EXPERIMENTAL TRANSVERSAL EQUALIZER FOR TD-2 



1435 



Now it will be shown that, by the adjustment of the two parameters 

 Ka and A'fc , it is possible to realize independent control of a cosine gain 

 term and a cosine delay term. 



Since, in general, Ka 9^ Kb , let us define 



Ka = Kg -\- Kp 



and 



Then 



Kr 



Substituting the trigonometric form: 



Bt = Ee'"''\\ + 2Kg cos ix>t + j 2Kp sin oif]. 



(2) 



(3) 



(4) 



Note that for Ka equal to Kb , the sine phase term is zero and that for 

 Ka eciual to —Kb the cosine gain term is zero. Similarly, by proper pro- 

 portioning of Ka and Kb , Kg and Kp may be assigned any desired values. 

 If we normalize (3) by setting Co = Ee^"^' = 1, the expression in 

 brackets can yield two vector diagrams which are useful in explaining 

 the functioning of the eciualizer. To obtain the diagram shown in Fig. 

 4(a), we have set Kp = 0. We then have a unit vector, representing the 

 main signal, a leading echo K„e~^"^, and a lagging echo KgE^"^. The 



en = i 



Knf 



er= 1 + 2KnCOSaJ7' 



(a) 



Kpf-J'^^ 



eo=i 



(b) 



Fig. 4 — Vector diagrams of paired echos. (a) Kqual eclios of same polarity 

 produce magnitude change without phase change, (b) Equal echos of opposite 

 pohirity produce a change in phase shift with a minor change in magnitude. 



