ecture 6&7 Modulation Eytan Modiano AA Dept
Lectures 6&7 Modulation Eytan Modiano AA Dept. Eytan Modiano Slide 1
Modulation Representing digital signals as analog waveforms ° Baseband signals Signals whose frequency components are concentrated around zero ● Passband signals Signals whose frequency components are centered at some frequency fc away from zero Baseband signals can be converted to passband signals through modulation Multiplication by a sinusoid with frequency fc
Modulation • Representing digital signals as analog waveforms • Baseband signals – Signals whose frequency components are concentrated around zero • Passband signals – Signals whose frequency components are centered at some frequency fc away from zero • Baseband signals can be converted to passband signals through modulation – Multiplication by a sinusoid with frequency fc Eytan Modiano Slide 2
Baseband signals The simplest signaling scheme is pulse amplitude modulation(PAM) With binary pam a pulse of amplitude a is used to represent a"1" and a pulse with amplitude-a to represent a0 The simplest pulse is a rectangular pulse, but in practice other type of pulses are used For our discussion we will generally assume a rectangular pulse If we let g(t be the basic pulse shape than with pam we transmit gt) to represent a“1and-g(t) to represent a“0” 1→>S(t)=g(t) A 0=>S(t)=-g(t)
Baseband signals • The simplest signaling scheme is pulse amplitude modulation (PAM) – With binary PAM a pulse of amplitude A is used to represent a “1” and a pulse with amplitude -A to represent a “0” • The simplest pulse is a rectangular pulse, but in practice other type of pulses are used – For our discussion we will generally assume a rectangular pulse • If we let g(t) be the basic pulse shape, than with PAM we transmit g(t) to represent a “1” and -g(t) to represent a “0” g(t) 1 => S(t) = g(t) A 0 => S(t) = -g(t) Tb Eytan Modiano Slide 3
M-ary PAM Use M signal levels, Ay. A Each level can be used to represent Log2(M)bits °Eg,M=4=A1=3,A2=-1,A3=1A4=3 s()=A1g(t) Mapping of bits to signals si b1b2 SSs 011
M-ary PAM • Use M signal levels, A1…AM – Each level can be used to represent Log2(M) bits • E.g., M = 4 => A1 = -3, A2 = -1, A3 = 1, A4 = 3 – Si(t) = Ai g(t) • Mapping of bits to signals Si b1b2 S1 00 S2 01 S3 11 S4 10 Eytan Modiano Slide 4
Signal Energy Em=(Sm()dt=(Am)L(g )dt=(Am)E g The signal energy depends on the amplitude Eo is the energy of the signal pulse g(t) For rectangular pulse with energy ea=> A dt=TA=>A=E/2 g(t) 0<t≤T E。/2 g() otherwise
g t t T Signal Energy T T Em = ∫0 ( (t))2 dt = ( Am )2 ∫0 ( )2 dt = ( Am )2 Eg Sm gt • The signal energy depends on the amplitude • Eg is the energy of the signal pulse g(t) • For rectangular pulse with energy Eg => T Eg = ∫0 A2 dt = TA2 => A = Eg / 2 g(t) Eg / 2 0 ≤≤ () = 0 otherwise Eg /2 Eytan Modiano Slide 5 T