Definition of Signals | Digital Signal Processing - Electronics and Communication Engineering (ECE) PDF Download

What is a Signal?

• Anything that carries information can be called a signal. It can also be defined as a physical quantity that varies with time, temperature, pressure, or with any independent variables such as speech signal or video signal.
• The process of operation in which the characteristics of a signal (Amplitude, shape, phase, frequency, etc.) undergoes a change is known as signal processing.

Note: Any unwanted signal interfering with the main signal is termed as noise. So, noise is also a signal but unwanted.

According to their representation and processing, signals can be classified into various categories details of which are discussed below.

Continuous Time Signals

• Continuous-time signals are defined along a continuum of time and are thus, represented by a continuous independent variable. Continuous-time signals are often referred to as analog signals.
• This type of signal shows continuity both in amplitude and time. These will have values at each instant of time. Sine and cosine functions are the best example of Continuous time signal.

Continuous Time Signal

• The signal shown above is an example of a continuous-time signal because we can get value of signal at each instant of time.

Discrete-Time signals

• The signals, which are defined at discrete times are known as discrete signals. Therefore, every independent variable has distinct value. Thus, they are represented as sequence of numbers.
• Although speech and video signals have the privilege to be represented in both continuous and discrete time format; under certain circumstances, they are identical. Amplitudes also show discrete characteristics. Perfect example of this is a digital signal; whose amplitude and time both are discrete.

Example of a Discrete Time Signal

• The figure above depicts a discrete signal’s discrete amplitude characteristic over a period of time. Mathematically, these types of signals can be formularized as;
• 

Where, n is an integer.

• It is a sequence of numbers x, where n^th number in the sequence is represented as x[n].

Analog and Digital Signals

• Analog Signals: These are continuous signals that vary smoothly and can take on any value within a certain range. Examples include electrical voltages, sound waves, and temperature readings. Analog signals are represented as continuous waveforms and can have an infinite number of possible values.
• Digital Signals: These are discrete signals that have a finite number of defined values. Digital signals are typically represented using binary code (0s and 1s). They are commonly used in digital electronics, computers, and communication systems. Digital signals are more immune to noise and distortion compared to analog signals.

Real and Complex Signals

• Real Signals: Real signals are those that can be represented by a single real number at each point in time. These signals are physically measurable and correspond to real-world quantities. Examples include temperature, voltage, and pressure.
• Complex Signals: Complex signals, on the other hand, involve both a real part and an imaginary part. They are often used in complex analysis and are essential in the study of electrical circuits and electromagnetic fields. Complex signals are commonly encountered in AC (alternating current) analysis.

Deterministic and Random Signals

• Deterministic Signals: These are signals for which the values at any given time can be precisely predicted or determined based on a known mathematical function or algorithm. Examples include sine waves, square waves, and any signal with a well-defined pattern.
• Random Signals: Random signals, also known as stochastic signals, have values that are not predictable with certainty. They exhibit randomness or uncertainty in their values over time. Examples include noise in communication systems and random voltage fluctuations in electronic components.

Even and Odd Signals

• Even Signals: Even signals are symmetric with respect to the y-axis. Mathematically, f(-t) = f(t), meaning the signal is unchanged when reflected across the y-axis. An example of an even signal is a cosine wave.
• Odd Signals: Odd signals are antisymmetric with respect to the y-axis. Mathematically, f(-t) = -f(t), meaning the signal changes sign when reflected across the y-axis. An example of an odd signal is a sine wave.

Energy and Power Signals

• Energy Signals: These signals have finite energy over a specified time interval. They are typically associated with transient phenomena and can be visualized as impulses or pulses. Energy signals have zero power because they are of finite duration. Example: A unit step function.
• Power Signals: Power signals have finite power over time, and they exist over an extended time interval. These signals are often periodic or non-periodic and have non-zero power. Example: A continuous sine wave.

Periodic and Non-Periodic Signals

• Periodic Signals: These signals repeat their pattern or waveform at regular intervals. The fundamental property of a periodic signal is its period, which is the time it takes to complete one full cycle. Examples include sinusoidal waves and square waves.
• Non-Periodic Signals (Aperiodic): Non-periodic signals do not exhibit a repetitive pattern. They have no discernible period, and their behavior over time is not predictable based on regular intervals. Examples include transient signals and random noise.