2016/5/3

1

Discrete-time Signals and Systems

Chapter 8

What is in this chapter?

• Discrete-time signals

• Periodicity, symmetry, energy and power

• Basic discrete-time signals

• Discrete-time LTI systems

• Recursive and non-recursive systems

• Difference representation of systems

• Convolution sum

• Causality and stability

2016/5/3

2

Discrete-time Signals

2016/5/3

3

Periodic and Aperiodic Signals

2016/5/3

4

Discrete-time Periodic Sinusoids

2016/5/3

5

Finite Energy and Finite Power Discrete-time Signals

2016/5/3

6

Even and Odd Discrete-time Signals

2016/5/3

7

2016/5/3

8

Basic Discrete-time Signals

2016/5/3

9

Discrete-time Sinusoids

Discrete frequency

Discrete-time Unit-step and Unit-sample Signals

Generic representation of discrete-time signals

2016/5/3

10

Discrete-timeSystems

2016/5/3

11

2016/5/3

12

Recursive and Non-recursive Discrete-time Systems

2016/5/3

13

Convolution Sum

2016/5/3

14

2016/5/3

15

Linear and Non-linear Filtering

2016/5/3

16

Causality of Discrete-time Systems

2016/5/3

17

BIBO Stability of LTI Discrete-time Systems

2016/5/3

18

What have we accomplished?

• Z-transform analysis

Where do we go from here?

• Obtained similar theory for discrete- and continuous-time signals and systems with distinct differences

• Discrete frequency is finite but circular

• Sampling period determines radian frequency of discrete signals

• Discrete-time Fourier transform and relation with Z-transform

• Z-transform relation to Laplace transform

• Discrete sinusoids not necessarily periodic