Signals Represent Information

The Fundamentals of Analog and Digital Signals in Electrical Engineering

In the realm of electrical engineering, signals serve as the fundamental building blocks for representing and transmitting information. Signals can be categorized as analog or digital, depending on their underlying characteristics. In this article, we will explore the nature of analog and digital signals, their representations, and their significance in various domains. Understanding these concepts is essential for anyone venturing into the field of electrical engineering.

Analog Signals

Analog signals are characterized by their continuous nature, meaning they are defined over continuous independent variables. Consider speech as an example. When we speak, our vocal cords generate acoustic resonances in the vocal tract, resulting in the propagation of pressure waves in the air. The speech signal can be represented as a function that accounts for spatial coordinates (denoted by vector notation) and time, with the value corresponding to air pressure. When we record speech, we capture the signal’s evaluation at a specific spatial location. Figure 1 illustrates an example waveform of a recorded speech signal. $s\left( {\textbf{\textit{x}},t} \right)$ (Here we use vector notation ) $\textbf{\textit{x}}$ denote spatial coordinates). When you record someone talking, you are evaluating the speech signal at a particular spatial location, $\textbf{\textit{x}}_{0}$ say. An example of the resulting waveform is shown in Figure 1.

Speech Example

Figure 1. A speech signal’s amplitude relates to tiny air pressure variations. Shown is a recording of the vowel “e” (as in “speech”).

Photographs are static, and are continuous-valued signals defined over space. Black-and-white images have only one value at each point in space, which amounts to its optical reflection properties. In Figure 2, an image is shown, demonstrating that it (and all other images as well) are functions of two independent spatial variables.

Figure 2. On the left is the classic Lena image, which is used ubiquitously as a test image. It contains straight and curved lines, complicated textures, and a face. On the right is a perspective display of the Lena image as a signal: a function of two spatial variables. The colors merely help show what signal values are about the same size. In this image, signal values range between 0 and 255; why is that?

Color Images: Multivalued Analog Signals

Color images, on the other hand, introduce a multivalued aspect to analog signals. These images express how reflectivity depends on the optical spectrum. By combining different amounts of primary colors (e.g., red, green, and blue), intricate and realistic color images can be created. Mathematically, color images are treated as vector-valued signals, with each point in space having three values denoting the presence of red, green, and blue components.

Discrete Variables in Analog Signals

In certain scenarios, analog signals can depend on discrete variables instead of continuous ones. For example, temperature readings taken at hourly intervals possess analog (continuous) values, but their independent variable is essentially an integer sequence. These discrete variables provide valuable information for analysis and interpretation in various applications.

Digital Signals

Digital signals are characterized by their discrete values and integer-valued independent variables. The term “digital” signifies the representation of information using numbers and symbols. Computers heavily rely on digital signals to manipulate and transform information. Symbols, such as characters typed on a keyboard, are represented by unique numbers. The ASCII character code, for instance, associates upper- and lowercase letters, numbers, punctuation marks, and various symbols with seven-bit integers. Table X showcases the international convention for character-to-integer associations according to the ASCII code.

nul

soh

stx

etx

eot

enq

ack

bel

dle

dc1

dc2

dc3

dc4

nak

syn

etb

car

sub

esc

“

‘

(

)

–

;

[

]

‘

{

}

del

Analog and digital signals serve as the foundation of information representation in electrical engineering. Analog signals, with their continuous nature, provide a comprehensive representation of real-world phenomena, whether in speech, images, or other sensory experiences. On the other hand, digital signals, with their discrete values, enable efficient manipulation and processing of information in modern computing systems. By understanding the characteristics and representations of both analog and digital signals, electrical engineers can design innovative solutions, create advanced communication systems, and unlock the potential for technological advancements across various industries.