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# LINEAR SYSTEMS ECEN 3300

GPA 3.9

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This 4 page Class Notes was uploaded by Mrs. Lacy Schneider on Thursday October 29, 2015. The Class Notes belongs to ECEN 3300 at University of Colorado at Boulder taught by Staff in Fall. Since its upload, it has received 21 views. For similar materials see /class/231797/ecen-3300-university-of-colorado-at-boulder in ELECTRICAL AND COMPUTER ENGINEERING at University of Colorado at Boulder.

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Date Created: 10/29/15

ECEN 3300 Linear Systems Fall 2008 10 03 08 P Mathys Recitation Problem Set 5 For Wed 10 08 08 recitation session 1 z Transform Practice Assume the unilateral z transform for all parts of this problem 21 Use the derivative property of the z transform to nd Xz if xn n n l a un b Find the rst ve terms 0 1 4 of xn if 1 7 2 2 1 3 2 2 XltZgt 1 2 1 2 2 2 3 c Determine xn in closed form when 6 i 5 21 1312 2 MFW39 1 Determine xn in closed form when 2 Consider the rst order CT system with system function 7104112 s0lw1 i wl s10w2 H5 7 W2 gt 101 a Determine the step response gt b Let 9 gnFs where FS is the sampling rate be the step response of a step invariant DT system that corresponds to the CT system Use the de nitions 91 LoyFS and 92 LuzF5 to convert M and Luz from the CT to the DT system c Determine the system function of the DT system whose step response you found in Find the poles and zeros of 1 Draw and label a block diagram using only adders gains and delay elements with input xn and output yn that implements 3 The difference equation of a linear DT system is n n7 n7 7 n ni y y 1 8 y 2 1 a Determine the system function Hz assuming zero initial conditions b Find all poles and zeros of c Using only adders gains and delay elements draw and label a block diagram with input xn and output yn that implements this DT system 1 Determine the unit step response 9 of this system 4 The system function of a DT system is given by 1 7 2 2 1 2 2 1 f 34 2 1 39 Determine the magnitude and the phase of the frequency response at z em for Q 0 01 02 05 1030 What type of lter highlowband pass is this 200272008 P Mathys Last revised 1006 08 PM ECEN 3300 Linear Systems Fall 2008 9 05 08 P Mathys Recitation Problem Set 2 For Wed 9 10 08 recitation session 1 A CT system has input zt and output yt as shown below W 9525 2A What can you say about the following system properties a Memory b Causality c Time Invariance d Linearity If the given information is insuf cient to answer one of the questions7 state what is missing 2 Consider the following circuit with input voltage t and output voltage R1 L O AVAVA 23905 gt xt R2 105 a Determine the differential equation that relates the input t to the state variable z t Then express yt in terms of z t b Use the integrator block shown below as a starting point to draw a labeled blockdiagram7 consisting only of adders7 gains7 and integrators7 that solves the differential equation in a for z t and then computes the output yt from it Mos 225 3 Determine the missing parts of the following unilateral t 2 0 Laplace transform pairs 3 b er 7 lt1atgtgtulttgt C d te m cos wotut ltgt ltgt ltgt ltgt 1 7 675T2 82 l 52 s 1 4 Math Practice Evaluate the following sums N71 21 Z n a N b 2 KW n7N 200272008 P Mathys Last revised 9 05 08 PM

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