EE450-U6-PhysicalLayer-Nazarian-Spring10

# EE450-U6-PhysicalLayer-Nazarian-Spring10 - University...

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University of Southern California Viterbi School of Engineering EE450 omputer Networks Computer Networks hysical Layer Physical Layer Shahin Nazarian Spring 2010

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Data and Signal Data can be analog or digital. Analog data are continuous and take continuous values. Digital data have discrete states and take discrete values Signals can be analog or digital. Analog signals can have an infinite number of values in a range, for example sound or ideo (like real numbers ) Digital signals can have only a limited video (like real numbers.) Digital signals can have only a limited number of discrete values like integer numbers, however it typically has two levels, e.g., 0 and 1 or -1 and +1 ignals are a way of representing the data The representation Signals are a way of representing the data . The representation could be electrical, electromagnetic (i.e., transmission via radio), or optical (i.e., transmission via optical fiber) Shahin Nazarian/EE450/Spring 2010 2
Periodic Signals A signal that repeats itself is periodic, e.g., periodic sine or cosine signal waveforms periodic signal can be recognized by three A periodic signal can be recognized by three parameters, its frequency , its peak amplitude and its phase T (Period) Shahin Nazarian/EE450/Spring 2010 3

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Signal Key Parameters (frequency, Amplitude and Phase Frequency (or inverse of period, i.e., 1/T,) denoted by f , is the signal’s rate of change and is measured in Hertz or cycles per second Peak amplitude , A , is the maximum strength of a ignal and is measured in volts or amps signal and is measured in volts or amps Phase , φ , describes the position of the waveform relative to time 0 Example: Sine wave representation: A Sin(2 π f t + ) Voltage olts) A (Volts) Shahin Nazarian/EE450/Spring 2010 4 T Time (sec)
Periodic Signals A periodic signal with period T can be represented as sum of sinusoids using Fourier Series: x(t) = a 0 + a 1 Sin(2 π f 0 t + φ 1 ) + a 2 Sin(2 π 2 f 0 t + 2 ) + … + a k Sin(2 kf 0 t + k ) + … “DC” long-term average fundamental frequency f 0 =1/ T first harmonic k th harmonic Amplitude Spectrum | a 0 |, | 1 |, | 2 |, … Shahin Nazarian/EE450/Spring 2010 | k | determines amount of power in k th harmonic

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Periodic Signals (Cont.) Change in a short span of time means high frequency Change over a long span of time means low frequency If a signal does not change at all, its frequency is zero If a signal changes instantaneously, its frequency is infinite he interesting fact about periodic signals is that if The interesting fact about periodic signals is that if you know the waveform for one cycle (for T seconds) you will be able to predict the signal behavior at any ime; another words if you know its frequency its time; another words if you know its frequency, its peak amplitude, and its phase you can predict it nformation is all about predictability not how Shahin Nazarian/EE450/Spring 2010 6 Information is all about predictability not how frequently or rarely it happens
Units of Period and Frequency Example 1: Express a period of 100ms in microseconds

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EE450-U6-PhysicalLayer-Nazarian-Spring10 - University...

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