ch2 - TN HIU& H THNG RI RC TRONG MINTHI GIAN Tn hiu ri...

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Unformatted text preview: TN HIU & H THNG RI RC TRONG MINTHI GIAN Tn hiu ri rc H thng thi gian ri rc H thng tuyn tnh bt bin Phng trnh sai phn tuyn tnh h s hng Tng quan ca cc tn hiu ThS. Trn Thanh Tng THI GIAN RI RC CHUN HA Tn hiu tng t x(t) c ly mu u vi chu k Ts , gi tr ca x(t) ti mi tn = nTS l x(nTs) c gi l mu th n ca x(t) Chun ha trc thi gian t theo chu k Ts tn nTs = =n Ts Ts x(n) Mu th n ca tn hiu ri rc thi gian chun ha ThS. Trn Thanh Tng THI GIAN RI RC CHUN HA x (nTs) x (n) 0 1Ts 2Ts 3Ts 4Ts 5Ts 6Ts nTs 0 1 2 3 4 5 6 n ThS. Trn Thanh Tng t BIU DIN TN HIU RI RC Biu din ton hc: biu din bng biu thc bin n Ex: Biu din mt tn hiu ri rc n , 0 n 4 1 - x(n ) = 4 0 , n khc Biu din bng th: minh ha trc quan tn x(n) hiu ThS. Trn Thanh Tng n BIU DIN TN HIU RI RC Mt tn hiu ri rc (dy): dy cc gi tr thc hoc phc x = {x(n)} vi - < n < Mt phn t th n ca tn hiu ri rc (dy) x(n) Biu din dy s: lit k cc gi tr ca x(n) trong cp du { } x(n) = { ..., 0, 0, 0, 1, , , , 0, 0,...} ThS. Trn Thanh Tng TN HIU RI RC C BN Tn hiu xung n v 1 , n = 0 (n ) = 0 , n khc x(n ) = k = - (n) x(k ) (n - k ) n x(n) Tn hiu hng x(n) = A = {..., A, A, A,...} ThS. Trn Thanh Tng n TN HIU RI RC C BN Tn hiu xung n v 1 , n 0 u (n ) = 0 , n < 0 n u(n) u (n ) = k = - (n ) n (n ) = u (n ) - u (n - 1) Tn hiu hm m x(n ) = A n ThS. Trn Thanh Tng TN HIU RI RC C BN A >0 0 < <1 A>0 -1 < < 0 -4 -3 -2 -1 0 1 2 3 4 A>0 || > 0 ThS. Trn Thanh Tng TN HIU RI RC C BN Tn hiu tun han: x(n) = x(n+N) x(n) n x(n) ThS. Trn Thanh Tng PHP TON TRN DY Nhn 2 dy: nhn tng phn t ca dy x1(n) 2 1 y(n)= x1(n).x2(n) y(n) 4 x2(n) 2 1 n X 1 n n ThS. Trn Thanh Tng PHP TON TRN DY Nhn dy vi hng s y(n) = a.x(n) = {a.x(n)} y(n) x(n) 2 1 X 4 2 2 n n ThS. Trn Thanh Tng PHP TON TRN DY Php cng 2 dy: cng tng phn t x1(n) 1 3 x2(n) 2 1 n n n 2 y(n)= {x1(n)+x2(n)} 2 y(n) 4 + 1 ThS. Trn Thanh Tng PHP TON TRN DY Php dch mt dy x(n): dich (N0>0) mu y(n) = x(n-N0) : dch phi x(n) N0 mu y(n) = x(n+N0) : dch tri x(n) N0 mu x(n 2) + 2 1 -4 -3 -2 -1 0 1 x(n) 2 3 4 5 n ThS. Trn Thanh Tng PHP TON TRN DY Php dch mt dy x(-n): dich (N0 >0) mu y(n) = x(-n-N0) : dch tri x(-n) N0 mu y(n) = x(-n+N0) : dch phi x(-n) N0 mu 2 x(-n + 2) x(-n -2) 1 -4 -3 -2 -1 0 1 x(-n) 2 3 4 5 n ThS. Trn Thanh Tng TN HIU CNG SUT V NNG LNG Nng lng ca tn hiu ri rc Ex = x(n ) 2 - Cng sut ca tn hiu ri rc 1 Px = N Tn hiu tun han (N) 2 N -1 Tn hiu khng tun han x (n ) n=0 p Px = lim K 1 x(n ) K 2K + 1 n=-K 2 Tn hiu Cng sut (0 <Px <) Tn hiu nng lng (0 <Ex <) ThS. Trn Thanh Tng H THNG RI RC H thng ri rc: mt thit b hoc thut tan SYSTEM x(n) Tc ng Kch thch Device Algorithm y(n) p ng y(n) = T{x(n)} x(n) T y(n) p ng xung: p ng vi kch thch l (n) (n) SYSTEM Device Algorithm n h(n) = T{(n)} p ng xung ThS. Trn Thanh Tng BIU DIN H THNG Phn t nhn dy X x2 (n) ThS. Trn Thanh Tng x1(n) y(n) = x1(n). x2 (n) Phn t nhn dy x1(n) y(n) = A. x2 (n) BIU DIN H THNG Phn t cng dy x1(n) x2 (n) Phn t tr mt mu x(n) Z-1 y(n) = x (n-1) ThS. Trn Thanh Tng X A + y(n) = x1(n)+ x2 (n) PHN LOI H THNG RI RC H thng khng nh (h thng tnh) SYSTEM x(n) n y(n) ch ph thuc vo x(n) cng thi im n y(n) n y(n) = T{x(n)} = |x(n)|2 H thng c nh (h thng ng) 2 x(n) SYSTEM y(n) khng ch ph thuc x(n) vo thi im n m cn cc mu sm v tr so vi n y(n) n y(n)=x(n+1)+x(n)+x(n-1)/3 n+1 n n-1 ThS. Trn Thanh Tng PHN LOI H THNG RI RC H thng tuyn tnh SYSTEM x(n) T{ax1(n) +bx2(n)}=aT{x1(n)}+bT{x2(n)}=ay1(n)+by2(n) y(n) p ng ca tng cc tc ng bng tng cc p ng ca tng tc ng ring l H thng phi tuyn p ng ca tng cc tc ng bng tng cc p ng ca tng tc ng ring l ThS. Trn Thanh Tng PHN LOI H THNG RI RC H thng bt bin theo thi gian SYSTEM x(n) y(n)=T{x(n)} y(n-1)=T{x(n-1)} y(n) T -1 0 1 T 0 1 2 0 1 2 -1 0 1 ThS. Trn Thanh Tng PHN LOI H THNG RI RC H thng nhn qu p ng ca h thng ch ph thuc v tc ng qu kh v hin ti, khng ph thuc vo tc ng tng lai SYSTEM x(n) y(n)=T{x(n)}=F{x(n), x(n-1), x(n-2),.....} y(n) Phng trnh sai phn ti v sai phn li y(n)=x(n+1) x(n) H thng khng nhn qu y(n)=x(n) x(n-1) H thng nhn qu ThS. Trn Thanh Tng PHN LOI H THNG RI RC H thng n nh |x(n)| Bx < + x(n) Tc ng b gii hn -----------> p ng b gii hn |y(n)| Bx < + y(n) y(n)=T{x(n)} Bx By ThS. Trn Thanh Tng H THNG TUYN TNH BT BIN H LTI = Tuyn tnh + Bt bin p ng ca h thng LTI y (n ) = k = - x ( k )h( n - k ) p ng ca h thng LTI = tng chp ca tc ng v p ng xung y(n) = x(n)*h(n) ThS. Trn Thanh Tng TNH TNG CHP BNG TH y (n ) = x1 (n) * x 2 (n) = x1 (n) k = - x (k ) x 1 2 (n - k ) x2 (n) n n ThS. Trn Thanh Tng Thay n bi k ta c x1(k) v x2(k) x1 (k) x2 (k) Ly i xng x2(k) c x2(-k) x2 (-k) k k ThS. Trn Thanh Tng k Dch tri x2(-k) |n| nu n<0 Dch phi x2(-k) |n| nu n>0(-k) x 2 2 k n-3 n-2 n-1 n n+1 |n| ThS. Trn Thanh Tng Nhn x1(k) vi x2(n-k), vi mi k Tnh tng cc kt qu trn c y(n) Lp li cho mi gi tr ca n x2 (-k) x1 (k) n-3 n-2 n-1 n n+1 |n| ThS. Trn Thanh Tng n < -1 x2 (-k) x1 (k) n-3 n-2 n-1 n n+1 -1 0 1 2 3 y (n ) = x1 (n) * x2 (n) = k = - x (k ) x (n - k ) = 0 1 2 ThS. Trn Thanh Tng n = -1 x2 (-k) x1 (k) n-3 n-2 n-1 n n+1 -1 0 1 2 3 y (n ) = x1 (n) * x2 (n) = k = - x (k ) x (n - k ) = 1 1 2 ThS. Trn Thanh Tng n=0 x2 (-k) x1 (k) n-3 n-2 n-1 n n+1 -1 0 1 2 3 y (n ) = x1 (n) * x2 (n) = k = - x (k ) x (n - k ) = 2 1 2 ThS. Trn Thanh Tng n=1 x2 (-k) x1 (k) n-3 n-2 n-1 n n+1 -1 0 1 2 3 y (n ) = x1 (n) * x2 (n) = k = - x (k ) x (n - k ) = 3 1 2 ThS. Trn Thanh Tng n=2 x2 (-k) x1 (k) n-3 n-2 n-1 n n+1 -1 0 1 2 3 y (n ) = x1 (n) * x2 (n) = k = - x (k ) x (n - k ) = 4 1 2 ThS. Trn Thanh Tng n=3 x2 (-k) x1 (k) n-3 n-2 n-1 n n+1 -1 0 1 2 3 y (n ) = x1 (n) * x2 (n) = k = - x (k ) x (n - k ) = 4 1 2 ThS. Trn Thanh Tng y(n) = x1(n)*x2(n) = { ....,0,0,0, 1, 2, 3, 4, 4, 3, 2, 1, 0,0,0, . . . } y (n) 4 3 2 1 -1 0 1 2 3 4 5 6 ThS. Trn Thanh Tng TNH CHT CA TNG CHP Giao hon y(n) = x(n)*h(n) = h(n)*x(n) Phi hp y(n) = [x(n)*h1(n) ]*h2(n) = x(n)* [h1(n)*h2(n)] Phn b vi php cng y(n) = x(n)* [h1(n)+h2(n)] = [x(n)*h1(n)]+ [x(n)*h2(n)] ThS. Trn Thanh Tng H THNG LTI C BIT H thng LTI n nh H thng LTI nhn qu h(n) = 0 , vi mi n < 0 H thng FIR ( Finite-duration Impulse Response) p ng xung h(n) tn ti m s hu hn khc 0 FIR n nh nu cc mu ca h(n) c gi tr hu hn ThS. Trn Thanh Tng k = - h(k ) < H THNG LTI C BIT H thng IIR ( Infinite-duration Impulse Response) p ng xung h(n) tn ti v hn s hu hn khc 0 IIR c th n nh hoc khng n nh H thng o (Inverse system) hi (n) gi l p ng xung h thng o ca h thng c p ng xung h(n) nu tho mn iu kin sau h(n)*hi(n) = hi(n)*h(n) = (n) ThS. Trn Thanh Tng PHONG TRNH SAI PHN TTHSH (LCCDE) H thng LTI c th biu din a k y( n - k ) = b r x ( n - r ) k =0 r =0 N M p ng ca h thng l nghim tng qut ca LCCDE Nghim phng trnh sai phn thun nht Nghim tng qut + Nghim ring ca phng trnh sai phn ThS. Trn Thanh Tng H THNH QUI & KHNG QUI H thng qui p ng y(n) mi thi im n ph thuc vo mt s mu y(n-1),y(n-2),.... x(n), x(n-1),x(n-2),.... c biu din bng LCCED c bc N 1 H thng khng qui p ng y(n) mi thi im n ph thuc vo x(n), x(n-1),x(n-2),.... c biu din bng LCCED c bc N = 0 H thng FIR nhn qu ThS. Trn Thanh Tng TNG QUAN TN HIU Tng quan cho (Cross-Correlation) rxy (n ) = k = - x ( k ) y( k - n ) x (k ) x (k - n ) ThS. Trn Thanh Tng n = 0, 1, 2, 3, . . . T tng quan (Auto-Correlation) rxx (n ) = k = - TNH CHT TNG QUAN TN HIU Ex = rxx(0) rxy(n)=r*yx(-n) rxx(n)=rxx(-n) |rxy(n)|2 rxx(0)rxy(0) Ex Ey ThS. Trn Thanh Tng ...
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