EE450-U6-PhysicalLayer-Nazarian-Summer11_complete

EE450-U6-PhysicalLayer-Nazarian-Summer11_complete - EE450...

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EE450 Computer Networks Physical Layer Shahin Nazarian Summer 2011
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Shahin Nazarian/EE450/Summer 2011 2 Data and Signal Data can be ____ or ______. Analog data are continuous and take continuous values. Digital data have discrete states and take discrete values Signals can be ____ or _____. Analog signals can have an _____ number of values in a range, for example sound or video (like real numbers.) Digital signals can have only a limited number of discrete values like integer numbers, however they typically have two levels, e.g., 0 and 1 or -1 and +1 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)
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Shahin Nazarian/EE450/Summer 2011 3 Periodic Signals A signal that repeats itself is periodic, e.g., periodic sine or cosine signal waveforms A periodic signal can be recognized by three parameters, its _______ , its _______ amplitude and its _______ T (Period)
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Shahin Nazarian/EE450/Summer 2011 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 ______ per second Peak amplitude , A , is the maximum strength of a signal and is measured in volts or _______ Phase , φ , describes the position of the waveform relative to time 0 Example: Sine wave representation: A Sin(2 π f t + φ ) 4 T A φ Time (sec) Voltage (Volts)
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Shahin Nazarian/EE450/Summer 2011 Periodic Signals A periodic signal with period T can be represented as sum of sinusoids using _______ Series: Amplitude Spectrum | a 0 |, | a 1 |, | a 2 |, … | a k | determines amount of power in k th harmonic “DC” long-term average fundamental frequency f 0 =1/ T first harmonic k th harmonic x(t) = a 0 + a 1 Sin(2 π f 0 t + φ 1 ) + a 2 Sin(2 π 2 f 0 t + φ 2 ) + … + a k Sin(2 π kf 0 t + φ k ) + …
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Shahin Nazarian/EE450/Summer 2011 Periodic Signals (Cont.) In general Fourier series of f(t) is defined as: Where f=1/T is the fundamental frequency, a n and b n are the sine and cosine amplitudes of the n th harmonics and c is a constant It can be shows: f(t) = 0.5 c + Σ { a n Cosine(2 π nft) + b n Sin(2 π nft) } __ n
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Shahin Nazarian/EE450/Summer 2011 [Optional] Higher Harmonics – Example Example: The Fourier series for a function that is defined as 0 if the input is between -2 and 0, and is the inputs if the input is between 0 and 2 http://www.sosmath.com/fourier/fourier1/fourier1.html 7
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Shahin Nazarian/EE450/Summer 2011 [Optional] Higher Harmonics Example (Cont.) Example: The Fourier series for a function that is defined as 0 if the input is between -2 and 0, and is the inputs if the input is between 0 and 2 http://www.sosmath.com/fourier/fourier1/fourier1.html 8 0.5c=
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Shahin Nazarian/EE450/Summer 2011 9 Periodic Signals (Cont.) Change in a short span of time means ____ frequency Change over a long span of time means ___ frequency If a signal does not change at all, its frequency is _____ If a signal changes instantaneously, its frequency is _____
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Shahin Nazarian/EE450/Summer 2011 10 Information
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