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2 通信方式第 2 版 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. このサンプルページの内容は, 第 2 版発行当時のものです.

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10 v(t) =v(t + n ), n =0, ± 1, ± 2, (1.1) (periodic waveform) (period) v(t) =A 0 + A n cos 2nπt + B n sin 2nπt (1.2) n=1 (Fourier series) A 0 (1.2) ( /2 /2) A 0 = 1 /2 /2 n=1 v(t) dt (1.3) v(t) 1 A n B n (1.2) cos(2πnt/) sin(2πnt/) 1 A n B n (n =1, 2 )

11 2 1 A n = 2 B n = 2 /2 /2 /2 /2 v(t)cos 2πnt v(t)sin 2πnt dt dt (1.4) A n B n (Fourier coefficient) v(t) v(t) =v( t) A 0 = 2 /2 v(t) dt 0 A n = 4 (1.5) /2 v(t)cos 2πnt dt, B n =0 0 v(t) v(t) = v( t) A 0 = A n =0 B n = 4 /2 v(t)sin 2πnt dt 0 (1.2) ( ) 2nπt v(t) =C 0 + C n cos + φ n n=1 (1.6) (1.7) (1.2) (1.7) C 0 = A 0, C n = A n2 + B 2 n (1.8) φ n = tan 1 B n A n f 0 =1/ C n nf 0 C n cos(2πnt/ + φ n ) φ n C n (amplitude spectrum) φ n (phase spectrum) (complex Fourier series) ( v(t) = V n exp j 2πnt ) (1.9) n= V n

12 V n = 1 /2 / ( v(t)exp j 2πnt ) dt (1.10) j j = 1 (1.9) (1.2) cos x = ejx + e jx, sin x = ejx e jx 2 2j A 0 = V 0 A n jb n 2 = V n, A n + jb n 2 = V n (1.11) (1.12) V n (1.7) C n V 0 = C 0 V n = C n 2 exp(jφ n), V n = C (1.13) n 2 exp( jφ n) V n exp(j2πnt/) V n V n = V n exp(jφ n ) (1.14) V n (frequency spectrum) v(t) (1.10) V n = V n, V n = V n (1.15) (1.10) v(t) V n v(t) V n nf 0 nf 0 nf 0 (1.15) V n = V n, φ n = φ n (1.16) V n ( )

13 4 1 V 0 = C 0, V n = V n = C n, n =1, 2, (1.17) 2 φ n ( ) ( /2 /2) v(t) (t 0 t 0 + ) (1.10) V n = 1 t0 + ( v(t)exp j 2πnt ) dt (1.18) t 0 v(t) (t 0 t 0 + ) V n v(t) ( ) A τ (0 <τ<) 1.1 B n 0 A 0 A n (1.5) (0 τ/2) A 0 = 2 τ/2 Adt= Aτ (1.19) 0 A n = 4 τ/2 A cos 2πnt [ ] 2Aτ sin(nπτ/ ) dt = (1.20) 0 nπτ/ (1.8) } C 0 = A 0, C n = A n (1.21) φ n =0 v(t) = Aτ + 2Aτ [ ] sin(nπτ/ ) cos 2πnt nπτ/ n=1 (1.22)

14 1.2 5 (1.10) (1.12) (1.13) V n = Aτ [ sin(nπτ/ ) nπτ/ ], V 0 = Aτ (1.23) v(t) V n v(t) = Aτ [ ] ( sin(nπτ/ ) exp j 2πnt ) (1.24) nπτ/ n= (1.22) (1.24) ( ) ( ) 1.2 τ/ =1/4 V n 1.2 (τ/ =1/4) S a (x) = sin x x (1.25) (sampling function) 1.3 S a (0) = 1, S a (±nπ) =0, n =1, 2, (1.26) x

15 S a (x) (Dirac s delta function) 1.4 ε 1/ε 1 0 { 0 x 0 δ(x) = x =0 (1.27) δ(x) dx = 1 (1.28) σ 2 0 ) 1 δ(x) = lim exp ( x2 σ 0 2πσ 2σ 2 (1.29) k δ(x) = lim k π S a(kx) (1.30) 1.4

16 1.2 7 a δ(x a) x = a f(x) f(x)δ(x a) dx = f(a) (1.31) 1.5 (unit step function) Aτ = I τ I (intensity) τ 0 ( ) sin(nπτ/ ) nπτ = S a 1 (1.32) nπτ/ v(t) = I + 2I cos 2πnt n=1 (1.33)

17 8 1 v(t) = I n= ( exp j 2πnt ) (1.34) 1.3 (linear system), (transfer function) V n exp(j2πf n t), n =0, ± 1, ± 2, (1.35) H(f n )= H(f n ) exp[jθ(f n )] (1.36) f n = n/ = nf 0 ( f 0 ) H(f n )V n exp(j2πf n t) (1.37) v i (t) = V n exp(j2πf n t) (1.38) n= v o (t) = H(f n )V n exp(j2πf n t) (1.39) n=

18 v o (t) =H(0)C H(f n ) C n cos[2πf n t + φ n + θ(f n )] (1.40) n=1, (1.35) V n exp(j2πf n t)+v n exp( j2πf n t) =2Re[V n exp(j2πf n t)] (1.41) H(f n )V n exp(j2πf n t)+h( f n )V n exp( j2πf n t) (1.42) (1.42), H(f n )=H ( f n ) (1.43) H(f n ) = H( f n ), θ(f n )= θ( f n ) (1.44) H(f n ) θ(f n ) 1.7 (a) RC (RC low-pass filter) (b) RC (RC high-pass filter) f V exp (j2πft) ( f = n/ ) ( ) H(f) = 1, f 1 = 1 1+jf/f 1 2πRC (1.45) 1.7 RC

19 10 1 f 1 H(f) H(0) 3[dB] (high-frequency cutoff) ( ) H(f) = 1 1 jf 2 /f, f 2 = 1 2πRC (1.46) f 2 H(f) H(± ) 3[dB] (low-frequency cutoff) H(f) 1.8 ( ) v(t) 1 P = 1 /2 /2 [v(t)] 2 dt (1.47) 1[Ω] P (normalized power) v(t) P v(t) (1.7) P = C 2 2 C n 0 + (1.48) 2 n=1 (1.40) H(f) P o = H 2 (0)C H(f n ) 2 2 C n (1.49) 2 n=1 v(t) (1.38) (1.47) 0 V RC

20 V n exp(j2πf n t) V n exp( j2πf n t), n = ±1, ±2, (1.50) V n = V n P = V n 2 = V V n 2 (1.51) n= n=1 V n 2 f n = nf 0 = n/ (power spectrum) P o = H(f n ) 2 V n 2 n= = H 2 (0)V H(f n ) 2 V n 2 (1.52) n=1 1.3 v o (t) = t t v i (t) dt (1.53) v i (t) =V exp(j2πft) (1.54) v o (t) = t t V exp(j2πft) dt [ ] 1 exp( j2πf) = V exp(j2πft) (1.55) j2πf H(f) = v o(t) v i (t) = 1 exp( j2πf) j2πf ( ) sin πf = exp( jπf) πf = S a (πf)exp( jπf) (1.56)

21 / 0 v(t) 1/ = Δf ( v(t) = V n exp j 2πnt ) = n= n= ( ) Vn exp(j2πnδft)δf (1.57) Δf Δf 0 nδf f v(t) v(t) = V (f) V (f) = V (f)exp(j2πft) df (1.58) V n lim Δf 0 Δf (frequency spectral density) V n = 1 /2 ( v(t)exp j 2πnt ) dt = Δf /2 1/2Δf 1/2Δf (1.59) v(t) exp( j2πnδft) dt (1.60) Δf 0 V (f) V (f) = v(t) exp( j2πft) dt (1.61) (1.58) (1.61) (Fourier transform pair) V (f) v(t) (Fourier transform) v(t) V (f) (inverse Fourier transform)

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23 60 3 (FDM) (AM), (SN ) 3.1 (baseband signal) (modulating signal) (carrier) (modulated wave) f f m f m f m =3.4 [khz] f m =4.5 [MHz] f c f m (double sideband ; DSB) m(t) cos 2πf c t DSB 1) v DSB (t) =m(t)cos2πf c t (3.1) 1) DSB DSB ( ) DSB DSB AM FM

24 m(t) M(f) DSB V DSB (f) = 1 2 [M(f f c)+m(f + f c )] (3.2) (3.2) DSB DSB 3.1 DSB f c ( ±f c ) (upper sideband; USB) (lower sideband; LSB) DSB 2 2f m DSB DSB (double sideband suppressed carrier; DSB-SC) 3.1 DSB DSB 3.2 AM (DSB ) AM 2 DSB-SC (balanced modulator)

25 DSB (demodulation) (detection) DSB DSB (synchronous detection) (coherent detection) DSB (product detector) DSB v DSB (t) =m(t)cos2πf c t (3.3) v DSB (t) ( ) c(t) =cos2πf c t (3.4) v DSB (t)c(t) =m(t)cos 2 2πf c t = 1 2 m(t)+ 1 2 m(t)cos4πf ct (3.5) V DSB (f) C(f) = 1 2 M(f)+1 4 [M(f 2f c)+m(f +2f c )] (3.6) (3.6) 1 2 ±2f c f m 3.3 DSB (3.3) DSB Δf Δφ

26 DSB c(t) =cos[2π(f c + Δf)t + Δφ] (3.7) v o (t) = 1 m(t)cos(2πδft + Δφ) (3.8) 2 Δf (offset) Δφ Δf Δφ (3.8) Δf =0 v o (t) = 1 m(t)cosδφ (3.9) 2 cos Δφ Δφ = nπ/2(n = ±1, 3, 5, ) DSB DSB ( 3.1 ) (pilot carrier) DSB DSB FM ( )

27 PCM ( ) ( ) (ASK) (FSK) (PSK) ( ) (amplitude shift keying ; ASK) 2 0 (on-off keying ; OOK) ( 1/f c ) OOK } s 1 (t) =A cos 2πf c t, 1, s 0 (t) =0, 0 2 t (6.1) 2 (6.1) (raised cosine) ( 1.1 )

28 OOK 6.1 OOK 1 0 (mark) (spece) OOK (6.1) ( 1) ( 0) OOK (bit error probability) OOK (noncoherent detection) AM ( ) 7 ( ) 6.2 OOK

29 134 6 n(t) =x(t)cos2πf c t y(t) sin 2πf c t (6.2) x(t) y(t) 0 s 1 (t)+n(t) =[A + x(t)] cos 2πf c t y(t) sin 2πf c t (6.3) R 1 (t) = [A + x(t)] 2 + y 2 (t) (6.4) R 0 (t) = x 2 (t)+y 2 (t) (6.5) - p 1 (R) = R [ N exp R2 + A 2 ] ( ) AR I 0 (6.6) 2N N N N = x 2 (t) =y 2 (t) (6.7) p 0 (R) = R ( ) N exp R2 2N (6.8) t = s R } R( s ) >R (6.9) R( s ) <R

30 ( ) 0( ) (incorrect dismissal) P e1 = = R 0 R 0 p 1 (R) dr R N exp [ R2 + A 2 2N ] ( ) AR I 0 dr (6.10) N Q Q(x, y) = exp ( t2 + x 2 ) I 0 (xt)tdt (6.11) 2 y P e1 =1 Q ( 2γ, α ) (6.12) γ = A2 2N, α = R N (6.13) γ SN ( ) A A 2 /2 N γ SN CN ( ) α 0( ) 1 ( ) (false alarm) ) ) R P e0 = p 0 (R) dr = ( R N exp R2 dr =exp ( α2 (6.14) 2N 2 R P e1 P e % ( 1/2) 2 P e = 1 2 (P e1 + P e0 )

31 2012 Printed in Japan ISBN

微分積分 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. このサンプルページの内容は, 初版 1 刷発行時のものです.

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