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:
$s(x, t)$
(Here we use vector notation
$x$
to denote spatial coordinates). When you record someone
talking, you are evaluating the speech signal at a particular
spatial location,
$x_{0}$ say. An example of the resulting waveform
$s(x_{0}, t)$
is shown in
this figure.

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 [link], an image is shown, demonstrating that it (and all other images as well) are functions of two independent spatial variables.

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:
$s(x)=\left(\begin{array}{c}r(x)\\ g(x)\\ b(x)\end{array}\right)$.

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
$65$.
[link] shows the
international convention on associating characters with
integers.

00 | nul | 01 | soh | 02 | stx | 03 | etx | 04 | eot | 05 | enq | 06 | ack | 07 | bel |

08 | bs | 09 | ht | 0A | nl | 0B | vt | 0C | np | 0D | cr | 0E | so | 0F | si |

10 | dle | 11 | dc1 | 12 | dc2 | 13 | dc3 | 14 | dc4 | 15 | nak | 16 | syn | 17 | etb |

18 | car | 19 | em | 1A | sub | 1B | esc | 1C | fs | 1D | gs | 1E | rs | 1F | us |

20 | sp | 21 | ! | 22 | " | 23 | # | 24 | $ | 25 | % | 26 | & | 27 | ' |

28 | ( | 29 | ) | 2A | * | 2B | + | 2C | , | 2D | - | 2E | . | 2F | / |

30 | 0 | 31 | 1 | 32 | 2 | 33 | 3 | 34 | 4 | 35 | 5 | 36 | 6 | 37 | 7 |

38 | 8 | 39 | 9 | 3A | : | 3B | ; | 3C | < | 3D | = | 3E | > | 3F | ? |

40 | @ | 41 | A | 42 | B | 43 | C | 44 | D | 45 | E | 46 | F | 47 | G |

48 | H | 49 | I | 4A | J | 4B | K | 4C | L | 4D | M | 4E | N | 4F | 0 |

50 | P | 51 | Q | 52 | R | 53 | S | 54 | T | 55 | U | 56 | V | 57 | W |

58 | X | 59 | Y | 5A | Z | 5B | [ | 5C | \ | 5D | ] | 5E | ^ | 5F | _ |

60 | ' | 61 | a | 62 | b | 63 | c | 64 | d | 65 | e | 66 | f | 67 | g |

68 | h | 69 | i | 6A | j | 6B | k | 6C | l | 6D | m | 6E | n | 6F | o |

70 | p | 71 | q | 72 | r | 73 | s | 74 | t | 75 | u | 76 | v | 77 | w |

78 | x | 79 | y | 7A | z | 7B | { | 7C | | | 7D | } | 7E | ~ | 7F | del |

### Tập tin đính kèm

- lenamesh.eps
- speechexample.eps
- lena.eps