Signals and Systems: Definition & Classification

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Signals and Systems Definition

It is a function which conveys information of a phenomenon. It represents the variation of a physical quantity or an abstract concept over time, space or any other independent variable.A system is any physical or abstract entity that processes signals & transforming input signal into the output signal.
They are classified based on their characteristics, Like discreteness, continuity, periodicity and a randomness.Systems can range from a simple electronic circuits to the complex biological processes. They can exhibit various characteristics based on their nature and purpose.
-: Types of Signals :-
Continuous-Time Signals
Discrete-Time Signals
Analog Signals
Digital Signals
Periodic Signals
Aperiodic Signals
Deterministic Signals
Random (Stochastic) Signals
-: Types of Systems :-
Linear Systems
Nonlinear Systems
Time-Invariant Systems
Time-Variant Systems
Causal Systems
Non-causal Systems
Linear Time-Invariant (LTI) Systems
Signals and Systems

Classification of Signals

Signals are classified based on various criteria:

1. Continuous-time & Discrete-time Signals:

Continuous-time signalsDiscrete-time signals
Continuous-time signals are defined for all real values of time. They are represented by mathematical functions of a continuous variable, usually time.Discrete-time signals are only defined at discrete instances of a time. They are sequences of a numbers indexed by integers.
Signals and Systems

2. Analog & Digital Signals:

Analog signalsDigital signals
These are continuous-time signals that can take any value within a certain range. Examples include voltage signals in the electronic circuits.These are discrete-time signals with a finite number of possible values. They are commonly used in the digital communication systems and computers.
Signals and Systems

3. Periodic & Aperiodic Signals:

Periodic signalsAperiodic signals
These signals repeat their pattern identically over time, with a fixed period. The Sinusoidal waves are classic examples.These signals do not repeat their pattern over the time. The Transients or random signals are examples of the aperiodic signals.
Signals and Systems

4. Deterministic & Random Signals:

Deterministic signalsRandom signals (Stochastic signals)
These signals can be precisely predicted for any given time. They are completely defined by a mathematical functions or an algorithms.These signals have an unpredictable component, often described by statistical properties. The Noise signals are typical examples of a random signals.
Signals and Systems

Classification of Systems

Systems can also be classified based on several criteria:

1. Linear vs. Nonlinear Systems:

Linear systemsNonlinear systems
Linear systems satisfy the principles of the superposition and homogeneity. Their output is directly proportional to the input.Nonlinear systems do not satisfy the principles of superposition and homogeneity. Their output is not directly proportional to the input.
Signals and Systems

2. Time-Invariant vs. Time-Variant Systems:

Time-invariant systemsTime-variant systems
These systems produce the same output for a given input regardless of when it is applied. The system’s characteristics do not change over time.These systems exhibit varying behavior over the time. The system’s characteristics change with time or with the input signal.
Signals and Systems

3. Causal vs. Non-causal Systems:

Causal systemsNon-causal systems
These systems produce output dependent only on a present and past inputs. The output at any given time depends only on the input at that time and earlier.These systems produce output dependent on a future inputs, making them theoretically challenging to implement in real-time.
Signals and Systems

4. Linear Time-Invariant (LTI) Systems:

It is a special Classification of systems that includes both the linear and time-invariant Systems. It is widely used in signal processing due to their mathematical tractability and practical significance.

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