1. Sept. 25, 2006 Assignment #1 Assignment #2 and Lab #3 Now Online Formula Cheat Sheet Cheat SheetCheat Sheet Review Time, Frequency, Fourier Bandwidth Bandwidth Review Bandlimiting Information Capacity

2. Time and Frequency Domain Time Domain Frequency Domain Fourier –Fundamental frequency –Harmonics

4. 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?

5. 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

6. 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)

8. 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.

9. 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

10. Information Capacity Measure of quantity of data through a channel Expressed as bit rate (bps) Claude Shannon

11. 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)

12. 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

13. 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

14. EM Spectrum Divisions

15. Frequency Allocations www.ntia.doc.gov/osmhome/allochrt.pdf