DATA RECONSTRUCTION 41 
dashed lines show the full-velocity-correction impulsive response from 
Fig. 3.9. The impulsive response can be decomposed into a number of 
elementary step and ramp functions, as shown in Fig. 3.14. The Laplace 
transform of the partial-velocity hold is the sum of the Laplace trans- 
forms of the components as follows: 
My ese OR bk Qk I 
s 
pa Ee = p—2Ts RBI GSI porn RATE BAS, fee —2Ts 
Ga(s) s 7 sh a Ts? Ts? ° a Ts? G* 
which, after combination and simplification, becomes 
G(s) = - (1 — es) E — ke-Ts + = (1 — ar) | G22) 
It is noted that when k is unity, (3.22) becomes identical with (3.19). 
Replacing s by jw in (3.22) the frequency response of the partial-velocity 
hold is obtained. This becomes, after some simplification, 
Giga) = 1 — HT (ene unr) [ ene 
Sina Zee. 
The frequency response G;,(jw) 1s plotted for three values of k in Fig. 3.15. 
It is seen that for full velocity correction (k = 1), the frequency response 

Fra. 3.14. Component functions of partial-velocity-correction data hold. 
in the passband is characterized by an overshoot of about 50 per cent. 
On the other hand, with partial-velocity correction of 0.5 and 0.3, the 
frequency response has an overshoot of 20 per cent and 0, respectively. 
It is seen, therefore, that in order to pass frequency components in the 
passband without overemphasis, a partial velocity correction of about 
