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Unformatted text preview: 6.003 Homework 2 Due at the beginning of recitation on Wednesday, February 17, 2010 . Problems 1. Black’s Equation than added. Y a. Determine the system functional H = X . This result is known as Black’s equation. b. Assume that F can be written as a ratio of polynomials in R . Let N F and D F represent the numerator and denominator polynomial, respectively. Similarly, assume that G can be written as a ratio of polynomials N G and D G . Express the system Y Y functional X in terms of N F , D F , N G , and D G . Can X be expressed as a ratio of polynomials in R ? c. Assume that F can be written as a ratio of polynomials in A . Let N F and D F represent the numerator and denominator polynomial, respectively. Similarly, assume that G can be written as a ratio of polynomials N G and D G . Express the system functional Y in terms of N F , D F , N G , and D G . Can Y be expressed as a ratio of X X polynomials in A ? 2. Characterizing block diagrams Consider the general form of a feedback problem: + F G − X Y Notice the minus sign on the adder: it indicates that the lower input is subtracted rather Consider the system defined by the following block diagram: A A A + + 3 2 1 2 X Y − − a. Determine the system functional H = Y X ....
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 Spring '11
 DennisM.Freeman
 Trigraph, difference equation, Block diagram representations

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