Slide 1Lecture-2
Gii thiu v tín hiu và h thng
Gii thiu chung
Các phép toán trên tín hiu
Các loi tín hiu thông dng
H thng và phân loi h thng
Signal & Systems - Tran Quang Viet – FEEE, HCMUT – Semester: 02/09-10
Các phép toán trên tín hiu
Chuyn dch trong min thi gian
Thay i (co, dãn) thang thi gian
o thi gian
Signal & Systems - Tran Quang Viet – FEEE, HCMUT – Semester: 02/09-10
Chuyn dch trong min thi gian
T>0 dch sang phi (delay)
T<0 dch sang trái (advance)
Ví d:
Co, dãn thang thi gian
a>1 : co thi gian bi mt h s là a
0<a<1 : dãn thi gian bi h s 1/a
Ví d:
o thi gian
Ví d:
Kt hp các phép toán
a>0 :
Method 1:
Ví d:
Method 2:
a<0:
Các tín hiu thông dng
Hàm nc n v
Xung n v (t)
Thành phn chn và l ca mt tín hiu
Signal & Systems - Tran Quang Viet – FEEE, HCMUT – Semester: 02/09-10
Hàm nc n v
u(t) tin dng trong vic mô t mt tín hiu vi nhiu mô t khác
nhau trong các khong thi gian khác nhau
Ví d 1:
Hàm nc n v
Xung n v (t)
Tính cht 1: Nu f(t) liên tc ti T thì
Ví d:
Xung n v (t)
Ex:
Hàm m
Ví d:
Hàm m
Hàm chn và hàm l
Hàm chn: fe(-t)=fe(t); i xng qua trc dc
Hàm l: fo(-t)=-fo(t); i xng ngc qua trc dc
Tính cht: even x odd = odd
odd x odd = even
even x even = even
Thành phn chn
Thành phn l
Ví d 2:
Thành phn chn
Thành phn l
H thng và phân loi h thng
H thng “x lý” các tín hiu vào và “to” các tín hiu u ra
System
5. H thng và phân loi h thng
Linear vs. nonlinear system
Time-invariant vs. time-varying system
Instantaneous vs. dynamic system
Causal vs. non-causal system
Continuous-time vs. discrete-time system
Analog vs. digital system
Lumped-parameter vs. Distributed-parameter system
Linear vs. nonlinear systems
system
A system is linear if it satisfies superposition property
A system is nonlinear if it violates ether scaling or additivity property
Signal & Systems - Tran Quang Viet – FEEE, HCMUT – Semester: 02/09-10
Linear and nonlinear systems
linear
Linear if {ai}, {bi} are constants or independent functions of t
Signal & Systems - Tran Quang Viet – FEEE, HCMUT – Semester: 02/09-10
Time-invariant vs. Time-varying system
Linear Time-invariant system if {ai}, {bi} are constants LTI
Linear Time-varying system if {ai}, {bi} are independent functions of t
Consideration the system with the equation:
t
f(t)
0
t
y(t)
0
t
f(t-T)
0
T
t
y(t-T)
0
T
Instantaneous vs. dynamic system
A system is instantaneous or memoryless if y(t) depends on f(t) only,
but it does NOT depend on f(t+T) for any T>0, i.e, resistive network
A system is dynamic or with memory if y(t) depends on f(t+T) for some
T>0, i.e, resistive network, i.e, circuits with C, L
Signal & Systems - Tran Quang Viet – FEEE, HCMUT – Semester: 02/09-10
Causal vs. non-causal system
A system is causal if for any t0, y(t0) depends only on f(t) for tT the
present output depends on only the part of present input
A system is non-causal if there is t0, such that y(t0) depends on f(t0+T)
for some T>0. ex: y(t)=f(t-2)+f(t+2)
Signal & Systems - Tran Quang Viet – FEEE, HCMUT – Semester: 02/09-10
Continuous-time vs. discrete-time system
Signal & Systems - Tran Quang Viet – FEEE, HCMUT – Semester: 02/09-10
Analog vs. digital system
Signal & Systems - Tran Quang Viet – FEEE, HCMUT – Semester: 02/09-10
Lumped-parameter vs. distributed-parameter system
Physical dimensions of a component (system) are very small compared
with wavelength lumped-parameter system. Otherwise distributed-
parameter system