ece111ps06 - The Cooper Union Department of Electrical...

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The Cooper Union Department of Electrical Engineering ECE111 Signal Processing & Systems Analysis Problem Set VI: State-Space Analysis April 1, 2014 1. Given: H ( z ) = b 0 + b 1 z ° 1 + b 2 z ° 2 a 0 + a 1 z ° 1 + a 2 z ° 2 It is written this way for convenience. (a) Sketch the direct form II and direct form II transposed realizations. (b) Find the f A; B; C; D g state-space realizations for each. Take the convention that the delay element on top is state-variable x 1 [ n ] , and the one below is x 2 [ n ] . Note: Sometimes the path from one input or state variable to an output or state variable goes through more than one multiplier and/or adder; you have to trace out the full path to get the proper coe¢ cients in A; B; C; D . (c) Take a = [1 ; 2 ; 3] (i.e., a 0 = 1 etc.), b = [4 ; 5 ; 6] . In MATLAB, use tf2ss to obtain the state-space realizations. Does MATLAB yield either direct form II or direct form II structure by default? (d) Take both f A; B; C; D g matrices that correspond to the a; b choice above (i.e. for
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