752 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1952 



picture elements per line of the standard television raster. Each dot can 

 have, say, 100 distinguishable brightness values in a good-quality pic- 

 ture. The rnimbei- of possible combinations is therefore approximately 

 ^qq2io.o()o ^^. ^q42o,ooo ^^ ^j^g ^^^^^^ j.^^^ ^f 3Q frames per second it would 



take approximately jq'*'^'^^^ years to transmit all these "pictures," which 

 our present television system is fully prepared to transmit! The vast 

 majority of these "pictures" will, of course, never be transmitted in this 

 age because the average picture statistics virtually preclude the pos- 

 siblity of their occurrence. 



If all of the redundancy alluded to in the preceding paragraph were 

 to be expressed in terms of statistics, the array of data would be stagger- 

 ing.* Redundancy encompassing even a small part of a single frame 

 implies statistics of enormously high order because of the large number 

 of possible past histories. The initial attention should therefore be 

 focused on local redundancy, encompassing only a few adjoining pic- 

 ture elements. Accordingly, measurements have been made of the fol- 

 lowing statistical quantities. 



1. Simple prohahility distribution of signal amplitudes corresponding 

 to picture brightness. This encompasses only a single picture element, 

 revealing the relative probabilities of this or any element's assuming 

 the various possible brightness values, in the absence of any past-his- 

 tory information. 



2. Simple probability distribution of error amplitudes resulting from 

 linear prediction of television signals. Only the simplest type of linear 

 prediction is considered here, so-called previous- value prediction, which 

 predicts each picture element to have the same brightness value as the 

 preceding one. The prediction error signal is simply the difference be- 

 tween the picture signal and a replica delayed by one Nyquist interval 

 (one-half the reciprocal bandwidth or the time interval corresponding 

 to the spacing between picture elements). The distribution of this error 

 signal encompasses two picture elements (past history of one element) 

 and therefore is a condensed version of the family of first-order joint 

 probability distributions. 



3. Autocorrelation of typical pictures. This statistical quantity is an 

 even more streamlined version of various families of different-order 

 joint probability distributions. Each family corresponds to just a single 

 point on the autocorrelation curve; the ordinates of the curve represent 

 the average correlation between picture elements spaced by various 



* Complete statistics extending, say, over one frame period, would comprise 

 one conditional probability distribution per picture element for each possible 

 past history. With the approximate figures cited above, the number of distribution 

 curves (many of which would be similar) is 210,000 X lO"^.^^^ or lO"" •»»■'■'. 



