2.   La representación de fenómenos: formatos

2.1.           Definiciones

Un formato, según el diccionario de FatorGIS, es la “forma por la cual, los datos son organizados sistemáticamente para su procesamiento y transmisión”.   Los datos son principalmente imagenes, sonidos, e información alfanumérica y para cada clase de dato existen diferentes formatos en los que se puede organizar para su procesamiento y/o transmisión

Los formatos son principalmente de dos clases: el formato análogo y el formato digital; dentro de cada uno de estos formatos existen divisiones que crean las distinciones particulares.

Por ejemplo, cuando se habla de formato “carta”, se refiere a un formato en papel (análogo), con unas dimensiones de 216 X 279 mm. o cuando se habla de formato de “sobre monarca” se habla de un formato análogo de 98 X 190 mm. Otro ejemplo de formato análogo es un disco de acetato (LP) medio que se usó por mucho tiempo como la mejor manera de almacenar sonidos.  También se clasifican dentro del formato análogo las fotografías convencionales sobre papel fotográfico o transparencia.

Los formatos digitales, son la forma de representar elementos, utilizando sistemas computarizados; y como sabemos, estos en su mas mínima expresión se reducen a secuencias de unos y ceros que combinados representan códigos que pueden ser interpretados como una letra, como un color, una frecuencia, etc.

Dentro de los formatos digitales se encuentran: Formatos gráficos como BMP, JPG, GIF, etc., formatos tipo texto, como: TXT, DOC, PDF, HTML etc., formatos de sonido, como: WAV, Real Audio ó MP3, formatos de video, como, AVI y MPEG, entre muchos otros.

Los fenómenos del mundo real son en su gran mayoría de naturaleza continua y los formatos son solo medios de representarlo aunque tanto los formatos análogo como digital son simples aproximaciones éste. El grado de exactitud o aproximación entre la representación y la realidad depende tanto de la escala utilizada como del tipo de formato.

Los formatos que más nos interesan en este curso son aquellos que son aplicables a los SIG, que por ser sistemas computarizados, utilizan principalmente formatos digitales o formatos análogos convertidos a digital. A continuación veremos como se realiza esta conversión y cuanta información del mundo real se pierde o se deja de incluir en el formato digital.

2.2.           Conversión de análogo a digital

Para simplicidad se presenta el ejemplo utilizando una onda de sonido ya que ésta solo tiene una dimensión, a diferencia de las imagenes que presentan al menos cinco variables aunque el concepto detrás de la conversión es el mismo. En el capitulo 7 se hablará de imagenes y en el numeral 7.2.5. se describirá este proceso de conversión de análogo a digital de una imagen al entender el funcionamiento de los sensores remotos y las cámaras digitales.

2.2.1.                    Analog Wave

What is it that the needle in Edison's phonograph is scratching onto the tin cylinder? It is an analog wave representing the vibrations created by your voice. For example, here is a graph showing the analog wave created by saying the word "hello":

This waveform was recorded electronically rather than on tinfoil, but the principle is the same. What this graph is showing is, essentially, the position of the microphone's diaphragm (Y axis) over time (X axis). The vibrations are very quick -- the diaphragm is vibrating on the order of 1,000 oscillations per second. This is the sort of wave scratched onto the tinfoil in Edison's device. Notice that the waveform for the word "hello" is fairly complex. A pure tone is simply a sine wave vibrating at a certain frequency, like this 500-hertz wave (500 hertz = 500 oscillations per second):

You can see that the storage and playback of an analog wave can be very simple -- scratching onto tin is certainly a direct and straightforward approach. The problem with the simple approach is that the fidelity is not very good. For example, when you use Edison's phonograph, there is a lot of scratchy noise stored with the intended signal, and the signal is distorted in several different ways. Also, if you play a phonograph repeatedly, eventually it will wear out -- when the needle passes over the groove it changes it slightly (and eventually erases it).

2.2.2.                    Digital Data

In a CD (and any other digital recording technology), the goal is to create a recording with very high fidelity (very high similarity between the original signal and the reproduced signal) and perfect reproduction (the recording sounds the same every single time you play it no matter how many times you play it).

To accomplish these two goals, digital recording converts the analog wave into a stream of numbers and records the numbers instead of the wave. The conversion is done by a device called an analog-to-digital converter (ADC). To play back the music, the stream of numbers is converted back to an analog wave by a digital-to-analog converter (DAC). The analog wave produced by the DAC is amplified and fed to the speakers to produce the sound.

The analog wave produced by the DAC will be the same every time, as long as the numbers are not corrupted. The analog wave produced by the DAC will also be very similar to the original analog wave if the analog-to-digital converter sampled at a high rate and produced accurate numbers.

You can understand why CDs have such high fidelity if you understand the analog-to-digital conversion process better. Let's say you have a sound wave, and you wish to sample it with an ADC. Here is a typical wave (assume here that each tick on the horizontal axis represents one-thousandth of a second):

When you sample the wave with an analog-to-digital converter, you have control over two variables:

·        The sampling rate - Controls how many samples are taken per second

·      The sampling precision - Controls how many different gradations (quantization levels) are possible when taking the sample

In the following figure, let's assume that the sampling rate is 1,000 per second and the precision is 10:

The green rectangles represent samples. Every one-thousandth of a second, the ADC looks at the wave and picks the closest number between 0 and 9. The number chosen is shown along the bottom of the figure. These numbers are a digital representation of the original wave. When the DAC recreates the wave from these numbers, you get the blue line shown in the following figure:

You can see that the blue line lost quite a bit of the detail originally found in the red line, and that means the fidelity of the reproduced wave is not very good. This is the sampling error. You reduce sampling error by increasing both the sampling rate and the precision. In the following figure, both the rate and the precision have been improved by a factor of 2 (20 gradations at a rate of 2,000 samples per second):

In the following figure, the rate and the precision have been doubled again (40 gradations at 4,000 samples per second):

You can see that as the rate and precision increase, the fidelity (the similarity between the original wave and the DAC's output) improves. In the case of CD sound, fidelity is an important goal, so the sampling rate is 44,100 samples per second and the number of gradations is 65,536. At this level, the output of the DAC so closely matches the original waveform that the sound is essentially "perfect" to most human ears.