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1 s(t) ( ) f c : A cos(2πf c t + ϕ) (AM, Amplitude Modulation) (FM, Frequency Modulation) (PM, Phase Modulation) 2
1.1 AM s(t) : A(αs(t) + 1) cos 2πf c t A, α : s(t) = cos 2πft (f f c ) ( A = α = 1 ) (α cos 2πft + 1) cos 2πf c t = α 2 {cos 2π(f c + f)t + cos 2π(f c f)t} + cos 2πf c t 3 f c f f c f c + f 3
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s(t) (baseband) (20Hz 20kHz ) ( 5.6MHz ) AM 3 (DSB: Double Side Band) (SSB: Signle Side Band) or SSB 5
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1.2 FM s(t) ( ) t A cos 2π f c t + α s(τ)dτ A cos 2π (f c + αs(t)) t 1.3 PM s(t) A cos 2π (f c t + αs(τ)) 7
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1.4 1 ( ) : 1 10
(SSB ) 11
1.5 1.5.1 ( ) L t L ( ) n = 0, ±1, ±2,... e n (t) = e 2πin 2L t = cos ( ) 2πn 2L t + i sin ( ) 2πn 2L t e n e n (t) e n, e n = 1 2L f, g = 1 2L L L L L f(t)g(t)dt e 2πin 2L t e 2πin 2L t dt = 1 2L L L dt = 1 12
m n e m, e n = 1 2L = L L 1 2πi(m n) e πim L t e πin L t dt = 1 2L [ e 2πi(m n) 2L ] L t L L t L g(t) c n = g, e n = 1 2L L L n = 0, ±1, ±2,... g(t) = g(t)e 2πin 2L t dt = 1 2L n= c n e 2πin 2L t L L = 0 L L e 2πi( m+n) 2L t dt g(t)e 2πin 2L t dt 13
1.5.2 [ L, L] 2L (g(t) = g(t 2L)) (, ) (, ) h(f) L n= h ( n ) 1 2L 2L f = n 2L h(f) df (L ) 14
f = n/2l ( ) 1 L g(t) = g(τ)e πin L τ dτ e πin L t 2L n= L ( ) L = g(τ)e 2πiτ ( 2L n ) dτ e 2πit ( 2L n ) 1 n= L 2L ( ) g(τ)e 2πifτ dτ e 2πift df (L ) 2 G(f) = g(t) = g(τ)e 2πifτ dτ G(f)e 2πift df 2 f 15
: : x(t) X(f) M X(f) = 0 ( f M) x(t) M ( ) π(t nt ) x(t) = x(nt ) sinc T (T 1/(2M)) sinc n= sinc(θ) = sin θ θ 16
t = nt x(nt ) T : 1/(2T ) : (aliasing) C.E.Shannon (1949) V.A.Kotelnikov ( ) 1932 17
( ) x(t) M X(f) = x(t) = x(t)e 2πift dt X(f)e 2πift df f M f M X(f) = 0 X(f) = a n e2m 2πinf = a n e 2πiT nf n= n= (T = 1/(2M)) X(f) 18
a n a n = 1 2M = T = T M M = T x( T n) f M X(f) = n= X(f)e 2πi 2M nf df X(f)e 2πiT nf df X(f)e 2πi( T n)f df T x( T n)e 2πiT nf 19
x(t) = = = = = = M M n= n= n= n= X(f)e 2πift df = n= x( T n) T x(t n) T M M X(f)e 2πift df T x( T n)e 2πiT nf e 2πift df M M M M e 2πi(t+T n)f df e 2πi(t T n)f df x(t n) sin ( π T (t nt ) ) π T (t nt ) ( π ) x(t n) sinc T (t nt ) 20
1.6 (PAM : Pulse Amplitude Modulation) (PWM : Pulse Widith Modulation) (PPM : Pulse Position Modulation) (PFM : Pulse Frequency Modulation) 21
1.7 (Analog Digital Conversion, ADC) 1/2 (8bit, 256 ) CD (16bit, 65536 ) 22
(Digital Analog Conversion, DAC) ( 350MHz ) (PNM : Pulse Number Modulation) (PCM : Pulse Code Modulation) (2 ) ( ) ( ) 23
µ-law DPCM (Differential PCM) : (Predict coding) ADPCM (Addaptive DPCM) : 24
2 bps (bit per second) 1 bit (0/1 ) 2.1 ( ) 0 1 0/1 ( ) ( ) 25
(Unipolar code) : 0, 1 RZ (Return-Zero) : 1 0 NRZ (Non-Return Zero) : 1 0 (Dipolar code) : 1 or 0 or 1 (RZ,NRZ) (Bipolar code) AMI (Alternate Mark Inversion Code)) : 0 0 1 1 +1 NRZI (Non-Return Zero Inversion Code ) : 0 +1 1 1 (Dicode code) : 0 1 +1 (Dicode code) : 1 0 0 0 1 +1/ 1 26
(Biphase code) : 1 0 0 1 (Manchester code) 0 1 0 1 0 1 (Block code) : 1 bit bit bit ( bit ) 27
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2.2 (shift keying) 1bit bit (broadband communication) ASK (Amplitude Shift Keying) : OOK (On-Off Keying) : { 0 for 0 S ASK (t) = A sin 2πf c t for 1 FSK (Frequency Shift Keying) { A sin 2πf0 t for 0 S FSK (t) = A sin 2πf 1 t for 1 29
(Modulation index) m = f 0 f 1 T MSK (Minimum Shift Keying) : f 0 f 1 2 T 0 sin 2πf 0 t sin 2πf 1 tdt = 0 0 n 2π(f 0 f 1 )T = nπ m = 0.5 sin 2πf 0 t sin 2πf 1 t = 1 2 ( cos 2π(f 0 + f 1 )t + cos 2π(f 0 f 1 )t) 1 2 0 T 1 0 2 cos 2π(f 0 f 1 )tdt = sin 2π(f 0 f 1 )T = T 4π(f 0 f 1 ) 2 sinc2π(f 0 f 1 )T 0 sinc 0 n 2π(f 0 f 1 )T = nπ 30
PSK (Phase Shift Keying) : { A sin 2πfc t for 0 S BPSK (t) = A sin(2πf c t + π) for 1 BPSK (Binary PSK) : 2 PSK 1 1bit QPSK (Quadri PSK) : 4 PSK 1 2bit A sin(2πf c t + ϕ) x = A cos ϕ y = A sin ϕ 1 31
APK (Amplitude Phase shift Keying) : 16APSK : 4 4 1 4bit (16APK ) QAM (Quardrature Amplitude Modulation) : 16QAM : 1 4bit 32
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2.2.1 1 (TDM, Time Division Multiplexing) : 1 ( ) 1 bit 1 byte (= 8bit) ( ) 39
( ) ( km 10km ) 40
2.2.2 (10 1000 ) : (DS, Direct Sequence) CDMA200 W-CDMA (FOMA) (CDMA : Code Division Multiple Access) (FH) Bluetooth (IEEE 802.15.1) 41
2.2.3 PN (Pseudo-randam Noise) 0, 1 M x n = EXOR(x n p, x n q ) ( ) (bit duration) : 1 bit (chip duration) : 1 bit (bit rate) : (chip rate) : W-CDMA ( 3.84 Mcps 5MHz) (spreading ration) : 42
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2.2.4 (hopping rate) Slow FH : (Bluetooth Slow FH ) Fast FH : 44
2.2.5 (OFDM) (OFDM : Orthogonal Frequency Division Multiplexing) LAN ( ) 3G (LTE : Long Term Evoluation, 4G) ( ) ( ) 45
( 2 ) : 1/4 2 : 0 1 0 1 0 1 46
MIMO (Mulitple Input Multiple Output) ( LAN 4 ) T T 2 T 2 e 2πift dt = e πit f e πit f 2πif = sin πt f πf = T sincπt f sinc 2/T 47
(SCM) : (MCM) : 1 bit bit : MCM : ( ) 48
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MCM T 2/T OFDM (QPSK ) S n (t) : n T : 1bit (T = NT s ) T sin(2πf n t + θ) sin 2πf n+1 t 0 S n (t)s n+1 (t)dt = 1 2 ( cos{2π(f n + f n+1 )t + θ} + cos{2π(f n f n+1 )t + θ}) 1 51
2 0 = = = T 1 0 2 cos{2π(f n f n+1 )t + θ}dt 1 4π(f n f n+1 ) [sin{2π(f n f n+1 )T + θ} sin θ] [ 2 sin 2π(f n f n+1 )T cos 2π(f ] n f n+1 )T + 2θ 4π(f n f n+1 ) 2 2 1 2π(f n f n+1 ) [sin{π(f n f n+1 )T } cos{π(f n f n+1 )T + 2θ}] f n+1 f n sin{π(f n f n+1 )T } π(f n f n+1 ) 1/T θ FSK 1/2T = 0 52
N OFDM N + 1 N T s ( N = 7 8/(7T s ) SCM 2/T s 4/7 OFDM 4/7 ) OFDM N 2 (FFT, Fast Fourier Transform) 53
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2.2.6 LAN LAN IEEE 802.11.b 11Mbps 2.4GHz DS-CDMA CSMA/CA IEEE 802.11.a 54Mbps 5.2/5.3GHz OFDM CSMA/CA IEEE 802.11.g 54Mbps 2.4GHz OFDM CSMA/CA IEEE 802.11.n 100 500Mbps 2.4GHz OFDM/ CSMA/CA MIMO (CSMA/CA: Carrier Sense Multiple Access with Collision Avoidance) (, AP) (PSP ) 55
SSID (Service Set ID), ESSID (Extended SSID) LAN ID SSID WEP (Wired Equivalent Privacy) LAN WPA (Wi-FI Protected Access) LAN TKIP (Temporal Key Integrity Protcol) WPA2 WPA WPS (Wi-Fi Protected Setup) WPA 56
2.2.7 BST-OFDM (Band Segmented Transmission OFDM) 6MHz 5.6MHz 13 6MHz ISDB (Integrated Services Digital Boradcasting) ( ATSC DVB CDMB SBTVD(ISBD )) 1 432 OFDM 13 12 HDTV 1 57
2.3 ( ) ( ) 1km % ( 1/10 ) ( 10 ) :0.125mm 0.05mm or 0.065mm :0.125mm 0.0092mm ((Dense) Wavelength Division Multiplex, (D)WDM) 1 Gbit/s 1 FSA-WDA 10.66Gbit/s 4, 100km( ) 58
3 ( OFDM 2 ) 59