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

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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 ...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online