7G8 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1952 



be shown, it is much easier to recognize circuit configurations that 

 reduce redundancy in the time domain. To this end, and for purposes 

 of encoding, the signal is thought of as signal samples uniformly spaced 

 at Nj^quist intervals. Thus, amplitude values obtained by sampHng 

 a 4.0 mc picture signal at | microsecond intervals serve to specify the 

 signal completely. Fig. 4 shows a small portion of a television raster where 

 the signal is represented by signal values spaced at Nyquist intervals, 

 T. The coordinates sho^vn are designated mth respect to the "present 

 value" of the signal, So,o ■ The positive coordinate directions are shown 

 by the arrows. The past is represented by positive coordinates — the future 

 by negative coordinates. In this way, the previous value of the signal 



LINES OF 



•INTERLACED 



FIELD 



3,0 2,0 1,0 



Sx,y 



r = NYQUIST INTERVAL 

 _ _1_ 

 " 2W 



X 



Fig. 4 — A small portion of a television raster showing geometrical location of 

 signal samples with relation to the "present value" of the signal, <So,o • 



taken one Nuquist interval before *So ,o is designated by *Si ,o - the pre^'ious 

 line samples by <So,i , etc. 



METHODS OF LINEAR PREDICTION 



As previously stated, with linear prediction the next signal sample, 

 Sp{t), is simply the sum of the previous signal samples each multiplied 

 by an appropriate weighting factor. Thus, 



^pW — C[l,0»Jl,0 + fl2,0'J2,0 4" fl3.0*J3,0 4" ' * ' dm.nSm.n 



represents the weighted sum of all the previous signal values. The error 

 signal, e, as shown in Fig. 2, is represented by the difference between the 

 present vaue of the signal, So,o and the predictor's prediction. 



e = So.o — Sp{t) 



There are several specific types of linear prediction that deserve fur- 



