102_1_midterm_practice

# 102_1_midterm_practice - f ( t ) using a period T . You...

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Systems and Signals Lee, Spring 2009-10 EE102 Midterm Practice Problems Problem 1. Computing Fourier Transforms The signal f ( t ) is plotted below: f ( t ) t 1 1 - 1 - 2 - 3 0 2 3 2 - 1 a) Find an expression for f ( t ) in terms sums and convolutions of signals deﬁned for all t such as rect( t ) and Δ( t ) ( i.e. do not express it as a piecewise signal, deﬁned over intervals). b) Find the Fourier transform of f ( t ). Simplify your answer. 1

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Problem 2. Fourier Series a) You compute the Fourier series of a signal
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Unformatted text preview: f ( t ) using a period T . You ﬁnd that all of the odd Fourier series coeﬃcients are zero (i.e. D 1 ,D-1 ,D 3 ,D-3 , ··· are all zero). What can you conclude about f ( t )? b) Two functions f ( t ) and ˜ f ( t ) have Fourier series coeﬃcients D n and ˜ D n , respectively, and ± ± ± ˜ D n ± ± ± = | D n | 6 ˜ D n = 6 D n + nπ Find a simple expression for ˜ f ( t ) in terms of f ( t ). 2...
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## This note was uploaded on 02/28/2011 for the course EE 102 taught by Professor Levan during the Spring '08 term at UCLA.

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102_1_midterm_practice - f ( t ) using a period T . You...

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