Download Bandwidth Cutoff Points

Sept. 25, 2006
Assignment #1
Assignment #2 and Lab #3 Now Online
Formula Cheat Sheet
Review Time, Frequency, Fourier
Bandwidth
Bandwidth Review
Bandlimiting
Information Capacity
Time and Frequency Domain
Time Domain
Frequency Domain
Fourier
– Fundamental frequency
– Harmonics
Bandwidth
Frequency range of signal or system
– Upper frequency – lower frequency
Data Rate is proportional to bandwidth
– Morse code < speech < audio < video
– Morse code has low dps. Video has high dps
Example: FM Radio
What if there is overlap…where are edges
defined?
Bandwidth Cutoff Points
How is cutoff determined
Depends on system
3dB point – b/w cutoff is frequency where
power of signal drops below 3dB of
strongest point
6 dB point – same as 3dB point, but use
6dB instead
Other, larger values are also used
Bandlimiting a Signal
Refers to keeping a signal within a range,
or below a certain frequency
May be purposeful or due to system
constraints
Square wave example
– Perfect square wave – infinite harmonics
– Cut off harmonics at some point (i.e., cut off
high frequencies)
Bandlimiting in Frequency Domain
Start with frequency
spectrum of signal
Multiply by frequency
range of system (filter)
Output is the part of the
frequency spectrum of
original signal that falls
inside range of the
system
This is ideal filter. Real
filter would not have
perfect cut off.
Bandlimiting - Filters
Low Pass Filter: Systems which cutoff high
frequencies and allow low frequencies through
High Pass Filter: Systems which cutoff low
frequencies and allow high frequencies through
Bandpass Filter: Systems which allow a range of
frequencies in the middle of the spectrum
through
Information Capacity
Measure of quantity of data through a
channel
Expressed as bit rate (bps)
Claude Shannon
Information Capacity Formula:
I = 3.32 x BW x log(1 + SNR)
I = information capacity (data rate in bps)
BW = bandwidth
SNR = signal to noise ratio
Gives theoretical max which may require many
bits to be sent per symbol
– Symbol is electronic representation of a bit or multiple
bits
– Eg. 2 different symbols can be used to transmit a 0 or
1 (1 bit system)
– Eg. 32 different symbols needed to transmit 5 bits per
symbol
– Number of symbols = 2(number of bits required)
Bandwidth Example – 802.11
802.11b and g use 2.4GHz band
They have 14 channels with 5MHz spacing
– Bandlimiting – at +/-11MHz, signal must be 30dB
down. At +/- 22MHz, signal must be 50dB down.
– Lots of overlap between channels, requires good
network design
Assume 5MHz bandwidth per channel, and all
channels transmitting equally, what is info
capacity?
– Noise from CH1 at CH3 makes SNR about 30dB
– Info Capacity = 3.32 x 5MHz x log(1+30) = 24.8Mbps
Electromagnetic Spectrum
range of all frequencies of electromagnetic
radiation broken into subranges
EM Spectrum - physical characteristic
Spectrum allocation - humans dividing
spectrum into different uses and
designating who can do what
EM Spectrum Divisions
Frequency Allocations
www.ntia.doc.gov/osmhome/allochrt.pdf