Finally combine the outputs for small parts using the principle of
superposition.
• A system is said to obey the property of superposition if it obeys the
properties of homogeneity and additivity and is then called a linear system.
Superposition is a powerful tool for analyzing complicated input signals.
Chapter-2 Time Domain Analysis of systems

4. Date : 30-7-2020
Time Invariant
LTI stands for Linear Time Invariant
Chapter-2 Time Domain Analysis of systems
t
0
x(t)
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2
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2
t
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t
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1

5. Date : 30-7-2020
Representation of DT Signals in Terms of Delta Functions
Chapter-2 Time Domain Analysis of systems
Eg. Consider a sequence given by
Decompose the sequence in linear combination of impulses and find the response to
input x[n].

6. Date : 30-7-2020
What is Convolution ?
• Convolution is a mathematical method to find the out of response of an system for a specified
input.
• It is basically doing shifting , multiplying and summing operation on the input and the system
function continuously. (Superposition Sum)
• A LTI system simply computes a convolution
Chapter-2 Time Domain Analysis of systems
(CT) LTI system in block diagram
form
(DT) LTI system in block diagram
form
Convolution sum
Convolution sum

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Tutorial Problem-1
Find the convolution sum of two sequences x1(n) and x2(n) given
below.
Chapter-2 Time Domain Analysis of systems

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8
References
• “Signals and Systems” by Oppenhehim, Willsky and Hamid,,
2nd edition, Pearson Education India, 2015.
• Signals and Systems :Principles and Applications by
Shaila Dinkar Apte , Cambridge University Press
Chapter-1