Signals and System: Signals and system is used in a wide range of engineering system. Its application is found in analog and digital signal processing, such as in communication, voice processing, image processing, consumer electronics, seismic data processing, etc. Here we will describe the definition of signals, systems, the relationship between signals and systems, their types and classification, and their examples.

Signals

Any physical quantity that changes with respect to time, space, or any other independent variable or factor is referred to as a signal. Mathematically, signals are represented as functions of independent variables.

A speech signal, for example, maybe mathematically described as acoustic pressure as a function of time, and a picture can be mathematically represented as brightness as a function of two spatial variables.

Signals may be processed further by the system, modifying them or extracting additional information from therm.

Systems

A system may be defined as an entity that manipulates one or more signals to accomplish a function, thereby creating a new signal.

A sound source or signal, for example, stimulates the vocal tract, which represents a system in speech communication.

Types of Systems

Some of the types of systems are:

Communication System

A communication system is one that defines the exchange of information between two locations.

Control System

A control system is a system that controls the output to create the required response.

Auditory System

In the central nervous system, the auditory system converts a wide variety of weak mechanical impulses into a complicated sequence of electrical signals.

Biomedical Signal Processing System

A biomedical signal processing system analyzes data such as heart rate, blood pressure, and oxygen saturation levels to give doctors relevant information on which to make judgments.

Remote Sensing System

By detecting the reflected and emitted radiation from a distance, a remote sensing system detects and monitors the physical properties of a region.

Relation Between Signals and System

The interaction between a system and its associated signals is shown in the block diagram below:

signals and system

The input and output signal descriptions are determined by the system’s intended application:

  • In an aircraft landing system, the input signal is the desired position of the aircraft relative to the runway. The system is the aircraft and the output is a correction on the aircraft’s lateral position.
  • In an automatic speaker recognition system, the input signal is a speech(voice) signal, the system is a computer & output is the identity of the speaker.
  • In a communication system, the input could be a speech signal or computer data, the system itself is made up of a combination of a transmitter, channel & receiver, and output is an estimate of the original message signal.

Classification of Signals

Signals can be classified as below:

Continuous-time and Discrete-time Signal

If a signal x(t) is specified for all time t, it is said to be a continuous-time signal.

Continuous-time signals and system

The figure above is an example of a continuous-time signal whose amplitude or value varies continuously with time.

A discrete signal is defined only at discrete instants of time.

Discrete-time Signals and system

The figure above is an example of a discrete signal. For discrete-time signals, time is discrete but amplitude is continuous.

Even and Odd Signals

When a signal meets the following criteria, it is considered to be even:
x(t) = x(-t) for all t

Example:
x(t) = cos t
x(-t)= cos(-t) = cos(t)
∴ x(t) = x(-t)

Even Signals and system

When a signal meets the following criteria, it is considered to be odd:
x(t) = -x(-t) for all t

Example: sin t, t, t3etc.

Even Signals and system

Deterministic and Non-deterministic Signals

A signal whose complete physical description is known, either in a mathematical form or in a graphical form is known as a deterministic signal. The type and magnitude of such a signal may be forecasted at any moment. The pattern of such a signal is regular.

Deterministic signals and system

A signal whose values cannot be predicted precisely but are known only in terms of probabilistic description such as mean value or mean square value is known as a random signal or non-deterministic signal. The nature and amplitude of such a signal cannot be predicted at any time. The pattern of such a signal is irregular.

Random Signals and System

Periodic and Non-periodic Signals

The function x(t) is a periodic signal that meets the requirement: x(t) = x(t+T) …(1) for all t
Where T is a positive constant.

Periodic Signals

The smallest value of T that satisfies the above equation(1) is called the ‘fundamental time period”.The fundamental frequency of the periodic signal is reciprocal of its fundamental time period T. It describes how frequently the periodic signal x(t) repeats itself. Here, f=1/T.

The frequency f is expressed in hertz (Hz), which is equal to cycles per second. The angular frequency is expressed in radians per second and is defined by ω = (2Π)/T.

Any signal x(t) for which there is no value of T to satisfy the condition of equation(1) is called a non-periodic or aperiodic signal.

Non-periodic Signals

Energy Signals and Power Signals

A signal is said to be a power/energy signal if the total power/energy transmitted is finite. Both signals can’t be finite at the same time. If the power of an energy signal is zero, the energy of the power signal is infinite.

0<E<∞ or 0<P<∞

The total energy transmitted to load is:

Energy signals expression

Average power is given by:

Power signals expression


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