problem_set_1

# problem_set_1 - Carleton University Department of Systems...

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Carleton University Department of Systems and Computer Engineering SYSC 3501 Communication Systems Summer 2009 Problem Set #1 1. The Fourier transform of a signal g(t) is denoted by G(f). a. Prove that if g(t) is real and even function of time t, the Fourier transform G(f) is a real function of f . b. Prove that if g(t) is real and even function of time t, the Fourier transform G(f) is an imaginary function of f 1

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2. Any function g(t) can be split unambiguously into an even part and an odd part as shown by: ( 29 ( 29 ( 29 t g t g t g o e + = 2
The even part is defined by ( 29 ( 29 ( 29 [ ] t g t g t g e - + = 2 1 and the odd part is defined by ( 29 ( 29 ( 29 [ ] t g t g t g o - - = 2 1 . Evaluate the even and odd parts of a rectangular pulse defined by ( 29 - = 2 1 T t Arect t g What are the Fourier transform of those two parts of the pulse. 3

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4
3. Determine the inverse Fourier transform of the frequency function G(f) defined by the amplitude and phase spectra shown in Figure P. 3.

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## This note was uploaded on 07/16/2009 for the course SYSC 3501 taught by Professor Osama during the Summer '09 term at Carleton CA.

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problem_set_1 - Carleton University Department of Systems...

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