Basics of Signals and Systems
Tags: signals, systems, basics
Published: 2022-10-04 19:40:38

A variety of engineering systems use [signals and systems](https://www.theengineeringprojects.com/2022/08/introduction-to-signal-and-systems.html). It is used in analog and digital signal processing for a variety of purposes, including seismic data processing, consumer electronics, speech and picture processing, and communication. Here, we'll go through the meaning of signal and systems, how they relate to one another, and how to classify and identify them.

## What is Signals?
The term "signal" is used to describe any change in a measurable physical quantity with regard to time, space, or any other parameter or variable. Mathematically, signals are shown as functions of variables that are not related to each other.

For instance, a mathematical description of a speech signal could be acoustic intensity as a function of time, and a mathematical description of an image would be brightness as a result of two spatial variables.

The system might perform additional processing on the signals, changing them or extracting new data.

## What is Systems?
An entity that modifies one or more signals to carry out a task and so produce a new signal is referred to as a system.

For instance, a sound source or signal can trigger the vocal tract, which is a system used for speech transmission.

## Relation Between Signals and System
The following is a block diagram depicting the relationship between signals and system it generates:

![Image description](https://dev-to-uploads.s3.amazonaws.com/uploads/articles/ryjxvfssvyrnwy31cr4g.jpg)

How the system's input and output signals are described is set by the task at hand:
The desired location of the plane with respect to the runway serves as the input signal for a

-  landing system. The output, a lateral position adjustment for the aircraft, is the system, which is the airplane.
- The speech or voice signal is fed into a computerized system, and the identity of the speaker is determined automatically.
- A communication system's input is a signal, which could be human speech or digital data; the system itself consists of a transmitter, a receiver, and a channel; and the system's output is a representation, or approximation, of the actual message signal.

## Classification of Signals
Here are the classifications for signals:

### Continuous-time and Discrete-time Signal
A continuous-time signal is one for which the value of the signal's x(t) is known for any given t.

![Image description](https://dev-to-uploads.s3.amazonaws.com/uploads/articles/4eboj9v8h06hexh5cx3m.png)

The signal's amplitude or value changes over time in a smooth, unbroken fashion, as depicted in the image.

Only at distinct points in time can a [discrete signal](https://www.mathworks.com/help/dsp/ug/discrete-time-signals.html) be characterized.

![Image description](https://dev-to-uploads.s3.amazonaws.com/uploads/articles/l6fcfqjhmqyj0jg6sudw.png)

A discrete signal is demonstrated in the image above. Signals with a discrete time period have a discrete time component but a continuous amplitude.

### Even and Odd Signals
A signal is deemed even if it satisfies the following requirements:
x(t) = x(-t) for all t

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

![Image description](https://dev-to-uploads.s3.amazonaws.com/uploads/articles/5d6lb68dzwy4128ul5u0.png)

A signal is deemed unusual if it satisfies the following requirements:
x(t) = -x(-t) for all t

Example: sin t, t, t3etc.

![Image description](https://dev-to-uploads.s3.amazonaws.com/uploads/articles/m9o6e2ffwn63nnpa925a.png)

### Deterministic and Non-deterministic Signals
A deterministic signal is one whose full physical description is known and can be represented mathematically or visually. One can predict the kind and size of such a signal at any time. This type of signal has a predictable pattern.

![Image description](https://dev-to-uploads.s3.amazonaws.com/uploads/articles/yw64gvhw3p8ntp1na3i9.png)

A random signal or non-deterministic signal is one whose values aren't known with any degree of certainty but are instead described using probabilistic measures like the mean or the mean square. Such a signal's characteristics and magnitude are unpredictable at all times. Such a signal has an erratic pattern.

![Image description](https://dev-to-uploads.s3.amazonaws.com/uploads/articles/axpnr558a0oqes189mq1.png)

### Periodic and Non-periodic Signals
Periodic signals satisfying the equation x(t) = x(t+T)... are represented by the function x(t). for every t, (1)
Where T = a positive constant.

![Image description](https://dev-to-uploads.s3.amazonaws.com/uploads/articles/99tab4fvfxipe7tuwdd9.png)

The term "fundamental time period" refers to the lowest value of T that fulfills the aforementioned equation (1).

The basic frequency of a signal that repeats is the same as its basic time period. It gives the frequency of repetition of the periodic signal x(t). Here, f = 1/T.

The unit of measurement for frequency, f, is hertz (Hz), or cycles per second. The definition of the angular frequency, which is measured in radians per second (ω), is = (2)/T.

The term "non-periodic" or "aperiodic" is used to describe a signal x(t) for which there isn't any value for T satisfying the criteria of equation(1).

![Image description](https://dev-to-uploads.s3.amazonaws.com/uploads/articles/bria40f1tm7fhlgcpkcg.png)

## Types of Systems
Some of the types of systems are:

### Communication System
A method of communicating outlines how data is transferred between two points.

### Regulatory System
A control system is a device that modifies an output in order to produce a desired response.

### Auditory System
The auditory system in the brain is responsible for converting a wide range of relatively modest mechanical impulses into an intricate series of [electrical signals](https://www.allaboutcircuits.com/textbook/digital/chpt-14/electrical-signal-types/).

### Biomedical Signal Processing System
An analysis of data from the heart rate, oxygen saturation levels, and blood pressure by a biomedical signal processing system provides doctors with pertinent information on which to base their decisions.

### Remote Sensing System
A remote sensing system identifies and monitors the physical parameters of a location by remotely monitoring the reflected and emitted radiation.

## Conclusion
The fundamentals of signal and systems are covered in this tutorial in order to help you comprehend the ideas behind digital image processing.