Unit Inputs, Systems, and System Properties August 30, 2000 EE 64, Section 1 ©Michael R. Gustafson II Pratt School of Engineering

Last Time Definition of a signal Signal energy and power Even and odd signals Even and odd parts of a signal

Important Discrete Signals Discrete unit impulse: Discrete unit step:

Discrete Signal Relationships The unit step can be written as a function of the unit impulse: The unit impulse can be written as a function of the unit step:

Important Continuous Signals Continuous unit impulse: Continuous unit step: ( ) î í ì > < = , 1 t u

Continuous Signal Relationships The unit step can be written as a function of the unit impulse: The unit impulse can be written as a function of the unit step: ( ) t u dt d =

Systems What is a system? "Physical systems in the broadest sense are an interconnection of components, devices, or subsystems" For this class, we will mostly be dealing with the relationship between the inputs to a system and the outputs from a system.

System Properties There are several system properties that describe how the inputs and outputs interact: Linearity Time Invariance Memory Causality Stability Invertibility

Linearity A system S is linear if it follows three basic rules:

Time Invariance A system S is time invariant if it follows one basic rule:

Other "Timing" Properties Memoryless: a system S is memoryless if the output is dependent solely on the input at the present time. Causal: a system S is causal if the output is dependent on the input at the present time or in the past but not in the future. Can a physical system be non-causal?

Stability A system S is stable if, for any bounded input, there is a bounded output. Usually in this class, you will seek to disprove stability by example rather than to prove stability through rigorous arithmetic.

Invertibility A system S is invertible if a distinct set of inputs leads to a distinct set of outputs. Invertibility is not critical to this class -- but is very important for communications systems, especially encrypted ones.

Examples

Assignment Read Chapter 1 and skim Chapter 2 of OW. Start the homework assignment. The TA's will be available as listed in the e-mail sent out last night

Next Time Block diagram introduction Review of Chapter 1

Questions ?