ANALOG TO DIGITAL: THE NEED
ANALOG TO DIGITAL: THE NEED
We consider a basic problem associated with the transmission of a signal over a noisy communication channel.
For the sake of being specific, suppose we require that a telephone conversation be transmitted from New York to Los Angeles.
If the signal is transmitted by radio, then, when the signal arrives at its destination, it will be greatly attenuated and also combined with noise due to thermal noise present in all receivers , and to all manner of random electrical disturbances which are added to the radio signal during its propagation across country.
(We neglect as irrelevant, for the present discussion, whether such direct radio communication is reliable over such long channel distances.)
As a result, the received signal may not be distinguishable against its background of noise .
The situation is not fundamentally different if the signal is transmitted over wires.
Any physical wire transmission path will both attenuate and distort a signal by an amount which increases with path length.
Unless the wire path is completely and perfectly shielded, as in the case of a perfect coaxial cable, electrical noise and crosstalk disturbances from neighboring wire paths will also be picked up in amounts increasing with the path length.
In this connection it is of interest to note that even coaxial cable does not provide complete freedom from crosstalk.
External low-frequency magnetic fields will penetrate the outer conductor of the coaxial cable and thereby induce signals on the cable.
In telephone cable, where coaxial cables are combined with parallel wire signal paths, it is common practice to wrap the coax in Permalloy for the sake of magnetic shielding.
Even the use of fiber optic cables which are relatively immune to such interference, does not significantly alter the problem since receiver noise is often the noise source of largest power.
One attempt to resolve this problem is simply to raise the signal level at the transmitting end to so high a level that, in spite of the attenuation, the received signal substantially overrides the noise.
(Signal distortion may be corrected separately by equalization.)
Such a solution is hardly feasible on the grounds that the signal power and consequent voltage levels at the transmitter would be simply astronomical and beyond the range of amplifiers to generate, and cables to handle.
For example, at 1 kHz, a telephone cable may be expected to produce an attenuation of the order of 1 dB per mile.
For a 3000 mile run, even if we were satisfied with a received signal of 1 mV, the voltage at the transmitting end would have to be 10147 volts.
An amplifier at the receiver will not help the above situation, since at this point both signal and noise levels will be increased together.
But suppose that a repeater (repeater is the term used for an amplifier in a communications channel) is located at the midpoint of the long communications path.
This repeater will raise the signal level; in addition, it will raise the level of only the noise introduced in the first half of the communications path.
Hence, such a midway repeater, as contrasted with an amplifier at the receiver, has the advantage of improving the received signal-to-noise ratio.
This midway repeater will relieve the burden imposed on transmitter and cable due to higher power requirements when the repeater is not used.
The next step is, of course, to use additional repeaters, say initially at the one-quarter and three quarter points, and thereafter at points in between.
Each added repeater serves to lower the maximum power level encountered on the communications link, and each repeater improves the signal-to-noise ratio over what would result if the corresponding gain were introduced at the receiver.
In the limit we might, conceptually at least, use an infinite number of repeaters.
We could even ad just the gain of each repeater to be infinitesimally greater than unity by just the amount to overcome the attenuation in the infinitesimal section between repeaters.
In the end, we would thereby have constructed a channel which had no attenuation.
The signal at the receiving terminal of the channel would then be the unattenuated transmitted signal.
We would then, in addition, have at the receiving end all the noise introduced at all points of the channel.
This noise is also received without attenuation, no matter how far away from the receiving end the noise was introduced.
If now, with this finite array of repeaters, the signal-to-noise ratio is not adequate, there is nothing to be done but to raise the signal level or to make the channel quieter.
The situation is a is actually somewhat more dismal than has just been intimated, since each repeater (transistor amplifier) introduces some noise on its own accord.
Hence, as more repeaters are cascaded, each repeater must be designed to more exacting standards with respect to noise figure.
The limitation of the system we have been describing for communicating over long channels is that once noise has been introduced any place along the channel, we are “stuck” with it.
If we now were to transmit a digital signal over the same channel, we would find that significantly less signal power would be needed in order to obtain the same performance at the receiver.
The reason for this is that the significant parameter is now not the signal-to-noise ratio but the probability of mistaking a digital signal for a different digital signal.
In practice we find that signal-to-noise ratios of 40-60 dB are required for analog signals while 10-12 dB are required for digital signals.
This reason and others, to be discussed subsequently, have resulted in a large commercial and military switch to digital communications.
( ANALOG TO DIGITAL )
Multiplying of two 8 bit number–
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