DSP g第七次课(第四章1)

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ChpaertF uor FI: RiFlteringand Co noluvtino1. lBok Pcocressnig :用举例应：a FI. Rflteiring fo ifine-durtaion stignlsa y boncvlution bo .fstac nvolution ofol no gsginal sc.DFT/ FFT pescrtm uomcputtioa d. nsepchean lysais an dsythenis e.s iame pgrcessonig2.Sample roPescisng(:tsaetsp-ac reeailations zf oLT fiIlert) s用举应例a. re:al-imet iltefirg nfolo g signnas lb. idgitla audi ofefcetsproce sisn c. gdiitgla conrolt ystess md.a aptdvi eigsnlapr cessonig

In

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ths chiatep,we rocsidnerbl co prkocsesnig na sdapml peorcessig nemthodsf o FIrRf ilterin gpplicataoin. 1)s lobc krocepssnigme thodsfo rFIR iltfeirngW deiscss tuh eompcuatiotnl asapets cof het ocnvolutin equotaois n(3..32 )ro(3 ..33) a shteya plypto F IR iftelsr na fdiite-ndrautoinin http://www.77cn.com.cna riosue quvialne formts o cfnvoluotoi:n: . 1Dreic torfm2 .oCvonutionl tbale 3. TLIfor m4 .Mtraixf rom5 F.ip-anldslide -(转反动) 滑ormf 6.O erlav-adp dblock ocvnoultoi nfro

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m) s2ampelp rocesisng etmods fohr FI Rfitelrign Thne,ewgo o no ditcsus ssmapl-ey-sbampe plocersins gmehots fodr FIRf iltesr ad nidscss ulocb dkiaramg ealizrtiano hiwhcp ovrdie amecha izatnon oi fth easmlp peorcessng aligrothims .

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.14 BolkcPr oecssignMeth od s4.1.1 Convoutlon 1i)t eh udratoniof the d ta reacrodTL =L T)输2入信 号输入信

(号.1.1)4P1.25

L图= TL fs (41..2 ()41..)

x 3= [x 0, x 1, L , x L 1 ]

)3the drecti adn LT foIrmsof c ovnloutiony( n = )∑ h m)(x n ( m )= ∑ x ( m )h ( n m ) mm(.41.4)

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4.12.D iectr oFrm*当输 入xn(和h())n是有限长因都果列序确定dire时c fortm的 和 求范围 y : ( n)= ∑h ( m) x ( n m) m0≤m≤M 0 ≤ ≤nL +1M (.4.101) 0 ≤n m ≤L 1 axm(0,n L + 1 ) m≤≤ m i(n, n M ().1.415)y (n )=imn( n , )

M m =max( 0, n L+ )1 ∑ ( hm ) (xn m )(.1.164)* 0 ≤n ≤ L 1 M + 输数据出的块度长：L = Ly x+Lh 1 (4..1.1)3

yL =L +M

( .14.12)

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* dAvntaaes : leadgsdi ercty to lblcok dagiam realiratzois no fhet iflter andthe coresprnoidn gamspleb--symape plorcessign aglriotm .h P.(241)

通这过节一学习的大关键要家握求掌积卷和求和的范的围通用 法

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4.方.3 1onvoluCtino abTl P1e2 (491..81 )acE houptu ytn n Ei.q(.1418) .i tshesum o flla opssibel proudtsc i xhj wi th +i =jn y n( = )∑ h (m x)( m)n =m

∑h

x i,ij i +j=

jn(.41.5)Fig..4.1 Ex2mpae 4.l1.1* Advanatgse: is cnoveninet fro uick coqmupationst b yhan . (d.P14)2

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.41. LTI 4ormF

(yn ) =∑ x (m h)( n mm)

例输入如列序度长为5:y (n) = x h0(n ) x+h1( n 1) + 2x (nh )2 + x3(n h 3 +)x 4h( n 4) 1)TI foLmr用 向量和示：P表31 用向量和表示12) LT Iofm 用表r格形表式 示iFg4.1.3. 表格形用表式示:

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3)输当入 输当x(入n)h(和n都)是有长限果序列时因定确都是有限长 因序果列确定时TLI orf m的和求当 输入 和 都是有限长因序列果时确 定围：范

范围: y(n ) = ∑ x m)( h(n m) m0≤n m≤ M 0 ≤ n≤ L 1 + M 0 ≤ m≤ L 1 mx(a, n 0 )M ≤m ≤m n(n, i L 1 )y n( =m)n( in L , )1

m m=x( a0, n M ) ∑ x ()m h ( nm)

(41..9)1

*Adv antagse :the LT fIom irs f ofudnmenatal imorpanctebe cuae it sncirporatoest he conesqenues oc flinaertiyand tiem ivaniartn (P.12.)4

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4.15 .MtaixrForm (41..1)6和(.141.9)可写成矩阵都式形。 阵矩的H数维：L y× Lx =( L + M ) ×L 阵X矩的数维：L × LHy= ( L + M ) ×( + 1M)

*A vadtnaegs :prviods aecom apt vccteroai lrerpsenetatoi no thef fitleirn gopretaoinand iswi edylu sedi nosm epplaicationss chuas imaegp ocesrsin.g( .P214)

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41.6. Fli-pna-Slided Fromy( n ) ∑ =x (m h) (n m)

miF g41..

4 A*dvanagtes: sohw cselral ytheinpu -tn aod nipunt-off tarnisnte andste aydsta-et behavio of arfi tel (rP.21)4注: 然也可以当xn( )反滑转动，对应其FI着 filter的 sRmale procpesings

。

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41..7 rTansine andtStea ydState-Be havir 在Foil-apnd-Siled Form中n将成分三分部：

≤n<0 (Mnipu tno tarsninest M ) ≤n ≤L 1 ( seatydst ta)eL 1 <n L≤ 1 + M(i punt of franstiens)t注：暂 态(ransitens )t:波器滤作的还没完用全示显出来稳 态(tsadeys-ttae)滤波器的作：完全显用出来示

d

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riect fomr y:(n )=mi( n , nM

)m =amx(0 , n L+)1∑ xm(h)(-nm )n y () n=∑ x m)h(n- m() 0≤n < M in(upt no m =) 0 M y n( ) =∑x (m)(hn-m ) M ≤ n≤ L 1 (tesdya tsate)m =0 M y ()n =∑ x(m)h (n m) -L < n1≤ L 1 + M(niupt o f f m = )n L +1

)1ipunt-on: he ntmbuero tefrm in sthesum is n 1+ and s inicrasine ) g)2stedya state :teh unmer ob fetmsri s qeua to tleh unber mf filtore) we ihtsg ,M+1,an d remain fisxde . ) i3npt-uno: hetn ubme rf oertsmkee spd creesaingd wo not on e be)auces tehlow er sumamiot limni tisi ncraesing.