Sept. 25, 2006Sept. 25, 2006

Assignment #1Assignment #1Assignment #2 and Lab #3 Now OnlineAssignment #2 and Lab #3 Now OnlineFormula Formula Cheat SheetCheat SheetReview Time, Frequency, Fourier Review Time, Frequency, Fourier BandwidthBandwidthBandwidth ReviewBandwidth ReviewBandlimitingBandlimitingInformation CapacityInformation Capacity

Time and Frequency DomainTime and Frequency Domain

Time DomainTime Domain

Frequency DomainFrequency Domain

FourierFourier– Fundamental frequencyFundamental frequency– HarmonicsHarmonics

BandwidthBandwidth

Frequency range of signal or systemFrequency range of signal or system– Upper frequency – lower frequencyUpper frequency – lower frequency

Data Rate is proportional to bandwidthData Rate is proportional to bandwidth– Morse code < speech < audio < videoMorse code < speech < audio < video– Morse code has low dps. Video has high dpsMorse code has low dps. Video has high dps

Example: FM RadioExample: FM Radio

What if there is overlap…where are edges What if there is overlap…where are edges defined?defined?

Bandwidth Cutoff PointsBandwidth Cutoff Points

How is cutoff determinedHow is cutoff determined

Depends on systemDepends on system

3dB point – b/w cutoff is frequency where 3dB point – b/w cutoff is frequency where power of signal drops below 3dB of power of signal drops below 3dB of strongest pointstrongest point

6 dB point – same as 3dB point, but use 6 dB point – same as 3dB point, but use 6dB instead6dB instead

Other, larger values are also usedOther, larger values are also used

Bandlimiting a SignalBandlimiting a Signal

Refers to keeping a signal within a range, Refers to keeping a signal within a range, or below a certain frequencyor below a certain frequency

May be purposeful or due to system May be purposeful or due to system constraintsconstraints

Square wave exampleSquare wave example– Perfect square wave – infinite harmonicsPerfect square wave – infinite harmonics– Cut off harmonics at some point (i.e., cut off Cut off harmonics at some point (i.e., cut off

high frequencies)high frequencies)

Bandlimiting in Frequency DomainBandlimiting in Frequency Domain

Start with frequency Start with frequency spectrum of signalspectrum of signal

Multiply by frequency Multiply by frequency range of system (filter)range of system (filter)

Output is the part of the Output is the part of the frequency spectrum of frequency spectrum of original signal that falls original signal that falls inside range of the inside range of the systemsystem

This is ideal filter. Real This is ideal filter. Real filter would not have filter would not have perfect cut off.perfect cut off.

Bandlimiting - FiltersBandlimiting - Filters

Low Pass Filter: Systems which cutoff high Low Pass Filter: Systems which cutoff high frequencies and allow low frequencies throughfrequencies and allow low frequencies through

High Pass Filter: Systems which cutoff low High Pass Filter: Systems which cutoff low frequencies and allow high frequencies throughfrequencies and allow high frequencies through

Bandpass Filter: Systems which allow a range of Bandpass Filter: Systems which allow a range of frequencies in the middle of the spectrum frequencies in the middle of the spectrum throughthrough

Information CapacityInformation Capacity

Measure of quantity of data through a Measure of quantity of data through a channelchannel

Expressed as bit rate (bps)Expressed as bit rate (bps)

Claude ShannonClaude Shannon

Information Capacity Formula:Information Capacity Formula:I = 3.32 x BW x log(1 + SNR)I = 3.32 x BW x log(1 + SNR)

I = information capacity (data rate in bps)I = information capacity (data rate in bps)BW = bandwidthBW = bandwidthSNR = signal to noise ratioSNR = signal to noise ratioGives theoretical max which may require many Gives theoretical max which may require many bits to be sent per symbolbits to be sent per symbol– Symbol is electronic representation of a bit or multiple Symbol is electronic representation of a bit or multiple

bitsbits– Eg. 2 different symbols can be used to transmit a 0 or Eg. 2 different symbols can be used to transmit a 0 or

1 (1 bit system)1 (1 bit system)– Eg. 32 different symbols needed to transmit 5 bits per Eg. 32 different symbols needed to transmit 5 bits per

symbolsymbol– Number of symbols = 2Number of symbols = 2(number of bits required)(number of bits required)

Bandwidth Example – 802.11Bandwidth Example – 802.11

802.11b and g use 2.4GHz band802.11b and g use 2.4GHz bandThey have 14 channels with 5MHz spacingThey have 14 channels with 5MHz spacing– Bandlimiting – at +/-11MHz, signal must be 30dB Bandlimiting – at +/-11MHz, signal must be 30dB

down. At +/- 22MHz, signal must be 50dB down.down. At +/- 22MHz, signal must be 50dB down.– Lots of overlap between channels, requires good Lots of overlap between channels, requires good

network designnetwork design

Assume 5MHz bandwidth per channel, and all Assume 5MHz bandwidth per channel, and all channels transmitting equally, what is info channels transmitting equally, what is info capacity?capacity?– Noise from CH1 at CH3 makes SNR about 30dBNoise from CH1 at CH3 makes SNR about 30dB– Info Capacity = 3.32 x 5MHz x log(1+30) = 24.8Mbps Info Capacity = 3.32 x 5MHz x log(1+30) = 24.8Mbps

Electromagnetic SpectrumElectromagnetic Spectrum

range of all frequencies of electromagnetic range of all frequencies of electromagnetic radiation broken into subrangesradiation broken into subranges

EM Spectrum - physical characteristic EM Spectrum - physical characteristic Spectrum allocation - humans dividing Spectrum allocation - humans dividing spectrum into different uses and spectrum into different uses and designating who can do whatdesignating who can do what

EM Spectrum DivisionsEM Spectrum Divisions

Frequency AllocationsFrequency Allocations

www.ntia.doc.gov/osmhome/allochrt.pdfwww.ntia.doc.gov/osmhome/allochrt.pdf