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Phasor Analysis of Bandpass Signals Background: Phasors for Monochromatic Signals 1

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Phasor Analysis of Bandpass Signals Narrowband Signals: Define: 2

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Narrowband Signals: Continued 3

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Phasor Equivalent for Narrowband 4

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Transmitting Bandpass Signals through Bandpass Systems 5

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Amplitude Modulation ECE460 Spring, 2012

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Analog Modulation Techniques Modulation: The process by which some characteristic of a carrier wave is varied in accordance with an information-bearing signal Amplitude modulation 1.Amplitude modulation (AM) 2.Double sideband-suppressed carrier (DSB-SC) 3.Single sideband (SSB) 4.Vestigial sideband (VSB) 7

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Amplitude Modulation (AM) AM is formally defined as a process in which the amplitude of the carrier wave c(t) is varied about a mean value linearly with a message signal m(t). Message Signal: Sinusoidal Carrier: AM Wave: 8

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Amplitude Modulation 9

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Frequency Domain Message signal: Band-limited to W AM wave: Time Domain: Frequency Domain: 10

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Example Message signal AM Wave Time Domain: Frequency Domain: 12

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Varying m 13

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Envelope Detection 14

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Conclusions on AM Power Channel Bandwidth Complexity 15

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Double Sideband-Suppressed Carrier Modulation (DSB-SC) Message signal: Carrier Wave: Transmit Signal: 16

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Why Coherent Detection? 17 Local Oscillator Product modulator Low-pass filter

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Costas Receiver 18 Voltage Controlled Oscillator Product modulator Low-pass filter Product modulator Low-pass filter -90 Phase Shifter Phase discriminator

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Conclusions on DSB-SC Power Channel Bandwidth Complexity 19

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Single Modulation (SSB) 1.Creating an SSB signal via a Hilbert Transform 2.Filtering a DSB SC signal 20

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Filtering DSB-SC signal for SSB DSB-SC Signal: Filter: 21

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Find SSB Transmission Signal Message Signal: Begin by finding 22

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Demodulation of an SSB signal Requires a phase coherent demodulator like a DSB-SC demodulation Low-pass filtering leaves: 23

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Conclusions on SSB Power Channel Bandwidth Complexity 24

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Vestigial Sideband Modulation Compromise between DSB-SC and SSB: Keeps a trace, or vestige, of the other sideband A portion of the other sideband is transmitted Transmitted Signal: Received Signal: 25

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Vestigial Sideband Filter 26