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Unformatted text preview: 1 Introduction and Signal Analysis SYSC3501 Communication Theory 2 Introduction • The function of a communication system is to produce at the receiver the same signal at the transmitter • The communication channel may be a transmission line, optical fiber, coaxial cable, or free space (wireless) • The communication channel corrupts the transmitted signal by filtering effects, interference and noise. • The function of the transmitter is to adapt the signal to the channel conditions by performing modulation and coding. • The function of the receiver is to recover the transmitted signal in the presence of channel distortion by performing demodulation and decoding. • Two factors contributing to system performance: transmitted power and channel bandwidth communication systems are usually classified as powerlimited or bandlimited. Transmitter Channel Receiver t s t s t s ˆ 3 Signal Analysis The first step in studying a communication system is to study signal analysis and frequency representation, Tools used are Fourier series, Fourier transform, linear system analysis, etc. Signal Types Periodic Signals T t g t g p p time T Energy Signals dt t g E 2 4 Example: Square Pulse A T otherwise T t A t g T A dt A E T 2 2 Power Signals The average power of asignal is given by: T T T dt t g T P 2 2 1 lim g(t) is a power signal iff 0<P<∞ 5 Complex numbers and Complex Variables 2 1 2 1 2 1 2 1 2 1 2 1 * 2 * 1 2 2 sin cos tan j j e r r r r b b j a a r r r r r jb a r r b r a a b b a r e r r jb a r Real Imaginary a b r Complex Numbers Complex Variables t jy t x t z Example: t t y t t x sin cos z(t) 1 x y Trigonometric Identities 6 sin sin 2 1 cos sin cos cos 2 1 cos cos cos cos 2 1 sin sin tan tan 1 tan tan tan sin sin cos cos cos sin cos cos sin sin 2 sin cos sin 2 2 cos 1 2 1 sin 2 cos 1 2 1 cos 2 cos sin cos 1 cos sin 2 1 sin 2 1 cos sin cos 2 2 2 2 2 2 j j j j j e e e e e Euler Identity 7 Fourier Series A periodic signal with period T can be represented using Fourier series expansion as...
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This note was uploaded on 07/15/2009 for the course SYSC 3501 taught by Professor Osama during the Spring '09 term at Carleton CA.
 Spring '09
 Osama

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