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ee20-hw04-f08 - EECS 20N Structure and Interpretation of...

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EECS 20N: Structure and Interpretation of Signals and Systems Department of EECS University of California Berkeley Problem Set 4 Issued: 10 October 2008 Due: 17 October 2008, 5pm The Absolute Necessity of Seeking Inspiration in Nature We may learn a great deal from books, but we learn much more from the contemplation of nature—the reason and occasion for all books. The direct examination of phenomena has an indescribably disturbing and leavening effect on our mental inertia—a certain exciting and re- vitalizing quality altogether absent, or barely perceptible, in even the most faithful copies and descriptions of reality. a a Excerpts from Advice for a Young Investigator , by Santiago Ram´on y Cajal, translated by Neely Swanson and Larry W. Swanson, The MIT Press, 1999, ISBN: 0-262-68150-1. Policy Statement You are encouraged to collaborate, but only in a group of up to five current EECS 20N students. On the solution document that you turn in for grading, you must write the names of your collaborators below your own; each teammate must submit for our evaluation a distinct, self-prepared solution document containing original contributions to the collaborative effort. Please write neatly and legibly, because if we can’t read it, we can’t grade it. Unless we explicitly state otherwise, you will receive full credit only if you explain your work succinctly, but clearly and convincingly. Typically, we evaluate your solutions for only a subset of the assigned problems. A priori, you do not know which subset we will grade. It is to your advantage to make a bona fide effort at tackling every assigned problem. If you are asked to provide a ”sketch,” it refers to a hand-drawn sketch, well- labeled to indicate all the salient features—not a plot generated by a computing device. 1
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Overview, Subject Matter, and Reading This problem set explores some of the salient properties of discrete-time convolution and frequency responses of discrete-time systems. It also covers some of the salient properties of the Dirac delta. You should read all of the material in Chapters 8 and 9 of the textbook (Lee & Varaiya). HW4.1 (Impulse Response and Step Response of DT-LTI Systems) The discrete- time unit-impulse signal δ , characterized by the Kronecker delta function δ ( n ) = ( 1 n = 0 0 n 6 = 0 , is applied to a discrete-time linear time-invariant (DT-LTI) system. The corresponding output signal h is called the impulse response of the system.
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