STATISTICS OF TELEVISION SIGNALS 701 



light limits the useful range of the probabiloscope to approximately two 

 decades. In obtaining those sections of the curve corresponding to the 

 few and far-between large errors, a long exposure was used and the 

 cathode-ray beam was blanked whenever passing through the range of 

 zero or small errors. The vertical scale on all ciu'ves is determined solely 

 by the density taper of the optical density wedge. If this scale is to repre- 

 sent true probability density, instead of a proportional quantity, it 

 should be sliifted up or down so as to make the area under the curve 

 equal to unity. 



APPLICATION OF RESULTS 



The statistics measured can be put to various uses, such as in the 

 design of better predicting or coding schemes. The most interesting 

 application is probably in estimating the reduction in channel capacity 

 which the measured statistics show to be theoretically possible. In 

 other words, the results can give us various lower bounds to the re- 

 dundancy of television signals. 



For the sake of illustration, suppose that the signal is quantized into 

 64 amplitude levels. An ordinary television channel assumes all 64 

 levels to be equally likely, hence is prepared to accommodate log2 64 

 or 6 bits per sample. But the simple amplitude distribution of the 

 signal is not flat, so that all 64 levels are 7iot equally likely. The maximum 

 possible associated average information content per sample is given by 



64 



^max = JL Pi log Pi , (4) 



t 



where pi is the simple probability of the signal's falling into the iih 

 level. Since the 64 p,'s are unequal, //max is necessarily less than 6 bits. 

 For all available data the average value of //max turns out to be ap- 

 proximately 5 bits, indicating a one-bit redundancy. The latter figure 

 is essentially independent of quantization. 



The prediction error signal still contains all the useful picture in- 

 formation. The maximum possible information content per sample (max- 

 imum in that all samples are assumed to be completely independent) 

 is still given by (4) but in this case the 64 values of p.- are obtained 

 from the peaked error distribution. The average* result from all available 

 data turns out to be approximately 3.4 bits below the 6-bit ceihng, show- 



* This average was computed by averaging the various redundancy values ob- 

 tained for the individual pictures, rather than averaging all statistical data and 

 then finding one corresponding average redundancy. The average computed here 

 is more favorable and can be realized onl}^ if optimum coding is performed on a 

 short-term basis rather than on the basis of one set of long-term statistics. 



