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practical t a&, the aim i s to iecognise knoRii signal for 1115, which irieaiii identifying wliat point in t irirc thry emir and distinguishing ti-tein irorri otlirr signal forrrrs Exainplcs of thcse tasks are sp 11 recognition objcrt recognition 111 inuriy sinciple: In tlre sirnpleist rase wc \\rilnt to recogni5e when a sigiial corrrponent 7rr(t) occiirs That niearrs we :ale dealiirg with B sigiiA of t h t forni r ( f )= m(t - to) j8.72) wlierr the f m r t i o i r m ( t ) is known hut thc lime lo by ~ l r i c hnr(t) is drifted i5 iiot ltnown For exarnple, we could trarrsiriit wri izconsttc~51gi-1al? i t ( t ) ,a i d with r ( l ) , tlrteimiiiih tlie ~inlrnc~wri time taken for it to retiirn To achieve Iliis, the ieerivrtl signal s(2) is filtcwd with a n LTI-sy a11 irripulsc response derived from the signal forin ) U ( 1): h ( t )= rrt,( tj (8.73) The rniiius sign in m( -t) cancels out) the reversal of the signal ii-i convolution, so t,he o i t t p t signal is (S.75) -ou -0 The integral owr thc always positive d u e m2(r - to) must be at Itthan y ( t ) cxccpt a t f - t o Suilable choice of thc sigrial m ( l ) can nialtc thc wlur of y(t0) iiiix*h greater than all other vahes of ~ ( t ) and , thcn the unkiiowii tiiiic ognised as the peak in tlie sign;d y(/) Figiire 6.31 shows the (8 73) arid a pc->ak igerneiit of a filtcr with ilnpnlsr respo this kind is c;tllcv~i~ m i z t ~ k e dfilter
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