Signals & Systems FEEE, HCMUT

Ch-2: Phn tch h thng LTI trong min thi gian

Lecture-3

2.1. Gii thiu

2.2. H thng LTI: tch chp

2.3. Cc tnh cht ca h thng LTI

Signals & Systems FEEE, HCMUT

2.1. Gii thiu

Trong mn hc ny ta tp trung kho st h thng LTI:

Nhiu h thng vt l thc t c tnh LTI

H thng LTI tha nguyn l xp chng & bt bin: biu din

tn hiu vo thnh tng cc tn hiu c bn (hoc phin bn tr)

p ng ca h thng mt cch d dng.

Cc v d v biu din tnh hiu thnh tng cc tnh hiu c bn:

Biu din tnh hiu thnh tng ca cc xung n v

Biu din tnh hiu thnh tng cc tnh hiu hm m phc:

chui Fourier, bin i Fourier, bin i Laplace

Trong chng ny ta kho st vic biu din tn hiu thnh tng cc

xung n v tnh p ng ca h thng dng khi nim p ng

xung ca h thng v tch chp.

Signals & Systems FEEE, HCMUT

2.2. H thng LTI: Tch chp

2.2.1. Biu din tn hiu thnh tng cc xung n v

2.2.2. p ng xung v biu din h thng LTI bng tch chp

Signals & Systems FEEE, HCMUT

2.2.1. Biu din tn hiu thnh tng cc xung n v

nh ngha xung (t):

1 ; 0

Signals & Systems FEEE, HCMUT

2.2.2. p ng xung v biu din h thng LTI bng tch chp

p ng xung ca h thng LTI: l p ng ca h thng vi (t)

V d: (a) h thng n v y(t)=f(t) h(t)= (t)

(b) h thng c phng trnh: t

-y(t)= f ( )d

t

-h(t)= ( )d u(t)

p ng ca h thng LTI vi xung (t):

0lim h (t)=h(t)

Signals & Systems FEEE, HCMUT

2.2.2. p ng xung v biu din h thng LTI bng tch chp

p ng ca h thng LTI vi tn hiu gn ng ca f(t) ~

n

f (t)= f(n ) (t n )Vi:

Do h thng LTI nn: ~

n

y(t)= f(n )h (t n )

Signals & Systems FEEE, HCMUT

2.2.2. p ng xung v biu din h thng LTI bng tch chp

p ng ca h thng LTI vi tn hiu vo f(t)

~

0f(t) lim f (t)= f( ) (t )dTa c:

Suy ra: ~

0 0n

y(t)= lim y(t)= lim f(n )h (t n )

y(t) f( )h(t )d y(t) f(t) h(t) (tch chp)

Trong phn tch v thit k ngi ta hay biu din m hnh h

thng LTI theo tch chp vi p ng xung h(t)

Signals & Systems FEEE, HCMUT

2.2.2. p ng xung v biu din h thng LTI bng tch chp

Tnh tch chp: f(t) h(t)= f( )h(t )d

(Lu : ta s tnh tch phn trn tnh theo thang thi gian cn t l

tham s cng chnh l bin thi gian ca kt qu)

Xc nh h(t- ) theo bin :

Nhn f( ) vi h(t- )

Ly tch phn trn ton thang

Signals & Systems FEEE, HCMUT

2.2.2. p ng xung v biu din h thng LTI bng tch chp

V d: cho f(t)=e-atu(t); a>0 l ng vo ca h thng LTI c p

ng xung h(t)=u(t). Xc nh p ng y(t) ca h thng?

f(t) h(t)=0

ta at1

a0

f(t) h(t)= e d (1-e )

at1a

y(t)=f(t) h(t)= (1-e )u(t)

t0

Signals & Systems FEEE, HCMUT

2.3. Cc tnh cht ca h thng LTI

Tnh giao hon: +

y(t)=f(t) h(t)= f ( )h(t )d

t: 1 t 1t 1d d

1 1 1 1 1 1+

y(t)= f (t )h( )d h( )f(t ) =h(t) f(t)d

Tnh phn phi: 1 2 1 2y(t)=f(t) [h (t)+h (t)]=f(t) h (t)+f(t) h (t)

Signals & Systems FEEE, HCMUT

2.3. Cc tnh cht ca h thng LTI

Tnh kt hp: 1 2 1 2y(t)=[f(t) h (t)] h (t)=f(t) [h (t) h (t)]

H thng LTI khng nh: h(t)=K (t)

y(t)=f(t) h(t)=f(t) K (t)=Kf(t)

Tnh kh ngch: ta d dng chng minh c h thng nghch o

ca mt h thng LTI cng l h thng LTI. Do h thng LTI

kh nghch khi tn ti hi(t) sao cho ih(t) h (t)= (t)

Signals & Systems FEEE, HCMUT

2.3. Cc tnh cht ca h thng LTI

Tnh nhn qu: h thng LTI nhn qu khi h(t)=0 khi t