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lecture3 - • Elementary trigonometric relation t t t t...

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Lecture 3 Outline Amplitude Modulation, Basics Supplementary Reading: Read Communication System Eng. 3.1, 3.2.1 Material covered: 1. Reviewed basic operations of Fourier Transform (material of last lecture) 2. Amplitude Modulation: Transducer produces a signal ) ( t m e.g. an electrical signal representing speech through a carbon microphone. The electrical signal may be transmitted directly over a copper twisted pair. Such transmission is in baseband. Received signal is reproduced, e.g. by a speaker. For transmission media such as coaxial cable and electromagnetic waves, there is a carrier. We use the signal ) ( t m to modulate the carrier, i.e. ) 2000 cos( ) ( ) ( t t m t u π = for a carrier frequency of 1 Kilo-Hertz: Frequency domain representations. Signal is recovered by envelope detection (circuit with diode and capacitor/resistor) 3. Basics of AM Modulation:
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Multiplication of sinusoids shifts frequency.
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Unformatted text preview: • Elementary trigonometric relation: t t t t ) cos( 2 1 ) cos( 2 1 cos cos 2 1 2 1 2 1 ϖ-+ + = × • Using complex notations: 4. Double Side Band Amplitude Modulation: • Notations for DSB-SC AM (i.e. no carrier impulse/tone at carrier frequency): Equation Time domain Frequency domain-Message signal:-Carrier:-Modulation (message modulating carrier):-Derivation of frequency spectrum: • Bandwidth of 2W is required the signal. Two sidebands (upper and lower). • Example: Consider modulation by the signal on a 1000 hertz carrier: ) 40 cos( 2 ) 20 sin( ) ( t t t m π + = and ) 2000 cos( ) ( ) ( t t m t u = • Time domain representations: • Fourier transform of the message: • Fourier transform of the modulated signal showing upper and lower sidebands:...
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lecture3 - • Elementary trigonometric relation t t t t...

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