EE200_Weber_12-2

EE200_Weber_12-2 - EE 200 Chapter 1 - Signals and Systems...

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1 EE 200 Chapter 1 - Signals and Systems Signals carry information to and from systems, and internally within a system. Information can be in many forms Electrical - voltage, current, phase, bits Audio (sound) - amplitude, frequencies Light - color, brightness, images Represent signals by mathematical functions Domain - input values the function defined over Range - output values the function can take on
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2 EE 200 Chapter 1 - Signals and Systems Continuous-time signals Domain is a real number Signal defined for all values of the input variable (time or spatial postion) x(t) = Acos(2 π ft) = Acos( ω t) f = frequency (Hz) = 1/P P = period (time) ω = 2 π f Range can be real, complex, integer, etc.
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3 EE 200 Chapter 1 - Signals and Systems Discrete-time signals Domain is a integer Signal only defined for discrete values of the input variable (time or spatial postion) x(n) = Acos(2 π fn) = Acos( ω n) f = frequency (Hz) = 1/P P = period (number of samples) ω = 2 π f Range can be real, complex, integer, etc.
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4 EE 200 Chapter 1 - Signals and Systems Sequences Signal consists of a stream of symbols representing data or events. Domain is a an index (integer) in the stream of symbols. Index doesn’t say anything about when the symbol will appear in the input stream. Range is the set of symbols defined for this signal. State machines operate on an input sequence(s) and produce an output sequence(s).
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5 EE 200 Chapter 2 - Defining Signals and Systems Signals and systems are both defined by functions with a domain and range. The domain and range of a system are “signal spaces” A system maps one signal space into another signal space. Example: a system input is a continuous time signal (a voltage) and the output is a discrete time signal (a color). S: [Reals Voltage] [Integer Color]
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6 EE 200 Chapter 2 - Defining Signals and Systems Functions For each member of set X (the domain), the function assigns a value in set Y (the range) f: X Y Functions can be defined by Declarative statement Graphs Tables
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7 EE 200 Chapter 2 - Defining Signals and Systems Declare the function by the mathematical relationship between the value in the domain and the value in the range: Function to square a number: square: Reals Reals x Reals: square(x) = x 2 Unit step function: step: Reals {0, 1} t Reals: step(t) = 1 if t 0, 0 if t < 0
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8 EE 200 Chapter 2 - Defining Signals and Systems Define functions by combining other functions. Output of one function becomes the input of another.
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This note was uploaded on 12/03/2008 for the course EE 200 taught by Professor Zadeh during the Fall '08 term at USC.

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EE200_Weber_12-2 - EE 200 Chapter 1 - Signals and Systems...

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