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Four - PULSE CODE MODULATION

  The language of truth is simple.
Seneca
 

The purpose of a communication system is to move some form of information accurately from one point in space or time to another point in space or time. This task often requires changing the means of communication to one which is more suitable for the purpose. For example, voice communication from one individual to another is the process of (1) coding into words that which is in the mind of the sender, (2) coding the words into nerve pulses (3) sending the nerve pulses from the sender's brain to his organs of speech, (4) transmitting the words via sound waves to the ear of the receiver, (5) coding the words into nerve pulses (6) sending the nerve pulses to the receiver's brain, and (7) translating the words into ideas which may be close to what the sender intended them to be. This system has worked in varying degrees for senders and receivers who are in close proximity to one another. Yet, it is inadequate for communication at greater distances.

Smoke signals were an early form of pulse coding messages for long distance communication, with each puff of smoke acting as a pulse and a lack of a puff acting as a lack of a pulse. This was a binary system, meaning it had two possible states: (1) puff and (2) no puff. Later, Samuel Finley Breese Morse invented the telegraph and the code which was named after him. Morse code was also a binary system in which there were either short pulses (dots) or long pulses (dashes). Each coded binary system was able to transmit only a small amount of information in any particular length of time. However, what it did transmit was relatively coherent and would tolerate extensive interference before the information was too distorted to be understood.

When teletype was invented, it used essentially the same principle but was much faster. The teletype used five positions in time as a coded "frame." Each of the five positions could either have a pulse or not have a pulse, so it was a binary system (with only two possible states) used to denote one of 32 characters (2⁵ = 32) with each frame. This is an oversimplified explanation, but will serve the purpose of explaining the principle involved.

Early types of electronic audio communication were what we call "analog" systems. A microphone translated the energies of the sound waves into electrical energy so that the crests of the waves caused more electrical amplitude than the troughs. This wave form was added to another electrical wave form of constant frequency which "carried" the information-containing wave form. This total wave form was transmitted via wire or "ether" to a distant device which removed the constant-frequency "carrier" wave, leaving only the information-containing wave portion to be translated back into sound waves via speakers or earphones.

During the time in which the total signal was being transmitted, interference in the form of lightning, power lines, or other communication devices would often either alter or obliterate it. This was a major problem in analog wave forms of communication. The form of the sound wave was never actually changed as it passed through the various transformations of the analog system and any sudden alteration in its amplitude (due to interference) changed its character to one which often proved to be unrecognizable.

Ideally, a system of audio communication should have the form of a binary code with the information-carrying ability of the analog system. Furthermore, it should be quickly repeatable so that any repetition which was altered by interference could be checked against another repetition and the better repetition used as the correct version. These were the considerations when our present-day digital communications systems were developed.

"Pulse code" refers to the system having a binary type of code in which a pulse is either present or not present. This meant that there were two possible states at any point in time. Where the analog systems relied upon literally an infinity of amplitudes to create an infinity of possible states for any point in time, the digital systems relied only upon two possible states. The two-state systems could be repeated to be certain that the correct state was being received. As long as it was repeated an odd number of times, the receiving mechanism could "vote" for the correct state for any given point in time without a tie-vote being possible.

For instance, if we assume that a state is repeated five times, then a majority of three of the five repetitions, indicating that a pulse was present would be sufficient for the "vote" to swing in that direction. The receiving device would accept this majority decision as being correct. Of course, should four of the five agree or should the "vote" be unanimous, so much the better.

This "voting" was - and still is - accomplished by means of a cut-off point for pulse amplitude. If the pulse amplitude is below the cut-off point for any particular repetition, then whatever amplitude is present is "voted" to be "noise" as opposed to the presence of a pulse. And if the pulse amplitude is above the cut-off point for any particular repetition, then that amplitude is "voted" to be the actual presence of a pulse. The cut-off amplitude is equal to half of the average amplitude of the known pulses (the synchronizing pulses).

Two defining characteristics of pulse code modulation are (1) use of a binary state, and (2) repetition of each state. These have been mentioned already. The next defining characteristic is the "code." If we are sending music, for instance, the music consists of a total wave form. By sampling a tiny instant (say one millionth of a second) of this wave form, we can code it into a "frame."

In reality, the points on the music wave form can be divided into an infinite number of classifications for height. However, our code must have a finite number of classifications. So we must limit the number of classifications for possible heights to what is reasonable for what we are attempting to accomplish.

A frame consists of a number of points in time, each of which would have one of two possible states (pulse present or pulse not present). If we use seven points in time for each frame, we have two to the seventh power ( 2⁷ ) possible heights for each sampled point on the music wave form. This comes to 128 possible classifications for height, which has proved to be sufficient for the range of the human voice. For a greater range, the number of possible heights can be doubled by adding another point in time to the frame. Each time we add a point in time to a frame, we double the number of possible heights for a point in the music wave form. If each frame were to have only one point in time, there would be only two levels possible for a point on the music wave form. If there were to be two points in time per frame, the number of possible heights would be four. For three points in time per frame, the possible heights would be eight. Another point in time gives us sixteen possible heights - and so on.

Each subsequent frame is a code for the classification of height for each subsequent sampled point on the music wave form. For instance, we might sample a point on the wave form in the space of one microsecond (one millionth of a second), wait for thirty microseconds, sample another point for the space of a microsecond, and so on. Each sample is given the nearest possible classification for height and then coded into a frame.

Each point in time on a frame is a place where a pulse can be present or not be present. There are 128 different combinations of present versus not-present for a seven-point frame. But each frame must be separated from the other frames and each must be given a distinct time in which to appear relative to the other frames, so a "synchronizing" pulse is needed, between each two frames, which is always present. This means that, in reality, each frame has one more point in time than the number needed to show the code for height samplings.

We prefer to have at least five repetitions of each sampling. This, along with the other considerations, means that our sampling must be done very quickly and that each time-point on a frame must be very short. Years ago, we did not have the technology for such speed, but today such speed is commonplace, so we can and do use pulse code modulation in telephone conversations, satellite communications, space probe communications, and other aspects of our daily lives. Sometimes only elements of PCM (pulse code modulation) are used. Basically, everything that we think of as digital is using at least part of PCM technology.

PCM can be adapted to many mediums. Wires, fiber optics (glass filaments), local "ether", or the "ether" in deep space. It can be used slowly if speed is not possible. It has only one basic
 

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