S. Mandayam/ ECOMMS/ECE Dept./Rowan University Electrical Communications Systems ECE Spring 2008 Shreekanth Mandayam ECE Department Rowan University Lecture 6b February 27, 2008

S. Mandayam/ ECOMMS/ECE Dept./Rowan UniversityPlan Complex Envelope Representation Spectrum of a bandpass signal DSB-SC Modulation Costas Loop QAM SSB Signals Systems Time Domain Complex Envelope Spectrum Power Performance Transmitters Receivers Standards Modulation Index Efficiency Bandwidth Noise

S. Mandayam/ ECOMMS/ECE Dept./Rowan University ECOMMS: Topics

S. Mandayam/ ECOMMS/ECE Dept./Rowan University 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 Signal P rocessing Carrier circuits Channel Carrier circuits Signal processing m(t) g(t) s(t) r(t) n(t)

S. Mandayam/ ECOMMS/ECE Dept./Rowan University 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 Modulator message: m(t) carrier: c(t) s(t): radio signal

S. Mandayam/ ECOMMS/ECE Dept./Rowan University Spectrum of a Bandpass Signal

S. Mandayam/ ECOMMS/ECE Dept./Rowan University DSB-SC Modulation Signals Systems Time Domain Complex Envelope Spectrum Power Performance Transmitters Receivers Standards Modulation Index Efficiency Bandwidth Noise -B 0 +B |M(f)| f -f c -B -f c -f c +B 0 f c -B f c f c +B |S(f)| f Message Spectrum DSB-SC Spectrum Matlab Demo /~shreek/spring08/ecomms/ demos/dsbsc.m

S. Mandayam/ ECOMMS/ECE Dept./Rowan University DSB-SC: Coherent Detector Product Modulator A o cos2  f c t s(t) Local Oscillator Baseband LPF v(t)

S. Mandayam/ ECOMMS/ECE Dept./Rowan University Synchronous Coherent Detection: Costas PLL s(t) v 1 (t) Product Modulator Baseband LPF VCO LPF -90 o Phase Shift X v 2 (t) Product Modulator Baseband LPF v 3 (t) v 4 (t) Phase Discriminator I-Channel Q-Channel

S. Mandayam/ ECOMMS/ECE Dept./Rowan University Quadrature Amplitude Modulation (QAM) Product Modulator Local Oscillator -90 o Phase Shift Product Modulator m 1 (t) m 2 (t)  s(t) Product Modulator Local Oscillator -90 o Phase Shift Product Modulator LPF Tx Rx I-Channel Q-Channel

S. Mandayam/ ECOMMS/ECE Dept./Rowan University Single Sideband (SSB) Modulation Recall: DSB-SC Spectrum USSB - Signal with zero-valued spectrum for |f| < f c LSSB - Signal with zero-valued spectrum for |f| > f c -f c -B -f c -f c +B 0 f c -B f c f c +B |S(f)| f

S. Mandayam/ ECOMMS/ECE Dept./Rowan University The Hilbert Transform time, t in sec » 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')

S. Mandayam/ ECOMMS/ECE Dept./Rowan University SSB Generation Product Modulator Carrier -90 o Phase Shift Product Modulator -90 o Phase Shift m(t)  s(t) Sideband Filter Carrier Product Modulator m(t) s(t) Phasing Method Filter Method

S. Mandayam/ ECOMMS/ECE Dept./Rowan University SSB Generation: Weaver’s Method

S. Mandayam/ ECOMMS/ECE Dept./Rowan UniversitySummary