Signals Represent Information

Whether analog or digital, information is represented by the fundamental quantity in electrical engineering: the signal. Stated in mathematical terms, a signal is merely a function. Analog signals are continuous-valued; digital signals are discrete-valued. The independent variable of the signal could be time (speech, for example), space (images), or the integers (denoting the sequencing of letters and numbers in the football score).

Analog Signals

Analog signals are usually signals defined over continuous independent variable(s). Speech is produced by your vocal cords exciting acoustic resonances in your vocal tract. The result is pressure waves propagating in the air, and the speech signal thus corresponds to a function having independent variables of space and time and a value corresponding to air pressure:

(Here we use vector notation

to denote spatial coordinates). When you record someone talking, you are evaluating the speech signal at a particular spatial location,

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.

(a)
(b)

Color images have values that express how reflectivity depends on the optical spectrum. Painters long ago found that mixing together combinations of the so-called primary colors--red, yellow and blue--can produce very realistic color images. Thus, images today are usually thought of as having three values at every point in space, but a different set of colors is used: How much of red, green and blue is present. Mathematically, color pictures are multivalued--vector-valued--signals:

.

Interesting cases abound where the analog signal depends not on a continuous variable, such as time, but on a discrete variable. For example, temperature readings taken every hour have continuous--analog--values, but the signal's independent variable is (essentially) the integers.

Digital Signals

The word "digital" means discrete-valued and implies the signal has an integer-valued independent variable. Digital information includes numbers and symbols (characters typed on the keyboard, for example). Computers rely on the digital representation of information to manipulate and transform information. Symbols do not have a numeric value, and each is represented by a unique number. The ASCII character code has the upper- and lowercase characters, the numbers, punctuation marks, and various other symbols represented by a seven-bit integer. For example, the ASCII code represents the letter a as the number 97 and the letter A as 65. Table shows the international convention on associating characters with integers.

00nul01soh02stx03etx04eot05enq06ack07bel
08bs09ht0Anl0Bvt0Cnp0Dcr0Eso0Fsi
10dle11dc112dc213dc314dc415nak16syn17etb
18car19em1Asub1Besc1Cfs1Dgs1Ers1Fus
20sp21!22"23#24$25%26&27'
28(29)2A*2B+2C,2D-2E.2F/
300311322333344355366377
3883993A:3B;3C<3D=3E>3F?
40@41A42B43C44D45E46F47G
48H49I4AJ4BK4CL4DM4EN4F0
50P51Q52R53S54T55U56V57W
58X59Y5AZ5B[5C\5D]5E^5F_
60'61a62b63c64d65e66f67g
68h69i6Aj6Bk6Cl6Dm6En6Fo
70p71q72r73s74t75u76v77w
78x79y7Az7B{7C|7D}7E~7Fdel

ASCII Table The ASCII translation table shows how standard keyboard characters are represented by integers. In pairs of columns, this table displays first the so-called 7-bit code (how many characters in a seven-bit code?), then the character the number represents. The numeric codes are represented in hexadecimal (base-16) notation. Mnemonic characters correspond to control characters, some of which may be familiar (like cr for carriage return) and some not (bel means a "bell").

 

This textbook is open source. Download for free at http://cnx.org/contents/778e36af-4c21-4ef7-9c02-dae860eb7d14@9.72.

 
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