By John G. Proakis
Thorough insurance of easy electronic verbal exchange approach ideas guarantees that readers are uncovered to all simple suitable subject matters in electronic conversation approach layout. using CD participant and JPEG photograph coding typical as examples of structures that hire glossy conversation ideas permits readers to narrate the idea to sensible platforms. Over one hundred eighty worked-out examples in the course of the publication aids readers in realizing easy techniques. Over 480 difficulties regarding purposes to sensible platforms akin to satellite tv for pc communications platforms, ionospheric channels, and cellular radio channels offers readers plentiful chance to perform the ideas they've got simply discovered. With an emphasis on electronic communications, Communication structures Engineering, moment Edition introduces the fundamental rules underlying the research and layout of verbal exchange platforms. additionally, this ebook supplies a fantastic advent to analog communications and a evaluation of vital mathematical starting place issues. New fabric has been extra on instant communique systems—GSM and CDMA/IS-94; rapid codes and iterative interpreting; multicarrier (OFDM) structures; a number of antenna structures. comprises thorough insurance of easy electronic conversation approach principles—including resource coding, channel coding, baseband and service modulation, channel distortion, channel equalization, synchronization, and instant communications. contains easy assurance of analog modulation equivalent to amplitude modulation, part modulation, and frequency modulation in addition to demodulation equipment. to be used as a reference for electric engineers for all simple proper issues in electronic verbal exchange procedure layout.
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2. . . . . . . . . r. 2) The average power in the carrier is Pcarrier = 1002 A2c = = 5000 2 2 The power in the sidebands is Psidebands = 502 502 2502 2502 + + + = 65000 2 2 2 2 3) The message signal can be written as m(t) = sin(2π103 t) + 5 cos(2π2 × 103 t) = −10 sin(2π103 t) + sin(2π103 t) + 5 As it is seen the minimum value of m(t) is −6 and is achieved for sin(2π103 t) = −1 or t = 3 + 1013 k, with k ∈ Z. Hence, the modulation index is α = 6. 025 and is achieved for sin(2π103 t) = 1 arcsin( 20 ) 2π103 + Since 2 × 103 k .
50 ...................... ✻ ✻ . . . . . . . . . 25 ................ 23, we obtain ∞ x(t − nTp ) v(t) = m(t)s(t) = m(t) n=−∞ 1 = m(t) Tp ∞ X( n=−∞ n j2π Tnp t )e Tp where T t + 4p n X( ) = F −Π Tp Tp +Π t− 2 = = Tp 4 Tp 2 f = Tn Tp Tp Tp Tp sinc(f ) e−j2πf 4 − ej2πf 4 2 2 p f = Tn p Tp n π sinc( )(−2j) sin(n ) 2 2 2 Hence, the Fourier transform of v(t) is V (f ) = π n n 1 ∞ sinc( )(−2j) sin(n )M (f − ) 2 n=−∞ 2 2 Tp The bandpass ﬁlter will cut-oﬀ all the frequencies except the ones centered at Thus, the output spectrum is 1 Tp , 1 1 1 1 U (f ) = sinc( )(−j)M (f − ) + sinc( )jM (f + ) 2 Tp 2 Tp 1 1 2 2 = − jM (f − ) + jM (f + ) π Tp π Tp = 4 M (f ) π 1 1 1 1 δ(f − ) − δ(f + ) 2j Tp 2j Tp Taking the inverse Fourier transform of the previous expression, we obtain u(t) = 4 1 m(t) sin(2π t) π Tp 47 that is for n = ±1.
404. 5 KHz. 29 The modulated PM signal is given by u(t) = Ac cos(2πfc t + kp m(t)) = Ac Re ej2πfc t ejkp m(t) = Ac Re ej2πfc t ejm(t) 60 The signal ejm(t) is periodic with period Tm = cn = = and Fourier series expansion ejm(t) e−j2πnfm t dt 0 Tm 2 1 Tm = − = Tm 1 Tm 1 fm ej e−j2πnfm t dt + 0 ej e−j2πnfm t Tm j2πnfm Tm 2 Hence, ejm(t) = − 0 (−1)n − 1 j j(e − e−j ) = 2πn Tm 1 Tm Tm 2 e−j e−j2πnfm t dt e−j e−j2πnfm t Tm j2πnfm 0 2 π(2l+1) Tm Tm 2 n = 2l sin(1) n = 2l + 1 ∞ 2 sin(1)ej2πlfm t π(2l + 1) l=−∞ and u(t) = Ac Re ej2πfc t ejm(t) = Ac Re ej2πfc t ∞ = Ac l=−∞ ∞ 2 sin(1)ej2πlfm t π(2l + 1) l=−∞ 2 sin(1) cos(2π(fc + lfm )t + φl ) π(2l + 1) where φl = 0 for l ≥ 0 and φl = π for negative values of l.