MATH 267 Study Guide - Midterm Guide: Long Term Ecological Research Network, High-Pass Filter, Linear Time-Invariant Theory
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Do not open this test until instructed to do so! This exam should have 17 pages, including this cover sheet. No textbooks, calculators, or other aids are allowed. Turn o any cell phones, pagers, etc. that could make noise during the exam. You must remain in this room until you have nished the exam. Use the back of the page if necessary. Problem 1 (18 points) (a) calculate f (t) = (rect sin)(t). (b) calculate the fourier transform of g(t) = rect(3t) cos(17t). (c) find the inverse fourier transform of bh( ) = (d) calculate z . Let f (t) be a 2 -periodic function and f (t) = t2 for < t . (a) plot f (t) in at least three periods. Is f (t) odd or even? (b) find the real fourier series of f (t). (c) use (b) to calculate the in nite sum.
