Suppose we transmit some data at 2Mbps. Note that data consisting of alternating 1s and 0s will give a periodic signal with the highest fundamental frequency. 2MBps 1MHz 1 0 1 0 1 0 1 0 1 0 0.5MHz 1 1 0 0 1 1 0 0 1 1 Bandwidth vs Receiver Discrimination S(f) 1.4 1.2 1.0 0.8 2Mbps 0.6 0.4 1 0 1 0 1 0 1 0 1 0 0.2 . 0.0 f 0 1f 2f 3f 4f 5f 6f 7f 8f 1MHz 1MHz 3MHz 5MHz 7MHz Bandwidth vs Receiver Discrimination S(f) 7MHz BW channel 1.4 1.2 1.0 0.8 2Mbps 0.6 0.4 1 0 1 0 1 0 1 0 1 0 0.2 . 0.0 f 0 1f 2f 3f 4f 5f 6f 7f 8f 1MHz 3MHz 5MHz 7MHz Bandwidth vs Receiver Discrimination S(f) 5MHz BW channel 1.4 1.2 1.0 0.8 2Mbps 0.6 0.4 1 0 1 0 1 0 1 0 1 0 0.2 . 0.0 f 0 1f 2f 3f 4f 5f 6f 7f 8f 1MHz 3MHz 5MHz 7MHz Bandwidth vs Receiver Discrimination S(f) 5MHz BW channel 1.4 1.2 1.0 0.8 2Mbps 0.6 0.4 1 0 1 0 1 0 1 0 1 0 0.2 . 0.0 f 0 1f 2f 3f 4f 5f 6f 7f 8f 1MHz 3MHz 5MHz 7MHz The receiver will need better discrimination as the channel bandwidth drops. Data Rate vs Bandwidth S(f) 5MHz BW channel 1.4 1.2 1.0 0.8 2Mbps 0.6 0.4 1 0 1 0 1 0 1 0 1 0 0.2 . 0.0 f 0 1f 2f 3f 4f 5f 6f 7f 8f 1MHz 3MHz 5MHz 7MHz Data Rate vs Bandwidth S(f) 10MHz BW channel 1.4 1.2 1.0 0.8 4Mbps 0.6 0.4 1 0 1 0 1 0 1 0 1 0 0.2 . 0.0 f 0 1f 2f 3f 4f 5f 6f 7f 8f 2MHz 6MHz 10MHz 14MHz Doubling the data rate requires roughly double the bandwidth (if the receiver has the same discrimination in each case) Bits: 1 0 1 1 1 1 0 1 1 Pulses before transmission: Bit rate 2000 bps Pulses after transmission: Bandwidth 500 Hz Bandwidth 900 Hz Bandwidth 1300 Hz Bandwidth 1700 Hz Bandwidth 2500 Hz Bandwidth 4000 Hz Figure 3.8 Effects of Bandwidth on a Digital Signal Upper limit of FM radio Upper limit of AM radio Telephone channel 0 Music s l e b i –20 c e Speech Approximate D dynamic range n i Approximate –30 dB o of music i t dynamic range a of voice R r –40 e w o P Noise –60 10 Hz 100 Hz 300 Hz 1 kHz 3300 Hz 10 kHz 100 kHz 102 102.48 103 103.52 104 Frequency Figure 3.9 Acoustic Spectrum of Speech and Music [CARN99a] Appendix 3A Decibels, Measuring Relative Power Pout (Gain) Gdb = 10 log 10 ( Pin ) Pout (Loss) Ldb = -10 log 10 ( Pin ) 1 -10 log = 3.01db ~ 3db (½ Power) 10 ( 2 ) Appendix 3A Decibels, Measuring Relative Power Pout (Gain) Gdb = 10 log 10 ( Pin ) Pout (Loss) Ldb = -10 log 10 ( Pin ) 1 -10 log = 3.01db ~ 3db (½ Power) 10 ( 2 ) L1 = 1/2 L2 = 1/4 P1 P2 P3 1 P2 = P1 ´ P3 = P2 ´ 1 ( 2 ) ( 4 ) P3 = P1 ´ 1 ´ 1 = P1 ´ 1 ( 2 ) ( 4 ) ( 8 ) 1 Ltot = -10 log = 9.03db 10 ( 8 ) Appendix 3A Decibels, Measuring Relative Power Pout (Gain) Gdb = 10 log 10 ( Pin ) Pout (Loss) Ldb = -10 log 10 ( Pin ) 1 -10 log = 3.01db ~ 3db (½ Power) 10 ( 2 ) L1 = 1/2 L2 = 1/4 L1 = 3.01db L2 = 6.02db P1 P2 P3 P1 P2 P3 1 P2 = P1 ´ P3 = P2 ´ 1 ( 2 ) ( 4 ) P3 = P1 ´ 1 ´ 1 = P1 ´ 1 ( 2 ) ( 4 ) ( 8 ) 1 Ltot = -10 log = 9.03db Ltot = 3.01db + 6.02db = 9.03db 10 ( 8 ) dB is nice because cumulative losses (in dB) simply add, Also, loss in a line (attenuation) can be reported as db/km, so to figure the overall loss of a line, we only need to multiply (rather than compute powers). Pout Vout (Loss) Ldb = -10 log = -20 log 10 ( Pin ) 10( Vin ) Note: dB measures relative power, The power units are lost in the division. dbW = 10 log P 10(1W ) dbmW = 10 log P 10(1mW) Upper limit of FM radio Upper limit of AM radio Telephone channel 0 Music s l e b i –20 c e Speech Approximate D dynamic range n i Approximate –30 dB o of music i t dynamic range a of voice R r –40 e w o P Noise –60 10 Hz 100 Hz 300 Hz 1 kHz 3300 Hz 10 kHz 100 kHz 102 102.48 103 103.52 104 Frequency Figure 3.9 Acoustic Spectrum of Speech and Music [CARN99a] Screen Scan line Horizontal C A retrace C A Vertical retrace D B D B (a) Even field only (b) Odd field only C A 480 i = 483 lines every 1/30 sec (241.5 every 1/60 sec -- interlacing avoids flicker) 241.5 lines = 69us / line 1/60 sec ~450 dots / line Maximum bandwidth will be needed if dots alternate white and black. D B 225 cycles = ~4MHz bandwidth (c) Odd and even fields 69us 6MHz for color Figure 3.10 Video Interlaced Scanning Analog vs. Digital Transmission Analog Signals: Represent data with continuously varying electromagnetic wave Analog Data Analog Signal (voice sound waves) Telephone Digital Data Analog Signal (binary voltage pulses) (modulated on Modem carrier frequency) Digital Signals: Represent data with sequence of voltage pulses Analog Data Digital Signal Codec Digital Data Digital Signal Digital Transceiver Figure 3.14 Analog and Digital Signaling of Analog and Digital Data Table 3.1 Analog and Digital Transm ission (a) Data and Signals Analog Signal Digital Signal Two alternatives: (1) signal Analog data are encoded using a Analog Data occupies the same spectrum as the codec to produce a digital bit analog data; (2) analog data are stream. Option (1) º baseband encoded to occupy a different modulated portion of spectrum. Digital data are encoded using a Two alternatives: (1) signal modem to produce analog signal. consists of two voltage levels to Digital Data represent the two binary values; (2) digital data are encoded to produce a digital signal with desired properties. (b) Treatment of Signals Analog Transmission Digital Transmission Is propagated through amplifiers; Assumes that the analog signal same treatment whether signal is represents digital data. Signal is used to represent analog data or propagated through repeaters; at Analog Signal digital data. each repeater, digital data are Modem Modem recovered from inbound signal and used to generate a new analog Repeater outbound signal. Not used Digital signal represents a stream of 1s and 0s, which may represent digital data or may be an encoding Digital Signal of analog data. Signal is propagated through repeaters; at each repeater, stream of 1s and 0s is recovered Digital Digital Transceiver Transceiver from inbound signal and used to generate a new digital outbound Repeater signal. .