IMPORTANT SIGNALS AND SYSTEMS WITH DEFINITION SIGNAL IN INDIA

IMPORTANT SIGNALS AND SYSTEMS WITH DEFINITION SIGNAL IN INDIA

Introduction:

Now, we are going to discuss about the important signals and systems with definition signal  in in India. Basically we will discuss that what is signal, type of signals with example and systems. Also we will study the unit step, unit ramp and unit impulse functions.

What is Signal:

A signal is defined as a physical quantity that varies with time, space or any other independent variable. The signal may depend on one or more independent variables. If a signal depends only one variable, then it is known as one dimensional signal. For example, ac power supply signal, speech signal.

Signal Modeling:

The representation of a signal by mathematical expression is known as signal modelling. If a signal can be represented by mathematical equation then the signal is said to be deterministic signal. Otherwise the signal is known as random signal.

Continuous-time signal:

The signals that are defined for every instant of time are known as continuous-time signal. They are denoted by x(t).a continuous-time signal is also called an analog signal.

Discrete-time signal:

The signals that are defined at discrete instant of time are known as discrete-time signals. The discrete-time signals are continuous in amplitude and discrete in time. They are denoted by x(n)

.

Digital signals:

The signals that are discrete in time and quantized in amplitude are digital signals. 

Unit step function:

The unit step function is defined as
u(k) = 1   for  k ≥ 0
        = 0   for k < 0
and is shown in fig

 Ramp function:

The unit ramp function is defined as
r(t) = t  for t ≥ 0
      = 0 for t < 0

unit impulse function:

The unit  impulse function occupies an important place in signal analysis. It is defined asꙎ(t) = 0  for t ≠ 0

Rectangular pulse function:

The rectangular function is defined asΠ(t) =   for ןtן ≤ 0
        = 0  otherwise

Sinusoidal signal:

A continuous time signal is given by               X(t) = A sin(Ὠt + Ⴔ)Where A is the amplitude, Ὠ is the frequency in radians per second and Ⴔ is the phase angle in radians.

Periodic and aperiodic signals:

A continuous time signal x(t) is said to be periodic if it satisfies the conditionX(t + T) = x(t)  for all  t
The smallest value of T that satisfies the above condition is known as fundamental period. A  signal is aperiodic if the condition is not satisfied for atleast one value of t.

Even and odd signals:

A continuous time signal is said to be symmetric (even) if it satisfies the condition
X(-t) = x(t)  for all  t
Example of a even signal is a cos signal.A continuous time signal x(t) is said to be anti- symmetric (odd) signal if it satisfies the condition
X(-t) = -x(t)   for all   t
Example of a odd signal is a sin signal.

Conclusion:

So, here we discussed  all about the signals  with the help of diagrams. Also we covered important signal and systems with definition in India. Mainly, we will discuss about the sysyems in the next class.

If you have any question regarding the topic please write it down in the comment section.

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