tailieunhanh - Proakis J. (2002) Communication Systems Engineering - Solutions Manual (299s) Episode 4

Tham khảo tài liệu 'proakis j. (2002) communication systems engineering - solutions manual (299s) episode 4', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | The power content is Fam A A aPM 200 200 236 The bandwidth of the signal is Wam 2W 20000 Hz. 4 If the modulation is FM with kf 50000 then A2 Pfm 2 200 and the effective bandwidth is approximated by Carson s rule as Bc 2 fi 1 W 2 i 50000 1 W 120000 Hz Problem 1 Since F sinc 400t 400 n 400 the bandwidth of the message signal is W 200 and the resulting modulation index g k max m t fc l0 6 kf 120 W W Hence the modulated signal is u t Acos 2nfct 2nkf m r dr J 100 cos 2nfct 2n1200 Ị sinc 400r dr 2 The maximum frequency deviation of the modulated signal is A max 3f W 6 X 200 1200 3 Since the modulated signal is essentially a sinusoidal signal with amplitude A 100 we have A2 P A- 5000 4 Using Carson s rule the effective bandwidth of the modulated signal can be approximated by Bc 2 ổf 1 W 2 6 1 200 2800 Hz Problem 1 The maximum phase deviation of the PM signal is A max kp max m t kp The phase of the FM modulated signal is 0 t 2nkf I m r dr 2nkf y m r dr 2nkf J0 rdr nkf t2 nkf 2nkf J1 dr nkf 2nkf t 1 nkf 2nkf 2nkf 2 dr 3nkf 2nkf t 2 nkf 0 t 1 1 t 2 2 t 3 3 t 58 The maximum value of ộ t is achieved for t 2 and is equal to 3nkf. Thus the desired relation between kp and kf is kp 3nkf 2 The instantaneous frequency for the PM modulated signal is fi t fc dộ t fc kpdm t 2n dt 2n dt For the m t given in Fig. the maximum value of dtm t is achieved for t in 0 1 and it is equal to one. Hence max fi t fc 71 2n For the FM signal fi t fc kf m t . Thus the maximum instantaneous frequency is max fi t fc kf fc 1 Problem 1 Since an angle modulated signal is essentially a sinusoidal signal with constant amplitude we have P Ad P 5000 2 2 The same result is obtained if we use the expansion u t Ể AcJn ii cOs 2vUc ft n - X along with the identity Jfa 2 Ễ Jn 0 1 n 1 2 The maximum phase deviation is Aộmax max 4sin 2000nt 4 3 The instantaneous frequency is fi fc A d t 2n dt fc m cos 2000nt 2000n fc 4000cos 2000nt 2n Hence the maximum frequency deviation is Afmax max Ifi