Back to Analog and Digital as Fundamental Concepts

The Universe is essentially continuous. That is, change exists over a continuum from zero to the end of some finite range (perhaps even to the end of some infinite range).

We generally experience the universe as continuous. We assume and accept that there are infinite numbers of hues and intensities within the range of colors we can see (detect). We assume and accept that there are infinite numbers of pitches and volumes of sounds within the range of sounds we can hear (detect). We assume that the progression in nature from one frequency to another is continuous, not incremental.

Analog media are designed to track continuous changes.

Questions: Are we unlimited in our ability to detect changes, incremental changes, in waveforms? Can we detect any amount of shift in frequency of a sound wave, or any difference in brightness or color of a light source, no matter how small?

Digital technology is betting that the answer is, "No."

Remember MCI commercial:

Excercise:

• Look through an open window. Use it as frame.
• Describe what you hear and see within the frame.
• Can you think of ways of measuring what you hear and see?
• To what elements of the scene in the frame can you assign value?
• Suppose you wish to use your measurements to reproduce the scene in another location. What can you say about the number of measurements you take and the accuracy of your subsequent reproduction?
• Pick the smallest element of the scene. What measurements could you make to help you describe it later?
• How is your measurement complicated by changes in the scene (a bird flies past the window)?
• What other things change in your scene? How fast do they change?

This is intended to be a very frustrating exercise. In fact, it is an impossible one. Almost any scene from almost any window would include a varying number of elements of varying size, shape, texture, color, state of motion, etc. There would be varying degrees of light and sound (odor and vibration too) emanating from differing parts of the scene at the same time. Complete measurement would require an infinite number of operations. It is impossible. But we try anyway. We have unlimited demands that we try to meet with limited technology. How do we try?

Digital Media

Assume we have the devices to measure at least some of the scene. We have to decide how much detail we need. The tree has green leaves on it. Are they the same color? How many shades of green are there? Eight, sixteen, thirty-two, two hundred fifty six, millions? The real question is how many will we settle for as "good enough" for our purposes. That bird over there; how many frequencies can he generate in calling? How many levels of loudness does he use? Dozens, thousands, millions? How many do we hear? Suppose he moves a few feet away?

No free lunch.

Make some decisions. What is essential? What is not? What can we live with? What are the limits of our capacity to make the measurements?

Binary numbers

Machines like computers, digital audio recorders, digital video cameras, and other devices handle all of the measurements we are talking about.

Machines do not actually handle complex decimal numbers like 3,457,077 (one of our shades of green).

Machines use simple forms of numbers that correspond to the values of things like: "on/off," "present/absent," or "yes/no."

Numerically, they use ones and zeroes.

Question: How many values can be represented a single "1 or 0" choice?

Question: How many values can be represented by two "1 or 0" choices?

Question: How many values can be represented by three "1 or 0" choices?

See a pattern?

Normally (using the decimal system) we humans can represent ten different values with a single digit (0-9), a hundred values with two digits (0-99), a thousand values with three digits (0-999), etc.

Digital devices like computers, DVD, DAT, CD use a binary system that requires more digits to represent the same number of values. Three digits can only represent eight values (0-7)

Consider the number 347. We know it contains:

How many tens to the zero power (units)?

How many tens to the first power (tens)?

How many tens to the second power (hundreds)?

7 ones + 4 tens + 3 hundreds = 347

Binary numbers contain twos instead of tens.

Consider the binary number 110. We know it contains:

How many twos to the zero power? None (zero)

How many twos to the first power? One (two)

How many twos to the second power? One (four)

Add them up, you get six. Binary 110 is equivalent to decimal 6.

Time to make some decisions about quality

Consider the question about the number of shades of green in a leaf. Better yet, consider how many colors of all hues there are in the leaf. Assume an infinite number in reality. How many of them do you need to capture in order to do the job to your satisfaction? Could you live with 8 colors, 32 colors, 256 colors or would you require millions of colors?

Notice the differences between the top turtle picture using thousands of colors (and 3943 Kb of space),the second turtle picture using 256 colors (and only 1314 Kb of space), and the bottom picture using only 16 colors (124 Kb of space). The frog also uses 256 colors but since it is a drawing done with 256 colors the representation looks true to the original.

Click on the appropriate link to see a larger version of the picture. The differences in color may not be so obvious with the smaller pictures. Why not?

Lunch anyone? By the way, did you notice which images loaded fastest?

Question: How many binary digits are required to represent 256 values of color?

Answer(or at least a hint): Think about how the system works. 256 values means you have to have numbers ranging from 0 - 255. Zero is a value. Just start adding 1 + 2 + 4 + 8 +16 and so on until you get a number big enough to contain 255. The number of operations you performed is the answer to the question.

Okay. It takes eight digits or eight bits to do the job. Now when you see something in digital system that says 8-bits, you know it can represent 256 values of some sort (colors, audio, etc.)

Question: Suppose you double the number of bits to 16. Does that double the number of values you can represent?

Answer: :) Its on you.

The bottom line here is the more detail you want to convey, the more numbers you have to use. The more numbers you have to use, the faster your device has to be in order to process the numbers (i.e. make the recording or take the picture). The faster your device has to be, the deeper your pockets have to be in order to pay for the speed. The deeper your pockets have to be, . . . . . and on into some deeper social commentary.

Lunch anyone?

1. The doubling of values shows up again and again in media work. Get used to seeing the progression; 2, 4, 8, 16, etc. It shows up in optics, photography, audio, computer specifications, lighting, and almost every where else.

2. Decisions about quality (resolution) are rarely dependent on a single factor. The limits of the technologies, the limits of the producer (finances and the "vision thing"), the limits of the audience (perceptual, financial, and aesthetic) and the complexity of the subject all come into play. Your job is to better understand the interplay.

Doing the MCI thing: Digitizing Information

Sampling: Remember that window you were looking out of? What about that bird that flew by? Any chance you could have missed it?

Sampling is the periodic measurement of some changing phenomenon. It is like a series of snapshots taken for purposes of approximating an ongoing event. How often or how rapidly one samples depends upon how rapidly the subject is changing and how much information one wishes to get about the change.

Sampling frequency: This is determined by the highest rate of change in the subject. In general, sampling must be at twice the maximum rate of change or twice the highest frequency of the subject. Known as the Nyquist sampling theorem. If you blink too slowly, you will miss the bird. If you want to miss none of the 16KHz audio, you must sample at 32KHz minimum.

Sampling depth: How much detail do you wish to capture? Is 256 levels enough (8-bit), or do you need thousands or millions of numbers to represent your subject (16, 24, or 32-bit)?

CD audio:

44,000 samples per second, 16 digits per sample, 700,000 digits (bits) per second of sound.

@74 minutes per CD, 3,100,000,000 bits of information per disc. 10 MB per minute of audio

Digital video:

30,000,000 bits/sec for a minimally acceptable picture.

100 MB/second at 128 levels of resolution (brightness and hue). This is not HDTV.

After sampling, a form of measuring, the digitized information must be rounded off to a usable number and coded in a way understandable to the system. The coding, like any coding can be arbitrary as long as the same code is used throughout the system. Its like language.