702 THE BELL SYSTEM TECHNICAL JOURNAL, JILY 1952 



ing that the original signal must have contained at least 3.4 hits of 

 redundancy. 



The autocorrelation can also furnish a lower bound to the redundancy, 

 as has been pointed out by P. Elias in his Letter to the Editor of the 

 Proceedings of the I.R.E. for July, 1951. If, for example, the correlation 

 Aio , between horizontally adjoining picture elements, is high, the cor- 

 responding lower-bound redundancy is \'er3^ roughly eriual to 



R ~ —^ log., (1 — .4io) bits/sample. (5) 



Alternatively, taking the Fourier transform of the autocorrelation yields 

 the power spectrum P(/), from which we can find the lower-bound re- 

 dundancy through the relation 



R = 



^ j logo P(/) df + i logo W -f log2 K bits/sample, (6) 



1 r^ 



where W = bandwidth in cps, and — = / P(/) df. 



K Jo 



Using either method, one obtains approximately 2.4 bits for the 

 average* of the a\'ailable data. This is an approximate bound, in that 

 it applies strictly only to functions having gaussian amplitude distri- 

 butions. 



Suppose, then, that we have exposed an average redundancy of at 

 least 3 bits per sample. This means a potential 3-bit reduction in the 

 chamiel capacity required for television transmission. In a 6-bit system 

 (64 amphtude levels) this means a 50 per cent reduction, and hence a 

 potential halving of the band^^^Ldth with the aid of an ideal coding scheme. 

 It is true that the decorrelated signal is somewhat "frail," i.e., \Tilner- 

 able to interference, so that it might be desirable to use a "rugged" 

 system of the PCM variety for transmission. Thus, if a Shannon-Fano 

 code were used, the 3-bit decorrelation should enable us to send tele- 

 ^'ision by an average of 3 on-off pulses per picture sample rather than 

 6. This represents a two-to-one saving over the usual PCM bandwidth. 

 More spectacular reductions are hkely to be achie^■able onlj^ by tap- 

 ping the large-scale redimdancies mentioned earlier. 



FRAME-TO-FRAME CORRELATION 



There is, of course, a great deal of interest in the possibility of utilizing 

 the similarity between successive frames. Accordingly, adjacent-frame 



* See previous footnote. 



