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Electrical Communications Systems ECE.09.331 Spring 2010. Lecture 7a March 2, 2010. Shreekanth Mandayam ECE Department Rowan University http://engineering.rowan.edu/~shreek/spring10/ecomms/. Signals Systems. Modulation Index Efficiency Bandwidth Noise.
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Electrical Communications SystemsECE.09.331Spring 2010 Lecture 7aMarch 2, 2010 Shreekanth Mandayam ECE Department Rowan University http://engineering.rowan.edu/~shreek/spring10/ecomms/
Signals Systems Modulation Index Efficiency Bandwidth Noise Performance Transmitters Receivers Standards Time Domain Complex Envelope Spectrum Power Plan • Complex Envelope Representation • Spectrum of a bandpass signal • DSB-SC Modulation • Costas Loop • QAM • SSB
message: m(t) carrier: c(t) Modulator s(t): radio signal Complex Envelope Representation • We want a common mathematical representation for • information transfer from baseband to bandpass • any bandpass signal • any time of modulation • signal/noise and signal+noise
|M(f)| -B 0+B Signals Systems Modulation Index Efficiency Bandwidth Noise Performance Transmitters Receivers Standards Time Domain Complex Envelope Spectrum Power DSB-SC Modulation Message Spectrum Matlab Demo http://engineering.rowan.edu/~shreek/spring10/ecomms/demos/dsbsc.m f DSB-SC Spectrum |S(f)| -fc-B -fc -fc+B 0fc-B fc fc+B f
DSB-SC: Coherent Detector Product Modulator Baseband LPF v(t) s(t) Aocos2pfct Local Oscillator
v1(t) Product Modulator Baseband LPF v3(t) v4(t) VCO LPF X s(t) -90o Phase Shift Phase Discriminator Product Modulator Baseband LPF v2(t) Synchronous Coherent Detection: Costas PLL I-Channel Q-Channel
Product Modulator S s(t) m1(t) LPF Product Modulator Local Oscillator Local Oscillator -90o Phase Shift -90o Phase Shift Product Modulator LPF m2(t) Product Modulator Quadrature Amplitude Modulation (QAM) Rx Tx I-Channel Q-Channel
|S(f)| -fc-B -fc -fc+B 0fc-B fc fc+B f Single Sideband (SSB) Modulation • Recall: DSB-SC Spectrum • USSB - Signal with zero-valued spectrum for |f| < fc • LSSB - Signal with zero-valued spectrum for |f| > fc
1.5 1 0.5 0 -0.5 -1 0 1 2 3 4 5 6 7 time, t in sec The Hilbert Transform » t=0:0.1:2*pi; » w=sin(t); » plot(t,w) » hold Current plot held » H=hilbert(w); » plot(t,imag(H),'r'); » xlabel('time, t in sec')
Product Modulator S s(t) m(t) Product Modulator -90o Phase Shift Sideband Filter Product Modulator m(t) s(t) Carrier -90o Phase Shift Carrier SSB Generation Phasing Method Filter Method