Signals and Systems: Basic Concepts, Types, and Examples in Everyday Life

 What Are Signals and Systems?

A signal is a representation of a physical quantity that changes over time. In the context of electrical engineering, signals can be voltage, current, temperature, sound, images, or even digital data that can be represented mathematically. Signals can be continuous (analog) or discrete (digital).

A system, on the other hand, is a device or process that converts one signal into another. A system can be an electronic circuit, signal processing software, or even a mathematical model that describes the behavior of a physical process.

Why Are Signals and Systems Important?

Think of digital communications like video calls or music streaming. They all involve signals (sound, images) that are processed by systems (compression, transmission, processing). Without an understanding of how signals work and how systems respond to them, we cannot build efficient and reliable technology.

In addition, many systems in electrical engineering such as motor control, radar systems, and medical devices such as ECG and EEG rely on signal processing and dynamic systems.

Types of Signals

1. Continuous Time Signals

These signals have values ​​at every measurable time. Examples: analog signals such as human voice or radio waves.

2. Discrete Time Signals

Only have values ​​at certain separate times. Usually produced from the sampling process of a continuous signal.

3. Deterministic vs Random Signals

- Deterministic: predictable (e.g. sinusoidal signal).

- Random: not exactly predictable (e.g. noise).

4. Periodic and Aperiodic Signals

- Periodic: repeats at regular intervals.

- Aperiodic: has no repeating pattern.

System Characteristics

In signals and systems, systems are categorized based on various characteristics:

- Linearity: whether the system obeys the superposition principle.

- Time-invariance: whether the system properties remain constant even when the input signal is shifted in time.

- Causality: whether the system output depends only on the present or past values ​​of the input signal.

- Stability: whether the system output remains finite for a finite input.

Linear and time-invariant (LTI) systems are a very common and important type of system because they have mathematical properties that are easy to analyze, especially using transforms such as Fourier and Laplace.

Transforms Used

- Fourier Transform

Used to analyze the frequency of a signal. For example, a speech signal can be separated into its frequency components.

- Laplace Transform

Useful for analyzing systems in the s-domain. Suitable for understanding the behavior of control systems and circuits.

- Z Transform

Used in digital (discrete-time) systems analysis, especially in digital signal processing and digital filter design.

System Response

Every system has two main types of responses:

- Natural response: the portion of the system output due to its initial conditions.

- Forced response: the portion of the output that comes from external inputs.

Knowing how a system responds to signals helps in designing systems that are stable and meet requirements.

Real Application Examples

1. Communication Systems

In digital communications, voice signals are converted into digital form, compressed, sent over a network, and then decoded back into voice. All of these stages involve signal processing systems.

2. Image Processing

Digital images are two-dimensional signals. Processes such as image enhancement, facial recognition, or compression (such as JPEG) are applications of the concept of signals and systems.

3. Automatic Control Systems

In controlling a motor or robot, signals from sensors are sent to a control system that processes them and gives output signals to the actuators. The analysis of these systems relies heavily on dynamic systems theory.

4. Electronics and Filters

The design of filter circuits (RC, RLC) uses the Laplace transform to understand the frequency response of the system and filter the signal as needed (low-pass, high-pass, band-pass).

Challenges in Learning Signals and Systems

Many electrical engineering students find the subject very mathematical. It requires a deep understanding of calculus, linear algebra, and mathematical transformations. In addition, visual interpretation of signals and systems requires intuition that develops over time.

However, with practice and real-world case studies, the subject can be very interesting and insightful into how the digital world works behind the scenes.

Tips for Understanding Signals and Systems

- Start with Visualization: Use software such as MATLAB or Python (NumPy & Matplotlib) to visualize signals and system responses.

- Understand Concepts, Not Just Formulas: Focus on why and how the system works, not just memorizing equations.

- Use Analogies: For example, LTI systems can be analogized to springs and dampers in physics to understand system responses.

-Practice Problems: Signals and systems are very suitable for problem-based and case-based learning.

- Follow Videos and Simulations: Many platforms such as YouTube, Coursera, or edX provide more intuitive and interactive explanations.