VIII. CONCLUDING DISCUSSION 



The specific results of this report are contained in Figures k 

 through 8. Although some explanation and interpretation of these graphs 

 was included in each of the individual sections where they initially- 

 appeared, this section will expand and clarify the results further. For 

 convenience in reference, the five figures are reproduced at the end of this 

 section. 



Figure h shows that the penalty for using an incorrect bandwidth 

 is not severe, though an intelligent choice of bandvridth can reduce this 

 loss by a significant amount. As an example, assume that the signal spec- 

 tra are expected to have relative slopes varying between -3 and -l8db/oct. 

 If the system used a bandwidth corresponding to m, = 5j "the loss (w.r.t. 

 optimum m-'s) in output SNE would vary between and lOdb . If the system 

 were redesigned so that u = 0-75 ^''as used, the loss v/ould be between and 



2 db an 8 db improvement in worst case system performance achieved veiy 



simply by choosing the "correct" bandwidth. If the occurrence of the various 

 signal slopes were not e qui -probable, the bandwidth choice might be altered. 

 For example, if slopes of -3 and -bdb/oct occurred 90% of the time, then 

 one might choose \i '^^ 2 since the "majority" signals woulri suffer less than 

 2 db of loss. With a p. of 2, the worst case loss is about 51" '^'^ more 

 than the worst case loss associated with M. = 0.75- But here, the v/orst 

 case loss is suffered by the least probable signals, while with M- = 0.75^ 

 the worst case loss of 2 db would, be suffered by one of the more probable 

 signals. All in all, of course, the final choice is a matter of the 



designer's judgement no "rules" can be given; however, Figure k does 



contain information which should be useful in making such a judgement. 



Figure 5 shows the additional losses entailed by not fully 

 utilizing spectral information ab.-ut the signal. Notice that if the 

 region of concern were again 1-^-6, the minimum worst case loss for a 

 conventional bandlimited pre-whitening system no longer occurs at (a = 0.75j 

 but at M- = O.Qj the change in the criterion of comparison has affected 

 the choice of "correct" bandv;idth, although not by a significant amount. 



30 



