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小波变换详解及应用2页PPT.pdf

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G pi G pi bo@ApiCX~A@kQ bHAkNOpiA no khHO u iHDG ]nO@BAHAo RO@RABA]A] @HAiHDbYWvW @jAp bWF@ ?Fh^oDAt@RH - (Fourier transform)C@ f )(t A F w ( ) = etf )( jw t dt 14kHzAoD|b oAH (localization)DbA HYOQDoSOWv|boAiH short-term Fourier transform STFTA STFT iNH f )(t T \hAoAo@ NiHDbWnHob@a 3 ¥ ¥ -
G pi FApbT]NOb bWPHRAOYO 2T 3T A]oF f )(t oN| (boundary effect)AHFnAb eAC@[W (window)ApGo )(tg Ah STFT G (2.1) tgtf ( )( tw ( ), dt F t * = jw t ) e pGoAh Tw STFT Gabor transformA STFT )(tg AH@TwWvRAoO (uncertainty principle)zMGAzOA@ (spread) 2 ts PWvi} 2 ws np 2/1 A )(tg Ai} A = s 2 t 2 tgt )( 2 tg )( 2 dt dt = 2 s w 2 w G w ( G w ( ) ) 2 2 d w d w ] [ ApGnbonRAn 2 ws A]NObWotRCQzH [AFpiCpiO@ Yi (scaling)P (translating)Aou 4 2 ts AOW STFT ¥ ¥ - -
G pi (transient)OwCHApi PWRC BWvAHBCWvSA]AX FWoAH F@u 2.1 pi (wavelet) 2.1.1 spi Aq@@Al jpYiPo@@oAo@@sp i (mother wavelet)AbWAiHYi (scaling) f )(t aN t t/aApGwq (norm)A iHoA tf )( 2 = f 2 t )( dt 2 f ( t a ) = )( tfa 2 pGnb nW Yi f )(t oPP (norm)A a/1 C t~AbW]iH (translating)@aN t t-b t+bA]A@pi )(ty AiHolA 5 ¥ ¥ -
G pi y )(, tba = 1 a y ( bt a ) wj ( ) = F y [ ( t )] wj ( , ba = ) F y [ )]( t , ba f )(t n (inner product)oY SllpiAG oolpiP AhpiYA (2.2) t )( t )( t )( dt y , f y f w ba , ba , ba , = = (2.2)hspi (continous WTA CWT)ABiHq baw , f )(t A (2.3) = f )( t ba y w , , ba )( t 1 C y dadb 2 a A (2.4) dw C y ¥= 0 j 2) ( w w n (2.4)nsbA yC A]NOn )0(j O )(ty A]ApinDs mean)A yC opq`\i condition)At@A]QnpiqA relationshipAiHgXA j )0( = 0 A`N (zero (admissibility Parseval’s (j w 2) ¥
G pi @D`pWaC 2.1.2 pi {bwgDFspiApi (discrete time wavelet transformA DTWT)npoO ?@oYA oYOq f )(t P aA b noA aA b npoO ?@Mk aA b A = a a 0 m , = b anb 0 0 m mA n AY =a 0 2 A =b 0 1 AiHopiXA (2.5) nm , a m 0 2/ y ( m ta 0 nb 0 ), Znm , y = t )( Y =a 0 2 A =b 0 1 A y , nm = )( t 2 m 2/ m y 2( nt ) `NAWMO@ApG (complete)A { Qgpi })(, tnmy w = (2.5)O (affine wavelets)AopiYA (2.6) nm , nm , 0 f y )( t ( m ta )( 0 nb ) dt f ( t y ), t )( = 2/ a m 0 f )(t iHqpiY^A (2.7) w , y nmnm , t )( f t )( = m n pihA@ Harr piApUA 7 - - - ˛ - -
G pi ty )( = 01 < t 1 1 2 t 1 2 < 1 Harr piL{C ALDnNv Harr N|bU@` 2.2 Harr pi epikh WAbDnOe{@pi transformA Harr piDnONvUWA MANU[BAHDoWpiYA [|VVjA]NOnTANO CWCaANtAYObv tAt|jAbvAt|pA HbpiAo|jWaAHoO WC jPW Harr pi BJ I. II.C 8 £ - £
G pi 2.2.1 Harr transform {b@i 44 · AY@ 4 O AB BB CB DAp 2.1 A 2.1 vl {bi@AX A+BB A-BB C+DB C-D BABOs^ ]OBBzA AB BB CB D | 2.2 mAlO 2.2 @ L NCWA H NWA@ 2.3 A]OO A+BB A-BB C+DB C-D BAP AH AUnAX Ap PzAl]OBBzAAsJ mA 9 4 2.4
G pi 2.3 2.4 @ LLB LHB HLB HH pi|PWvWa (subband)A oA]NoF@piAB ]hTC {bw@ Harr piy{AYnG LL WanWaA Harr piAhnp{O ?oun LL Wa A@pi@YiAN|oG l]NO@e@ Harr piA LL WaPy{AYi o {C n Harr piA 2.5 d@T Harr piy 10
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