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Basics of signal and system

The concepts of signals and systems are foundational to countless technologies we use every day. This post provides a clear introduction of signal and system, explaining how information-carrying signals are processed by various systems. Whether you're a student, an aspiring engineer, or simply curious, this guide will provide you with the essential starting points.


WHAT IS SIGNAL ?

We are define the signal in signal and system, a signal is a representation of information that varies over time, often in the form of voltage, current, or electromagnetic waves. 

  • continuous time signal defined for all instant of time and it represented by x(t).
  • discrete time signal defined only at discrete instant of time and it represented by x(n).

continuous time signal and discrete time signal both are represented by function or a graph.


Continuous time signal : a continuous time signal is defined for all values of time, there signal have a value for every point in time. they are represented as x(t), where 't' represents continuous time. examples include audio signals, temperature reading, and the position of an object over time.

Discrete time signal : a discrete time signal is only defined at specific , discrete points in time. they are typically represented as x(n). where 'n' is an integer representing the discrete time points. examples include digital images, digital audio, and data collected from sensors at regular intervals. 

There are many methods to representing a discrete time signal. 

1. Graphical representation

2. Functional representaion

3. Tabular representation

4. Sequence representaion

Ex. consider a signal x(n) with values x(-2) = -3,  x(-1) = 2,  x(0) = 0,  x(1) = 3,  x(2) = 1,  x(3) = 2, this discrete time signal can be represented by graphically.

1. graphical representation



2. functional representation                                 


3. tabular representation

4. sequence representation



WHAT IS SYSTEM?

We define system in signal and system, It is an entity that acts on an input signal and transform it into an output signal 
OR
Its a set of elements or functional blocks which are connected together and produces an output in response to an input signal.

The response of the system depends upon the transfer function of the system.
Ex: motor, amplifier, filter, boiler etc.


Classification of system:
  • Continuous time systems : it is one which transforms continuous time input signals into continuous time output signals. we can represent this system by y(t)=T[x(t)]



  • Discrete time systems  : it is one which transforms discrete time input signals into discrete time output signals. we can represent this system by y(n)=T[x(n)]

Both continuous and discrete time systems classified into following types:
1. lumped parameter and distributed parameter systems
2. static (memory less) and dynamic (memory) systems
3. causal and non causal systems
4. linear and non linear systems
5. time invariant and time varying systems
6. stable and unstable systems
7. invertible and non invertible systems
8. FIR and IIR systems

Conclusion:

In this introduction of signal and system, we've laid the groundwork for understanding the fundamental concepts of signals and systems. Signals, the carriers of information, can be continuous, existing at every point in time, or discrete, defined only at specific intervals. We explored how these signals can be represented in various ways, providing us with tools to analyze and interpret data.


Frequently Asked Questions (FAQs):

1. What is the main difference between a continuous-time signal and a discrete-time signal? 

A continuous-time signal is defined for all instants of time, while a discrete-time signal is only defined at specific, discrete points in time.


2. Can you give an example of a real-world continuous-time signal?

Examples include audio waves, temperature readings over time, and the velocity of a moving object.

3. What are some ways to represent a discrete-time signal?

Discrete-time signals can be represented graphically, functionally, in a table, or as a sequence.

4. What is the basic function of a system in the context of signals and systems?

A system takes an input signal, processes it, and transforms it into an output signal.

5. What's the difference between a continuous-time system and a discrete-time system?

A continuous-time system processes continuous-time input signals to produce continuous-time output signals, while a discrete-time system does the same for discrete-time signals.

6. Why is it important to classify different types of systems?

Classifying systems helps us understand their properties, predict their behavior, and choose appropriate analysis techniques.



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