The document discusses systems and their properties. It defines a system as a meaningful interconnection of components that transforms input signals to produce outputs. A system has inputs, outputs, and internal signals. Key properties of systems include memory, causality, time-invariance, linearity, stability, and invertibility. Systems can be used to process signals by modifying or extracting specific information from them.

1. Systems and their
Properties
Prarthan P
ENG19CS0228

2. INTRODUCTION
System is a device which operates on signals according to its characteristics.
The system can also be defined as meaningful interconnection of physical devices, components and
operations which transforms or modifies one or more input signals to accomplish a function and produces
the output.
EX: Filter
Filter that is used to reduce the noise in the information bearing signal is called as system. The operation
performed by tht system on the signal is called processing which involves elimination of noise and
interference from the signal.

3. EXPLANATION OF BLOCK DIAGRAM SYSTEM
Signals that enter a system from some external source are referred as input signal or Excitation signals
produced by the system by processing the input signals are called output signals or Responses.
Signals that occur within a system are neither input not output signals are called Internal signals. These
signals are functions of an independent variable such as time, distance etc… The responses will be
always more desirable that the excitation.
Ex:
● Communication system
● Remote sensing
● Control system
SYSTEM
Input signal Output signal

4. REAL LIFE EXAMPLES OF SYSTEMS
1. Communication system:
The three basic elements to every communication system are:
(1.) Transmitter (2.) Channel (3.) Receiver as shown in the diagram below
P.T.O

5. REAL LIFE EXAMPLES OF SYSTEMS
2. Control system:
The below diagram shows the block diagram representation of a closed loop
control systems or feedback control system.

6. PROPERTIES OF SYSTEMS
The properties of systems describes the characteristics of the operator. The
different properties of systems are:
1. Memory
2. Causality
3. Time Invariance
4. Linearity
5. Stability
6. Invertibility

7. Memory
A system is said to possess memory if its output signal depends on past and/or
future values of the input signal then the system is also referred as the dynamic
system.
Ex: Sequential logic element, indicator, flipflops, counters, etc..

8. Causality
A system is said to be causal if the output of the system is independent of future
values of input or if the output of the system is dependent only on the present
and past values of the input.
A system is said to be non-causal if the output at any instant of time depends on
the future values of the input signal.
Ex:
1. y(t) = x(t) Causal
2. y(t) = x(t) + x(t-1) Causal
3. y(n) = Non - Causal

9. Time Invariance
The system is said to be time variant if a time delay or advance of the input leads to an identical time shift in the output signal.
This implies that the time invariant systems responds identically no matter when the input signal is applied or the characteristics of a
time invariant system do not change with time.
Ex:
1.) y(t) = 2 + x(t)
x(t) y(t) = 2 + x(t)
To check whether it is time variant or time invariant
Step - 1: y(t) y(t - t0) = 2 + x[t - t0] ------------ (1)
Step - 2: x(t) x(t - t0) = y(t) = 2 + x(t - t0) ------------- (2)
Therefore by (1) and (2) y(t) = y(t - t0)
Therefore the given system is time invariant.
System

10. Linearity
A system is said to be linear in terms of the system input x(t) and the system
output y(t) if it satisfies the following properties i.e Law of Superposition and Law
of Homogeneity
1.) Law of Superposition is also called as Law of Additivity.
2.) Law of Homogeneity is also called as Law of Multiplication or Scalar
Multiplication.
A system which does not satisfies any of the above properties then it is called as
non - linear systems.

11. Stability
A system is said to be bounded input bounded output [BIBO] stable if and only if
every bounded input results in bounded output.
The output of such a system does not diverge if the input does not diverge.
Ex: For bounded signals, DC value, Sint, Cost, u(t), constant, -1 to 1, 1 to -1, 0 or 1

12. Invertibility
A system is said to be invertible if the input of the system can be recovered from
system output.
Alternatively a system is said to be invertible if distinct inputs leads to distinct
outputs i.e for any invertible system there should be one to one mapping
between input and output at each and every instant of time.
Ex:
-2
2
4
2
3
1
4
5
3

13. How are Signal and Systems Related ?
Design a system to restore or enhance a particular signal
● Remove high frequency background communication noise
● Enhance noisy images from spacecraft
Assume a signal is represented as
Design a system to remove the unknown “noise” component n(t), so that y(t) d(t)

14. How are Signal and Systems Related ?
How to design a system to extract specific pieces of information from signals
● Estimate the heart rate from an electrocardiogram.
● Estimate economic indicators (bear, bull) from stock market values.
Assume a signal is represented as
Design a system to “Invert” the transformation g(t), so that y(t) = d(t)

15. How are Signal and Systems Related ?
How to design a (dynamic) system to modify or control the output of another (dynamic)
system
● Control an aircraft’s altitude, velocity, heading by adjusting throttle, rudder,
ailerons.
● Control the temperature of a building by adjusting the heating/cooling energy
flow.
Assume a signal is represented as
Design a system to “Invert” the transformation g(t), so that y(t) = d(t)