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# HW4 - SCHOOL OF ENGINEERING SCIENCE SIMON FRASER UNIVERSITY...

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SCHOOL OF ENGINEERING SCIENCE SIMON FRASER UNIVERSITY ENSC 428 – Digital Communications Spring 2008 Homework #4 due Feb. 15, 2008 Friday Dear class, Apparently, many of you need to brush up on your knowledge of Fourier series and Fourier transforms. The purpose of this homework is to motivate you to sharpen your knowledge in background materials. Prof. Gallager’s Lecture Note 8 contains good review of Fourier analysis. - Daniel Lee 1. (On sequences) a) Consider a sequence { } ( 1) 1,2,. .. n n an =− = . Does this sequence converge? If it converges, what is its limit? Definition: A sequence { } n b of real numbers is said to be bounded above if , n bB n <∀ for some B . b) Is the sequence 3 2 1,2,. .. n n  =   bounded above? Justify your answer. Does this sequence converge? If it converges, what is its limit? Definition: A sequence { } n b of real numbers is said to be increasing if 1 , nn bb n + . Theorem: If a sequence of real numbers is increasing and bounded above, then this sequence converges.

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HW4 - SCHOOL OF ENGINEERING SCIENCE SIMON FRASER UNIVERSITY...

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