3.2 Pulse Amplitude Modulation(spectrum of a naturally sampled PAM) Theorem: the spectrum for a naturall sampled PAM signal is W()=Flo(O]=d 2 Sin na w(f-nys) =OO gn Where fs=1/Ts, Os=ifs, the duty cycle of s(t) is d=t/Ts and W(=Flo(t)I is the spectrum of the original unsampled waveform s()=(r-k7;1/r ∑Ⅱ(--k-)=∑∏(-kΣcnem0 k=-∞ k= 99 3.2 Pulse Amplitude Modulation(spectrum of a naturally sampled PAM) • Theorem: the spectrum for a naturally sampled PAM signal is : Where fs=1/Ts , ωs=2πfs , the duty cycle of s(t) is d=τ/Ts , and W(f)=F[ω(t)] is the spectrum of the original unsampled waveform. ∑ ∞ =-∞ ( - n ) πnd sin πnd ( ) = [ω ( )] = n s s s W f F t d W f f ( ) ∑∏ ∑∏ ∑ ∑∏ ∞ =-∞ ω ∞ =-∞ ∞ =-∞ ∞ =-∞ ) 1 - τ ) = ( τ - τ = ( s(t) = [ - ]/ τ k j n t n k k s k s s c e d k T t k t t k T ＝