ECE633F09_HW3solutio - ECE633 Signals and Systems I Fall 2009 Homework 3 Solutions From Linear Systems and Signals 2nd ed B P Lathi Oxford

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ECE633 Signals and Systems I, Fall 2009 – Homework 3 Solutions 1 From: Linear Systems and Signals, 2 nd ed . B. P. Lathi, Oxford University Press, 2005. 1.6-1 Write the input-output relationship for an ideal integrator. Determine the zero-input and zero-state components of the response. () () () () () N () 0 00 zero-input zero-state 0 tt t y tx dx d x d y x d τ ττ −∞ −∞ ==+ = + ∫∫∫ ±²³ ²´ 1.7-1 For the systems described by the following equations, with the input x t and the output yt , determine which of the systems are linear and which are nonlinear. (a) () () 2 2 dy x t dt += (e) 2 2 dy xt dt ⎛⎞ ⎜⎟ ⎝⎠ (b) 2 3 dy ty t t x t dt (f) ( ) sin 2 dy dx tyt dt dt + (c) ( ) ( ) 32 (g) 2 dy dx dt dt (d) 2 dy yt x t dt (h) () ( ) t x d −∞ = (a) () () () () 22 12 1 2 dy dy yt xt xt dt dt ++ + = + [ ] 2 2 dy y y ty t x t dt + + ⎡⎤ ⎣⎦ non-linear (b) 12 12 33 dy dy ty t ty t t x t t x t dt dt + = + [ ] 2 3 tyt yt t xt xt dt + =+ linear (c) () () () ( ) 1 2 2 2 xt xt + = + y t x t ≠+ non-linear (d) 121 2 dy dy yt yt xt xt dt dt + = + [ ] 2 y t x t dt + non-linear
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ECE633 Signals and Systems I, Fall 2009 – Homework 3 Solutions 2 (e) () () () () 22 12 1 2 dy dy yt yt xt xt dt dt
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This note was uploaded on 02/11/2010 for the course ECE 633 taught by Professor Staff during the Fall '09 term at University of Texas at Austin.

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ECE633F09_HW3solutio - ECE633 Signals and Systems I Fall 2009 Homework 3 Solutions From Linear Systems and Signals 2nd ed B P Lathi Oxford

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