In this presentation we can know across the LTI systems. Also classifying the system and defining it. Also there has been a basic graphical image to help understanding. Mathematical theorems are also provided in it. Overall its a small presentation, delivering engineering students the idea to basic systems.

1. • Infographic Style
LTI System:
With & Without
Memory

2. Contents 01System and its Classification
02LTI System
03Static – Dynamic System
04LTI System with & without memory
05Conclusion & References

3. System and its Classifications
Static or
Dynamic
Time Variant or
Time Invariant
Linear or
Non Linear
Causal or
Non Causal
Stable or
Unstable
A system is a physical device (or an algorithm) which performs required operation on a discrete
and continuous time signal.
Its classifications are:

4. LTI System
Linear time-invariant systems (LTI systems) are a class of systems used
in signal and systems that are both linear and time-invariant. Linear systems
are systems whose outputs for a linear combination of inputs are the same as a
linear combination of individual responses to those inputs. Time-invariant
systems are systems where the output does not depend on when an input was
applied. These properties make LTI systems easy to represent and understand
graphically.
X(t)
Input Signal
Y(t)
Output Signal

5. Static – Dynamic System
Static System:
A static system is a system in which output at any instant of time
depends on the input sample at the same time. In other words, the system in
which output depends only on the present input at any instant of time then this
system is known as the static system. A static system is a memoryless system.
Ex: y(n) = 9 x(n)
Dynamic System:
A dynamic system is a system in which output at any instant of time
depends on the input sample at the same time as well as at other times. In
other words, the system in which output depends on the past and/or future
input at any instant of time then this system is known as the dynamic system.
A dynamic system possesses memory.
Ex: y(n) = x(n) + 6x (n-2)

6. LTI Systems
With &Without Memory
The present output of a memoryless LTI system depends only on the present input. Exploiting the commutative
property of convolution, we may express the output of a discrete-time LTI system as:
y(n) = h(n) * x(n)
= σ𝑘=−∞
∞
ℎ 𝑘 𝑥(𝑛 − 𝑘)
= ….. + h(-2) x(n+2) + h(-1) x(n+1) + h(0) x(n) + h(1) x(n-1) + h(2) x(n-2) + …..
For this system to be memoryless, y(n) must depend only on x(n) and therefore cannot depend on x(n-k) for k≠0.
Hence, every term in the above equation must be zero, except h(0) x(n). This condition implies that h(k)=0 for k ≠ 0;
thus a discrete-time LTI system is memoryless if and only if
h(n) = K δ(n)
Where K=h(0) is a constant and the convolution sum reduces to the relation
y(n) = K x(n)

7. Prolongation
If a discrete-time LTI system has an impulse response h(n) that is not identically zero for n ≠ 0, then
the system has memory.
From the following equation
Sy = Sx Sh
We can deduce similar properties for continuous-time LTI systems with and without memory. In
particular, a continuous-time LTI system is a memoryless of h(t) = 0 for k ≠ 0, and such a
memoryless LTI system has the form
y(t) = K x(t)
for some constant K and has the impulse response
h(t) = K δ(t)

8. Conclusion
The LTI systems with and without memory is one of the relation between
LTI system and impulse response.
The impulse response completely characterizes the input-output behavior
of an LTI system. Hence, the properties of the system, such as memory,
causality, and stability, are related to the system's impulse response.

9. References
• https://en.wikipedia.org/wiki/Linear_time-invariant_system
• https://brilliant.org/wiki/linear-time-invariant-
systems/#:~:text=Linear%20time%2Dinvariant%20systems%20(LTI,individual%20responses%2
0to%20those%20inputs
• Signal and Systems by Tarun Kumar Rawat page 133

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YOU
For your precious time towards
our presentation