20112ee113_1_Hw2

20112ee113_1_Hw2 - Figure 1 Block diagram Problem B An...

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EE113: Digital Signal Processing Spring 2011 Prof. Mihaela van der Schaar (Instructor) Homework #2 This homework consists of two parts. Part 1 Solve the following problems from the electronic versions of the chapters of An Undergraduate Course on Discrete-Time Signal Processing by A.H. Sayed Problem 4.4. Problem 4.8. Problem 5.2. Problem 5.5 Problem 5.6. Part 2 Solve the following additional problems. Problem A. Analyze the block diagram in Fig. 1 and develop the relation between y [ n ] and x
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Unformatted text preview: ] Figure 1: Block diagram Problem B. An algorithm for the calculation of the square root of a number α is given by y [ n ] = x [ n ]-y 2 [ n-1] + y [ n-1] where x [ n ] = αu [ n ] with 0 < α < 1. If x [ n ] and y [ n ] are considered as the input and output of a discrete-time system, is the system linear or non-linear? Is it time-invariant? 1 As n → ∞ , show that y [ n ] → √ α . Note that y [-1] is a suitable initial approximation to √ α . 2...
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