Leo Lam © Signals and Systems EE235

Leo Lam © Today’s menu Sampling/Anti-Aliasing Communications (intro)

How to avoid aliasing? Leo Lam © We ANTI-alias. SampleReconstruct B w s > 2w c time signal x(t) X(w) Anti-aliasing filter w c < B Z(w) z(n)

Bandwidth Practice Leo Lam © Find the Nyquist frequency for:

Bandwidth Practice Leo Lam © Find the Nyquist frequency for: const[rect(  /200)*rect(  /200)] =

Bandwidth Practice Leo Lam © Find the Nyquist frequency for: (bandwidth = 100) + (bandwidth = 50)

Communications Leo Lam © Practical problem –One wire vs. hundreds of channels –One room vs. hundreds of people Dividing the wire – how? –Time –Frequency –Orthogonal signals (like CDMA)

FDM (Frequency Division Multiplexing) Leo Lam © Focus on Amplitude Modulation (AM) From Fourier Transform: X x(t) m(t)=e j 0 t y(t) Y()=X( 0 ) 00  X()  TimeFOURIER

FDM (Frequency Division Multiplexing) Leo Lam © Amplitude Modulation (AM) Frequency change – NOT LTI!  -55  F Multiply by cosine!

Double Side Band Amplitude Modulation Leo Lam © FDM – DSB modulation in time domain x(t)+B x(t)

Double Side Band Amplitude Modulation Leo Lam © FDM – DSB modulation in freq. domain For simplicity, let B=0 ! 0 X(w) 1 ! –!C–!C !C!C 0 1/2 Y(w)

DSB – How it’s done. Leo Lam © Modulation (Low-Pass First! Why?) y(t) !1!1 ! 0 !2!2 !3!3 1/2 Y(  ) ! 0 ! 0 ! 0 X3()X3() X1()X1() X2()X2() x 2 (t) x 1 (t) x 3 (t) cos(w 3 t) cos(w 1 t) cos(w 2 t)

DSB – Demodulation Leo Lam © Band-pass, Mix, Low-Pass x y(t)=x(t)cos(  0 t) m(t)=cos(  0 t)z(t) = y(t)m(t) = x(t)[cos(  0 t)] 2 = 0.5x(t)[1+cos(2  0 t)] 00  0  0  0 LPF Y(  ) Z(  ) X(  )    What assumptions? -- Matched phase of mod & demod cosines -- No noise -- No delay -- Ideal LPF

DSB – Demodulation (signal flow) Leo Lam © Band-pass, Mix, Low-Pass LPF BPF1 BPF2 BPF3 !1!1 ! 0 !2!2 !3!3 1/2 Y(  ) ! 0 ! 0 ! 0 X3()X3() X1()X1() X2()X2() cos(  1 t) cos(  2 t) cos(  3 t) y(t) x 1 (t) x 3 (t) x 2 (t)

DSB in Real Life (Frequency Division) Leo Lam © KARI 550 kHz Day DA2 BLAINE WA US 5.0 kW KPQ 560 kHz Day DAN WENATCHEE WA US 5.0 kW KVI 570 kHz Unl ND1 SEATTLE WA US 5.0 kW KQNT 590 kHz Unl ND1 SPOKANE WA US 5.0 kW KONA 610 kHz Day DA2 KENNEWICK-RICHLAND-P WA US 5.0 kW KCIS 630 kHz Day DAN EDMONDS WA US 5.0 kW KAPS 660 kHz Day DA2 MOUNT VERNON WA US 10.0 kW KOMW 680 kHz Day NDD OMAK WA US 5.0 kW KXLX 700 kHz Day DAN AIRWAY HEIGHTS WA US 10.0 kW KIRO 710 kHz Day DAN SEATTLE WA US 50.0 kW