S. Mandayam/ ECOMMS/ECE Dept./Rowan University Electrical Communications Systems ECE Spring 2011 Shreekanth Mandayam ECE Department Rowan University Lecture 4a February 8, 2011

S. Mandayam/ ECOMMS/ECE Dept./Rowan UniversityPlan Finish up – relationship between CFT and DFT Baseband and Bandpass Signals Modulation Battle Plan for Analyzing Comm Systems Amplitude Modulation (AM)

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

S. Mandayam/ ECOMMS/ECE Dept./Rowan University Discrete Fourier Transform (DFT) Discrete Domains Discrete Time: k = 0, 1, 2, 3, …………, N-1 Discrete Frequency:n = 0, 1, 2, 3, …………, N-1 Discrete Fourier Transform Inverse DFT Equal time intervals Equal frequency intervals n = 0, 1, 2,….., N-1 k = 0, 1, 2,….., N-1

S. Mandayam/ ECOMMS/ECE Dept./Rowan University Relation between CFT and DFT Windowing Sampling Generation of Periodic Samples

S. Mandayam/ ECOMMS/ECE Dept./Rowan University Baseband and Bandpass Signals Baseband signals: spectral magnitude is non-zero only near the origin and is zero (or negligible) elsewhere Bandpass signals: spectral magnitude is non-zero only near the vicinity of f = ± f c, were f c >> 0 - f m 0 +f m W(f) f - f c 0 +f c W(f) f AF Signals RF Signals Carrier Frequency

S. Mandayam/ ECOMMS/ECE Dept./Rowan UniversityModulation Modulating Signal Message Signal m(t) (Baseband) Modulated Signal s(t) (Bandpass) Information Modulation Frequency Translation What is it? How is it done? Modulator message: m(t) carrier: c(t) s(t): radio signal

S. Mandayam/ ECOMMS/ECE Dept./Rowan University Why Modulate? Antenna size considerations Narrow banding Frequency multiplexing Common processing

S. Mandayam/ ECOMMS/ECE Dept./Rowan University Battle Plan for Analyzing any Comm. Sys. Signals Systems Complex Envelope Time Domain Spectrum Power Performance Transmitters Receivers Standards Modulation Index Efficiency Bandwidth Noise

S. Mandayam/ ECOMMS/ECE Dept./Rowan University Amplitude Modulation (AM) Signals Systems Complex Envelope Time Domain Spectrum Power Performance Transmitters Receivers Standards Modulation Index Efficiency Bandwidth Noise

S. Mandayam/ ECOMMS/ECE Dept./Rowan University AM Spectrum -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 AM Spectrum

S. Mandayam/ ECOMMS/ECE Dept./Rowan University Single Tone AM s(t) = A c [1 + A m cos(2  f m t)]cos(2  f c t) c(t) = A c cos(2  f c t) m(t) = A m cos(2  f m t) t m(t) AmAm t c(t) AcAc s(t) t AcAc A c [1+A m ]

S. Mandayam/ ECOMMS/ECE Dept./Rowan University Spectrum of Single Tone AM Matlab Demo Instrument Demo

S. Mandayam/ ECOMMS/ECE Dept./Rowan University Percentage Modulation s(t) t AcAc A max = A c [1+A m ] A min = A c [1-A m ]

S. Mandayam/ ECOMMS/ECE Dept./Rowan University AM Bandwidth -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 AM Spectrum

S. Mandayam/ ECOMMS/ECE Dept./Rowan University AM Power & Efficiency

S. Mandayam/ ECOMMS/ECE Dept./Rowan University AM Standards See p. 308

S. Mandayam/ ECOMMS/ECE Dept./Rowan University AM: Features AM system is very cheap to build and maintain AM is wasteful of power - max efficiency is 33% AM is wasteful of bandwidth - twice the message bandwidth is required AM Modifications: DSB-SC SSB VSB

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/spring11/ecomms/d emos/dsbsc.m

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 UniversitySummary