SLIDE 1
ELG3125 Signal and System Analysis Fall 2010
School of Information Technology and Engineering
Outline
- 1. Differential equations
- 2. Difference equations
- 3. Convolution sums
ELG3 1 2 5 Signal and System Analysis Lab3: LTI Systems and - - PowerPoint PPT Presentation
ELG3 1 2 5 Signal and System Analysis Lab3: LTI Systems and - - PowerPoint PPT Presentation
ELG3 1 2 5 Signal and System Analysis Lab3: LTI Systems and Convolution Sum TA: Jungang Liu Fall 2010 School of Information Technology and Engineering (SITE) Outline 1. Differential equations 2. Difference equations 3. Convolution sums
SLIDE 2
SLIDE 3
ELG3125 Signal and System Analysis Fall 2010
School of Information Technology and Engineering
Objective
- To learn to simulate LTI systems in continuous
time and discrete time, represented by differential equations, difference equations, or impulse response
SLIDE 4
ELG3125 Signal and System Analysis Fall 2010
School of Information Technology and Engineering
Continuous-Time LTI System N-th order linear constant-coefficient differential equation Describe the system in Matlab
SLIDE 5
ELG3125 Signal and System Analysis Fall 2010
School of Information Technology and Engineering
To find the impulse response h(t) of the system impulse(B,A,t) To compute the output given the input x(t) lsim(B,A,x,t)
See the related questions in the assignments
Continuous-Time LTI System
SLIDE 6
ELG3125 Signal and System Analysis Fall 2010
School of Information Technology and Engineering
Example: Continuous-Time LTI System 2ed order LTI system Coefficients are highest-order first from left to right in the vector
] 6 1 [ ] 3 2 1 [ ) ( 6 ) ( ) ( 3 ) ( 2 ) (
2 2
= = + = + + B A t x dt t dx t y dt t dy dt t y d
SLIDE 7
ELG3125 Signal and System Analysis Fall 2010
School of Information Technology and Engineering
Nth-order linear constant-coefficient difference equation Describe the system in Matlab Discrete-Time LTI System
SLIDE 8
ELG3125 Signal and System Analysis Fall 2010
School of Information Technology and Engineering
- To find the impulse response h[n] of the system
impz(B,A,n)
- To compute the output given the input x[n]
filter(B,A,x)
See the related questions in the assignments
Discrete-Time LTI System
SLIDE 9
ELG3125 Signal and System Analysis Fall 2010
School of Information Technology and Engineering
Example: Discrete-Time LTI System
- 3rd order LTI system
- Coefficients are most present time first from left to right in
the vector
- Using zeros() to create vector B
B=[1,zeros(1,3)]
] 1 [ ] 8 1 5 2 [ ] [ ] 3 [ 8 ] 2 [ ] 1 [ 5 ] [ 2 = = = − + − + − + B A n x n y n y n y n y
SLIDE 10
ELG3125 Signal and System Analysis Fall 2010
School of Information Technology and Engineering
Convolution sum Mathematical formula
] [ * ] [ ] [ * ] [ ] [ ] [ ] [ n x n h n h n x k n h k x n y
k
= = ∑ − =
+∞ −∞ =
SLIDE 11
ELG3125 Signal and System Analysis Fall 2010
School of Information Technology and Engineering
Matlab function y=conv(x,h); Length of signal x[n] length(x); See the related questions in the assignments
Convolution sum
SLIDE 12
ELG3125 Signal and System Analysis Fall 2010
School of Information Technology and Engineering
Learn How to Operate Music Files
- Read a music file in Matlab
Wavread()
- Listen to the music
Sound() See the related questions in the assignments
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ELG3125 Signal and System Analysis Fall 2010
School of Information Technology and Engineering