STATISTICS OF THLEVISION SIGNALS 



759 



PROBABILITY DISTRIBUTIONS 



A i)i-()ba!nlity (list ribut ion of amplitiulcs is generally shown as a plot 

 of probability density' versus signal amplitude. Probability density, say, 

 corresponding to amplitude Xi , is the probability of finding the signal 

 amplitude between .ri and Xi + dx, divided by the differential amplitude 

 increment dx. Conversely, the probability of finding the signal ampli- 

 tude between .Ti and xy + dx is given by ])(xi)dx, p(x) being the pi'oba- 

 bility density corresponding to amplitude x. 



If a cathode-ray spot is deflected, say horizontally, by the signal in 

 (luestion, its average dwell time at any point is directly proportional to 

 the corresponding probability density. In the optical system shown in 

 Fig. 8, a cylindrical lens maps each point into a vertical line which is 



UNDEFLECTED 

 IMAGE ""n 



DEFLECTED 

 /IMAGE 



"^ LIGHT-PROOF 

 ■"ENCLOSURE 



Fig. 8 — Basic arrangement of probabiloscope. 



\HIGH 

 TRANSMISSION 



then tapered in intensity by an optical density wedge before reaching a 

 high-contrast photographic film. Depending on the dwell time at any 

 amplitude level, the corresponding tapered line has enough average 

 intensity to blacken the film up to a certain level. This level is pro- 

 portional to log p(x), since the density wedge is tapered exponentially 

 so that the intensity of each tapered line of light reaching the film 

 diminishes, say, by a factor of ten for each inch we travel up the line. 

 The film in effect traces out a contour of constant exposure. 



Two or three iterated photographic printings increase the effective 

 gamma sufficiently to yield a contour of ample sharpness. This contour 

 is then changed to a sharp line by a simple dark room trick: while the 

 film is in the development tray, already fully developed, it is momentarily 

 exposed to light. The blackened portion of the film is unaffected, the 

 clear portion is fully blackened, while the transition contour, being 

 partly opaque, is not fully blackened. By printing from this film we then 



