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Unformatted text preview: Eeng 360 1 Chapter4 Bandpass Signalling Definitions Complex Envelope Representation Representation of Modulated Signals Spectrum of Bandpass Signals Power of Bandpass Signals Examples Huseyin Bilgekul Eeng360 Communication Systems I Department of Electrical and Electronic Engineering Eastern Mediterranean University Eeng 360 2 Energy spectrum of a bandpass signal is concentrated around the carrier frequency f c . A time portion of a bandpass signal. Notice the carrier and the baseband envelope. Bandpass Signals Bandpass Signal Spectrum Time Waveform of Bandpass Signal Eeng 360 3 DEFINITIONS Definitions: The Bandpass communication signal is obtained by modulating a baseband analog or digital signal onto a carrier. A baseband waveform has a spectral magnitude that is nonzero for frequencies in the vicinity of the origin ( f =0) and negligible elsewhere. A bandpass waveform has a spectral magnitude that is nonzero for frequencies in some band concentrated about a frequency where f c >>0. f cCarrier frequency Modulation is process of imparting the source information onto a bandpass signal with a carrier frequency f c by the introduction of amplitude or phase perturbations or both. This bandpass signal is called the modulated signal s ( t ), and the baseband source signal is called the modulating signal m ( t ). c f f = Transmission medium (channel) Carrier circuits Signal processing Carrier circuits Signal processing Information m input m ~ ) ( ~ t g ) ( t r ) ( t s ) ( t g Communication System Eeng 360 4 Complex Envelope Representation The waveforms g ( t ) , x ( t ), R ( t ), and are all baseband waveforms. Additionally all of them except g ( t ) are real and g ( t ) is the Complex Envelope. ( 29 t g ( t ) is the Complex Envelope of v ( t ) x ( t ) is said to be the Inphase modulation associated with v ( t ) y ( t ) is said to be the Quadrature modulation associated with v ( t ) R ( t ) is said to be the Amplitude modulation (AM) on v ( t ) ( t ) is said to be the Phase modulation (PM) on v ( t ) In communications, frequencies in the baseband signal g(t) are said to be heterodyned up to f c THEOREM: Any physical bandpass waveform v ( t ) can be represented as below where f c is the CARRIER frequency and c =2 f c ( 29 ( ) ( ) ( ) ( ) ( ) ( ) j t j g t g t x t jy t g t e R t e + = = ( 29 ( 29 { } ( 29 ( 29 ( 29 ( 29 Re cos = cos sin c j t c c c v t g t e R t t t x t t y t t = = +  Eeng 360 5 Generalized transmitter using the AMPM generation technique. Eeng 360 6 Generalized transmitter using the quadrature generation technique. Eeng 360 7 v ( t ) bandpass waveform with nonzero spectrum concentrated near f=f c => c nonzero for n in the range The physical waveform is real, and using , Thus we have: Complex Envelope Representation...
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 Spring '11
 EmreAktaş

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