TARGET RESOLUTION: AMBIGUITY FUNCTIONS

By John P. Flight


Preface
The increasingly complex man-machine interactions of modern computer-based information systems have given a forced impetus to integrating previously unrelated pools of knowledge. What proportion of people anywhere have really learned to see? How many have learned how to hear? It is my hope that the way I have combined the two fields makes their joint study comprehensible and easy to grasp.

Miscellaneous advances
Historically, the cathode-ray tube has found its greatest application in the display of information derived from radar equipment; in recent years, this use has been expanded to include the display of computer-processed information. In addition, certain maps and satellite pictures are dispatched by HF radio facsimile, and by various special circuits, to ships at sea and to foreign countries. This is accomplished by multi-level signalling.

The data collected by the 673 is methodically decoded, analyzed, and computer-processed for use in chart (weather map) production. The discussion to this point has considered a situation in which the coupling strength (and hence the nonlinearity) is not too large and the dynamics are represented by invertible circle maps.
Much of it involves enormous computation volume – detailed sea and swell analyses and forecasts, mixed layer depth computations, large-scale atmospheric flow patterns on a hemispheric scale, and detailed predictions of weather conditions at a particular time and a particular place. These computer predictions determine equipment settings for submarine detection.


Problem checking
An ideal circulator is a device having three or more matched ports in which power incident on any port is conducted out of the next port in one particular direction with no loss and with no coupling to any other port. Even though the configurations may look different, the principles behind them seem to be recurring (Fig. 1). This latter innovation has made it possible to cut out some of the redundancy in transmission mileage.

 
 
 

Fig. 1 : Mit hilfe dieser platte kann die rumpelgeraeusch- und die rumpelfremdspannung von schallplatten-laufwerken ermitteld werden.
(Mess-schallplatten zum ermitteln der tonhoehenschwankungen (gleichlauf)
gibt es fuer 45 U/min mit 17 cm durchmesser und fuer 33U/min mit 30 cm durchmesser).

 
 
 

The pen moves back and forth along a straight arm, its deflection being proportional to one voltage. The arm itself moves in a perpendicular direction positioned by the second voltage.

The record of v03 vs. v02 (i.e. the result of the so called circle test) is a spiral whose exaggerated form is shown in Fig. 2a. To understand the effects of perturbation, it is important to understand the changes in dynamics (bifurcations) that arise as parameters in the circle map are varied. Similar conditions exist, incidentally, when phonograph records are cut.

Consider an array of N equally spaced elements about a circle of radius a in the xy plane of Fig. 2b. In practice, this is achieved by using two potentiometers which are ganged- i.e., mounted on a common shaft- and using a motor to turn this shaft. Thus the wipers on both pots follow every change in x, and the output from pot 2 is proportional to xy.
As shown in Fig. 2c, the actual output is xy/100.

 

 
 

Fig. 2a

Fig. 2b

Fig. 2c

 
 


One way to generate a three-dimensional wave is to translate the spiral waves perpendicular to the plane (Fig. 3)

 
 

Fig.3

 
 


In three dimensions, still more complex geometries called organizing centers are theoretically possible, but they are extremely difficult to observe experimentally.
Only questions of morality seem to limit the number of people engaged in the development of the field.

Delay distortion
Let us consider the dynamics in the neighborhood of steady states in two dimensions.
Unfortunately for measuring purposes, the earth’s speed of revolution can vary by as much as 3.10-9 and is also constantly decreasing because of friction loss. But our bodies are also full of microscopic processes, many of which are like vibrations. Many phenomena of physiological acoustics, to mention only one example, are the results of such phenomena. Vibrational massage is an example of this.

Resume
The chief limiting factor of multi-level schemes in general is that the greater the number of levels, the more critical becomes the task of discriminating between one level and the next at the receiver. We will not bother discussing these or other noises, but it should be pointed out that they exist and cause plenty of trouble in radar performance.

August 5, 1957