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1 . 4. 3 THE EFFEC T OF FINITE PROC ESSING TIME The uncertainty function o f a t rain of n identical pulses can be obtai n e d fr om n-I n- I L a(t - ik) L a * (t + T - ik) e -j w t dt i= O i=O _00 +00 Al th ough the in tegra t i on time runs fro m to Fig, 4. e . nk J for -k < T < O. -T In a p ract ical radar system the signal p rocessing is carried out over the d u ration o f a number o f pulses, n. w hic h is v e ry much smal ler than the number actually t ransmitted . Fu rther the processing t ime is not a ffected by the delay T o f the incoming sign a l .

9 and 4. 5 . " , \ \ , \ I \ I \ I \ I I \ I \ , \ I I , I , I I I ' , ,-, ,,-, : \; ,� , �: -- Correct t v ---- - - I n c o r r e c t t "" sett ing v sett i n g .... , Fig. 4. 9. Output of a lin ear FM F. T R x -- C o r r e c t t v ------ I ncorrect t Fig. 4. 1 0. sett ing v settIng O ut p u t of a con stant frequency pulse F. T Rx An i n t e re s t i ng c o n se q u en ce 01 d e l a y -D o ppler coupling a rises when t he F o u r i e r t r a n s form rece iver i s u se d w i t h a linear FM w a v e form .

W ) + X ( T + k , w ) \ = O . 4 t he a b ove b e com e s l ) fJ s i n l 1 e I/; ( T , w ) = e - J ( n -' e X( T . w ) S in " - X( T + � k , w ) { e - in fJ s i n [( n sin e - l )e 1 + sin e} T he expanded b r a c k e t e d ex pression becomes � { e - j n fJ ej (n - l ) fJ _ e - j n fJ e - j ( n - 1 ) fJ e W - - j e � e + ' 2J = ej e 2j { 1 . _ e - J2 n fJ } = e - J (n - l ) fJ s i n n e Hence I/; ( T , w ) = e - j ( n - I ) f) w h i ch is E q u a t i o n 4 . 6 . si n '18 { X ( T . w ) + X( T + k , w ) } S1 11 e e} Signal processing methods 57 4 .

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