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Signals and Systems Prof. Wonhee Kim Chapter 2

Signals and Systems - WordPress.com · 2017. 5. 12. · Signals and Systems Prof. Wonhee Kim Chapter 2. DISCRETE-TIME LTI SYSTEMS: THE CONVOLUTION SUM

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Page 1: Signals and Systems - WordPress.com · 2017. 5. 12. · Signals and Systems Prof. Wonhee Kim Chapter 2. DISCRETE-TIME LTI SYSTEMS: THE CONVOLUTION SUM

Signals and Systems

Prof. Wonhee KimChapter 2

Page 2: Signals and Systems - WordPress.com · 2017. 5. 12. · Signals and Systems Prof. Wonhee Kim Chapter 2. DISCRETE-TIME LTI SYSTEMS: THE CONVOLUTION SUM

DISCRETE-TIME LTI SYSTEMS: THE CONVOLUTION SUM

The Representation of Discrete-Time Signals in Terms of Impulses

2

Page 3: Signals and Systems - WordPress.com · 2017. 5. 12. · Signals and Systems Prof. Wonhee Kim Chapter 2. DISCRETE-TIME LTI SYSTEMS: THE CONVOLUTION SUM

DISCRETE-TIME LTI SYSTEMS: THE CONVOLUTION SUM

The Representation of Discrete-Time Signals in Terms of Impulses

3

Page 4: Signals and Systems - WordPress.com · 2017. 5. 12. · Signals and Systems Prof. Wonhee Kim Chapter 2. DISCRETE-TIME LTI SYSTEMS: THE CONVOLUTION SUM

DISCRETE-TIME LTI SYSTEMS: THE CONVOLUTION SUM

The Discrete-Time Unit Impulse Response and the Convolution-Sum Representation of LTI Systems

4

Page 5: Signals and Systems - WordPress.com · 2017. 5. 12. · Signals and Systems Prof. Wonhee Kim Chapter 2. DISCRETE-TIME LTI SYSTEMS: THE CONVOLUTION SUM

DISCRETE-TIME LTI SYSTEMS: THE CONVOLUTION SUM

The Discrete-Time Unit Impulse Response and the Convolution-Sum Representation of LTI Systems

5

Page 6: Signals and Systems - WordPress.com · 2017. 5. 12. · Signals and Systems Prof. Wonhee Kim Chapter 2. DISCRETE-TIME LTI SYSTEMS: THE CONVOLUTION SUM

DISCRETE-TIME LTI SYSTEMS: THE CONVOLUTION SUM

The Discrete-Time Unit Impulse Response and the Convolution-Sum Representation of LTI Systems

6

Page 7: Signals and Systems - WordPress.com · 2017. 5. 12. · Signals and Systems Prof. Wonhee Kim Chapter 2. DISCRETE-TIME LTI SYSTEMS: THE CONVOLUTION SUM

DISCRETE-TIME LTI SYSTEMS: THE CONVOLUTION SUM

The Discrete-Time Unit Impulse Response and the Convolution-Sum Representation of LTI Systems

7

Page 8: Signals and Systems - WordPress.com · 2017. 5. 12. · Signals and Systems Prof. Wonhee Kim Chapter 2. DISCRETE-TIME LTI SYSTEMS: THE CONVOLUTION SUM

DISCRETE-TIME LTI SYSTEMS: THE CONVOLUTION SUM

The Discrete-Time Unit Impulse Response and the Convolution-Sum Representation of LTI Systems

8

Page 9: Signals and Systems - WordPress.com · 2017. 5. 12. · Signals and Systems Prof. Wonhee Kim Chapter 2. DISCRETE-TIME LTI SYSTEMS: THE CONVOLUTION SUM

DISCRETE-TIME LTI SYSTEMS: THE CONVOLUTION SUM

The Discrete-Time Unit Impulse Response and the Convolution-Sum Representation of LTI Systems

9

Page 10: Signals and Systems - WordPress.com · 2017. 5. 12. · Signals and Systems Prof. Wonhee Kim Chapter 2. DISCRETE-TIME LTI SYSTEMS: THE CONVOLUTION SUM

DISCRETE-TIME LTI SYSTEMS: THE CONVOLUTION SUM

The Discrete-Time Unit Impulse Response and the Convolution-Sum Representation of LTI Systems

10

Page 11: Signals and Systems - WordPress.com · 2017. 5. 12. · Signals and Systems Prof. Wonhee Kim Chapter 2. DISCRETE-TIME LTI SYSTEMS: THE CONVOLUTION SUM

DISCRETE-TIME LTI SYSTEMS: THE CONVOLUTION SUM

The Discrete-Time Unit Impulse Response and the Convolution-Sum Representation of LTI Systems

11

Page 12: Signals and Systems - WordPress.com · 2017. 5. 12. · Signals and Systems Prof. Wonhee Kim Chapter 2. DISCRETE-TIME LTI SYSTEMS: THE CONVOLUTION SUM

CONTINUOUS-TIME LTI SYSTEMS: THE CONVOLUTION INTEGRAL

The Representation of Continuous-Time Signals in Terms of Impulses

12

Page 13: Signals and Systems - WordPress.com · 2017. 5. 12. · Signals and Systems Prof. Wonhee Kim Chapter 2. DISCRETE-TIME LTI SYSTEMS: THE CONVOLUTION SUM

CONTINUOUS-TIME LTI SYSTEMS: THE CONVOLUTION INTEGRAL

The Representation of Continuous-Time Signals in Terms of Impulses

13

Page 14: Signals and Systems - WordPress.com · 2017. 5. 12. · Signals and Systems Prof. Wonhee Kim Chapter 2. DISCRETE-TIME LTI SYSTEMS: THE CONVOLUTION SUM

CONTINUOUS-TIME LTI SYSTEMS: THE CONVOLUTION INTEGRAL

The Representation of Continuous-Time Signals in Terms of Impulses

14

Page 15: Signals and Systems - WordPress.com · 2017. 5. 12. · Signals and Systems Prof. Wonhee Kim Chapter 2. DISCRETE-TIME LTI SYSTEMS: THE CONVOLUTION SUM

CONTINUOUS-TIME LTI SYSTEMS: THE CONVOLUTION INTEGRAL

The Representation of Continuous-Time Signals in Terms of Impulses

15

Page 16: Signals and Systems - WordPress.com · 2017. 5. 12. · Signals and Systems Prof. Wonhee Kim Chapter 2. DISCRETE-TIME LTI SYSTEMS: THE CONVOLUTION SUM

CONTINUOUS-TIME LTI SYSTEMS: THE CONVOLUTION INTEGRAL

The Representation of Continuous-Time Signals in Terms of Impulses

16

Page 17: Signals and Systems - WordPress.com · 2017. 5. 12. · Signals and Systems Prof. Wonhee Kim Chapter 2. DISCRETE-TIME LTI SYSTEMS: THE CONVOLUTION SUM

CONTINUOUS-TIME LTI SYSTEMS: THE CONVOLUTION INTEGRAL The Continuous-Time Unit Impulse Response and the Convolution Integral Representation of LTI Systems

17

Page 18: Signals and Systems - WordPress.com · 2017. 5. 12. · Signals and Systems Prof. Wonhee Kim Chapter 2. DISCRETE-TIME LTI SYSTEMS: THE CONVOLUTION SUM

CONTINUOUS-TIME LTI SYSTEMS: THE CONVOLUTION INTEGRAL The Continuous-Time Unit Impulse Response and the Convolution Integral Representation of LTI Systems

18

Page 19: Signals and Systems - WordPress.com · 2017. 5. 12. · Signals and Systems Prof. Wonhee Kim Chapter 2. DISCRETE-TIME LTI SYSTEMS: THE CONVOLUTION SUM

CONTINUOUS-TIME LTI SYSTEMS: THE CONVOLUTION INTEGRAL The Continuous-Time Unit Impulse Response and the Convolution Integral Representation of LTI Systems

19

Page 20: Signals and Systems - WordPress.com · 2017. 5. 12. · Signals and Systems Prof. Wonhee Kim Chapter 2. DISCRETE-TIME LTI SYSTEMS: THE CONVOLUTION SUM

CONTINUOUS-TIME LTI SYSTEMS: THE CONVOLUTION INTEGRAL The Continuous-Time Unit Impulse Response and the Convolution Integral Representation of LTI Systems

20

Page 21: Signals and Systems - WordPress.com · 2017. 5. 12. · Signals and Systems Prof. Wonhee Kim Chapter 2. DISCRETE-TIME LTI SYSTEMS: THE CONVOLUTION SUM

CONTINUOUS-TIME LTI SYSTEMS: THE CONVOLUTION INTEGRAL The Continuous-Time Unit Impulse Response and the Convolution Integral Representation of LTI Systems

21

Page 22: Signals and Systems - WordPress.com · 2017. 5. 12. · Signals and Systems Prof. Wonhee Kim Chapter 2. DISCRETE-TIME LTI SYSTEMS: THE CONVOLUTION SUM

CONTINUOUS-TIME LTI SYSTEMS: THE CONVOLUTION INTEGRAL The Continuous-Time Unit Impulse Response and the Convolution Integral Representation of LTI Systems

22

Page 23: Signals and Systems - WordPress.com · 2017. 5. 12. · Signals and Systems Prof. Wonhee Kim Chapter 2. DISCRETE-TIME LTI SYSTEMS: THE CONVOLUTION SUM

CONTINUOUS-TIME LTI SYSTEMS: THE CONVOLUTION INTEGRAL The Continuous-Time Unit Impulse Response and the Convolution Integral Representation of LTI Systems

23

Page 24: Signals and Systems - WordPress.com · 2017. 5. 12. · Signals and Systems Prof. Wonhee Kim Chapter 2. DISCRETE-TIME LTI SYSTEMS: THE CONVOLUTION SUM

CONTINUOUS-TIME LTI SYSTEMS: THE CONVOLUTION INTEGRAL The Continuous-Time Unit Impulse Response and the Convolution Integral Representation of LTI Systems

24

Page 25: Signals and Systems - WordPress.com · 2017. 5. 12. · Signals and Systems Prof. Wonhee Kim Chapter 2. DISCRETE-TIME LTI SYSTEMS: THE CONVOLUTION SUM

CONTINUOUS-TIME LTI SYSTEMS: THE CONVOLUTION INTEGRAL The Continuous-Time Unit Impulse Response and the Convolution Integral Representation of LTI Systems

25

Page 26: Signals and Systems - WordPress.com · 2017. 5. 12. · Signals and Systems Prof. Wonhee Kim Chapter 2. DISCRETE-TIME LTI SYSTEMS: THE CONVOLUTION SUM

CONTINUOUS-TIME LTI SYSTEMS: THE CONVOLUTION INTEGRAL The Continuous-Time Unit Impulse Response and the Convolution Integral Representation of LTI Systems

26

Page 27: Signals and Systems - WordPress.com · 2017. 5. 12. · Signals and Systems Prof. Wonhee Kim Chapter 2. DISCRETE-TIME LTI SYSTEMS: THE CONVOLUTION SUM

PROPERTIES OF LINEAR TIME-INVARIANT SYSTEMS The Continuous-Time Unit Impulse Response and the Convolution Integral Representation of LTI Systems

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Page 28: Signals and Systems - WordPress.com · 2017. 5. 12. · Signals and Systems Prof. Wonhee Kim Chapter 2. DISCRETE-TIME LTI SYSTEMS: THE CONVOLUTION SUM

PROPERTIES OF LINEAR TIME-INVARIANT SYSTEMS

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Page 29: Signals and Systems - WordPress.com · 2017. 5. 12. · Signals and Systems Prof. Wonhee Kim Chapter 2. DISCRETE-TIME LTI SYSTEMS: THE CONVOLUTION SUM

PROPERTIES OF LINEAR TIME-INVARIANT SYSTEMS The Commutative Property

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Page 30: Signals and Systems - WordPress.com · 2017. 5. 12. · Signals and Systems Prof. Wonhee Kim Chapter 2. DISCRETE-TIME LTI SYSTEMS: THE CONVOLUTION SUM

PROPERTIES OF LINEAR TIME-INVARIANT SYSTEMS The Distributive Property

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Page 31: Signals and Systems - WordPress.com · 2017. 5. 12. · Signals and Systems Prof. Wonhee Kim Chapter 2. DISCRETE-TIME LTI SYSTEMS: THE CONVOLUTION SUM

PROPERTIES OF LINEAR TIME-INVARIANT SYSTEMS The Associative Property

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Page 32: Signals and Systems - WordPress.com · 2017. 5. 12. · Signals and Systems Prof. Wonhee Kim Chapter 2. DISCRETE-TIME LTI SYSTEMS: THE CONVOLUTION SUM

PROPERTIES OF LINEAR TIME-INVARIANT SYSTEMS LTI Systems with and without Memory

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Page 33: Signals and Systems - WordPress.com · 2017. 5. 12. · Signals and Systems Prof. Wonhee Kim Chapter 2. DISCRETE-TIME LTI SYSTEMS: THE CONVOLUTION SUM

PROPERTIES OF LINEAR TIME-INVARIANT SYSTEMS lnvertibility of LTI Systems

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Page 34: Signals and Systems - WordPress.com · 2017. 5. 12. · Signals and Systems Prof. Wonhee Kim Chapter 2. DISCRETE-TIME LTI SYSTEMS: THE CONVOLUTION SUM

PROPERTIES OF LINEAR TIME-INVARIANT SYSTEMS lnvertibility of LTI Systems

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Page 35: Signals and Systems - WordPress.com · 2017. 5. 12. · Signals and Systems Prof. Wonhee Kim Chapter 2. DISCRETE-TIME LTI SYSTEMS: THE CONVOLUTION SUM

PROPERTIES OF LINEAR TIME-INVARIANT SYSTEMS lnvertibility of LTI Systems

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Page 36: Signals and Systems - WordPress.com · 2017. 5. 12. · Signals and Systems Prof. Wonhee Kim Chapter 2. DISCRETE-TIME LTI SYSTEMS: THE CONVOLUTION SUM

PROPERTIES OF LINEAR TIME-INVARIANT SYSTEMS lnvertibility of LTI Systems

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Page 37: Signals and Systems - WordPress.com · 2017. 5. 12. · Signals and Systems Prof. Wonhee Kim Chapter 2. DISCRETE-TIME LTI SYSTEMS: THE CONVOLUTION SUM

PROPERTIES OF LINEAR TIME-INVARIANT SYSTEMS Causality for LTI Systems

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Page 38: Signals and Systems - WordPress.com · 2017. 5. 12. · Signals and Systems Prof. Wonhee Kim Chapter 2. DISCRETE-TIME LTI SYSTEMS: THE CONVOLUTION SUM

PROPERTIES OF LINEAR TIME-INVARIANT SYSTEMS Stability for LTI Systems

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Page 39: Signals and Systems - WordPress.com · 2017. 5. 12. · Signals and Systems Prof. Wonhee Kim Chapter 2. DISCRETE-TIME LTI SYSTEMS: THE CONVOLUTION SUM

PROPERTIES OF LINEAR TIME-INVARIANT SYSTEMS Stability for LTI Systems

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Page 40: Signals and Systems - WordPress.com · 2017. 5. 12. · Signals and Systems Prof. Wonhee Kim Chapter 2. DISCRETE-TIME LTI SYSTEMS: THE CONVOLUTION SUM

PROPERTIES OF LINEAR TIME-INVARIANT SYSTEMS The Unit Step Response of an LTI System

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Page 41: Signals and Systems - WordPress.com · 2017. 5. 12. · Signals and Systems Prof. Wonhee Kim Chapter 2. DISCRETE-TIME LTI SYSTEMS: THE CONVOLUTION SUM

PROPERTIES OF LINEAR TIME-INVARIANT SYSTEMS The Unit Step Response of an LTI System

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Page 42: Signals and Systems - WordPress.com · 2017. 5. 12. · Signals and Systems Prof. Wonhee Kim Chapter 2. DISCRETE-TIME LTI SYSTEMS: THE CONVOLUTION SUM

CAUSAL LTI SYSTEMS DESCRIBED BY DIFFERENTIALAND DIFFERENCE EQUATIONS Linear Constant-Coefficient Differential Equations

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Page 43: Signals and Systems - WordPress.com · 2017. 5. 12. · Signals and Systems Prof. Wonhee Kim Chapter 2. DISCRETE-TIME LTI SYSTEMS: THE CONVOLUTION SUM

CAUSAL LTI SYSTEMS DESCRIBED BY DIFFERENTIALAND DIFFERENCE EQUATIONS Linear Constant-Coefficient Differential Equations

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Page 44: Signals and Systems - WordPress.com · 2017. 5. 12. · Signals and Systems Prof. Wonhee Kim Chapter 2. DISCRETE-TIME LTI SYSTEMS: THE CONVOLUTION SUM

CAUSAL LTI SYSTEMS DESCRIBED BY DIFFERENTIALAND DIFFERENCE EQUATIONS Linear Constant-Coefficient Differential Equations

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Page 45: Signals and Systems - WordPress.com · 2017. 5. 12. · Signals and Systems Prof. Wonhee Kim Chapter 2. DISCRETE-TIME LTI SYSTEMS: THE CONVOLUTION SUM

CAUSAL LTI SYSTEMS DESCRIBED BY DIFFERENTIALAND DIFFERENCE EQUATIONS linear Constant-Coefficient Difference Equations

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Page 46: Signals and Systems - WordPress.com · 2017. 5. 12. · Signals and Systems Prof. Wonhee Kim Chapter 2. DISCRETE-TIME LTI SYSTEMS: THE CONVOLUTION SUM

CAUSAL LTI SYSTEMS DESCRIBED BY DIFFERENTIALAND DIFFERENCE EQUATIONS linear Constant-Coefficient Difference Equations

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Page 47: Signals and Systems - WordPress.com · 2017. 5. 12. · Signals and Systems Prof. Wonhee Kim Chapter 2. DISCRETE-TIME LTI SYSTEMS: THE CONVOLUTION SUM

CAUSAL LTI SYSTEMS DESCRIBED BY DIFFERENTIALAND DIFFERENCE EQUATIONS Block Diagram Representations of First-Order Systems Described by Differential and Difference Equations

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Page 48: Signals and Systems - WordPress.com · 2017. 5. 12. · Signals and Systems Prof. Wonhee Kim Chapter 2. DISCRETE-TIME LTI SYSTEMS: THE CONVOLUTION SUM

CAUSAL LTI SYSTEMS DESCRIBED BY DIFFERENTIALAND DIFFERENCE EQUATIONS Block Diagram Representations of First-Order Systems Described by Differential and Difference Equations

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Page 49: Signals and Systems - WordPress.com · 2017. 5. 12. · Signals and Systems Prof. Wonhee Kim Chapter 2. DISCRETE-TIME LTI SYSTEMS: THE CONVOLUTION SUM

CAUSAL LTI SYSTEMS DESCRIBED BY DIFFERENTIALAND DIFFERENCE EQUATIONS Block Diagram Representations of First-Order Systems Described by Differential and Difference Equations

49