Understanding Bandwidth and Information Capacity in Time and Frequency Domains

1. 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

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