Lecture 15

Lecture 15 - Lecture 15 Application to Communication...

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1 Lecture 15 – Application to Communication Systems ECSE304 Signals and Systems II ECSE 304 Signals and Systems II Lecture 15: Application of Transform Techniques to Communications Systems Reading: O and W – Sections 8.1, 8.2 Boulet – Chapter 16 Richard Rose McGill University Dept. of Electrical and Computer Engineering 2 Lecture 15 – Application to Communication Systems ECSE304 Signals and Systems II Course Outline • Discrete-Time Fourier Series and DT Fourier Transform • The Z – Transform • Time and Frequency Analysis of DT Signals and Systems • Sampling Systems – Lecture 12: The Sampling Theorem – Lecture 13: Discrete Time Processing of Continuous Time Signals – Lecture 14: Sampling of Discrete Time Signals • Application to Communications Systems – Lecture 15: Amplitude Modulation – Lecture 16: Single Sideband and Pulse Amplitude Modulation – Lecture 17: Frequency and Time Division Multiplexing and Angle Modulation • State Models of Continuous Time LTI Systems • Linear Feedback Systems
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3 Lecture 15 – Application to Communication Systems ECSE304 Signals and Systems II • Amplitude Modulation and Demodulation • Synchronous Demodulation • Asynchronous Demodulation Outline 4 Lecture 15 – Application to Communication Systems ECSE304 Signals and Systems II Amplitude modulation is based in the multiplication (Modulation) property of the C-T Fourier transform: • In the modulation system described by is the modulated signal is the modulating signal is the carrier signal • Motivation: Produce a signal that is suitable for transmission over a given communication channel – Microwave: 300 MHz – 300GHz Satellite: 300 MHz-40 GHz Amplitude Modulation with a Complex Exponential Carrier xtyt X j Y j ( ) ( ) ()() ↔∗ FT 1 2 π ωω y t x t c t () = yt x t ct
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5 Lecture 15 – Application to Communication Systems ECSE304 Signals and Systems II • Suppose the carrier signal is a complex exponential: • … where is the carrier frequency • If then the modulated signal is • … where the spectrum of is the input spectrum shifted in frequency by Amplitude Modulation with a Complex Exponential Carrier ct e jt cc () = + ωθ Cj c ( ) ω πδω = 2 1 () () 2 ( ) (( ) ) c c Yj Xj d ωω π υδω υ ω υ +∞ −∞ =∗ =−
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Lecture 15 - Lecture 15 Application to Communication...

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