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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

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Discrete-time Signals

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Periodic and Aperiodic Signals

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Discrete-time Periodic Sinusoids

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Finite Energy and Finite Power Discrete-time Signals

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Even and Odd Discrete-time Signals

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Basic Discrete-time Signals

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Discrete-time Sinusoids

Discrete frequency

Discrete-time Unit-step and Unit-sample Signals

Generic representation of discrete-time signals

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Discrete-timeSystems

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Recursive and Non-recursive Discrete-time Systems

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Convolution Sum

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Linear and Non-linear Filtering

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Causality of Discrete-time Systems

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BIBO Stability of LTI Discrete-time Systems

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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