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# Digital Signal Processing ENGR 361

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This 6 page Class Notes was uploaded by Clair Nolan PhD on Friday October 30, 2015. The Class Notes belongs to ENGR 361 at The University of Tennessee - Martin taught by Staff in Fall. Since its upload, it has received 11 views. For similar materials see /class/232381/engr-361-the-university-of-tennessee-martin in Engineering and Tech at The University of Tennessee - Martin.

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Date Created: 10/30/15

ENGR 361 Digital Signal Processing Midterm 1 Friday September 21 2007 Open books notes computer Name 1 Determine if the discrete time signal is periodic If it is find its period a A continuous signal x10 sin27rf1t where f1 500 Hz is sampled at the sampling frequency F 10000 Hz b x2ln 0763 cos 0324 cos 2 Determine and show whether or not the system is 1 causal 2 stable 3 time invariant 4 linear and 5 memoryless a yn1xn3 2 b yn 01 2 xn k where dis a non constant k0 3 For LTI system we are given a signal xn 6n 2 6n 6n 2 a If the system hn can be described by the following differential equation yn xn 2xn 1 3xn 2 xn 3 draw the discrete time signal of hn with appropriate indexing b Find the output yn and draw the figure with appropriate indexing 4 An LTI system is describe by the differential equation yn 05yn 1 025yn 2 xn 2xn 1 xn 3 a What is the frequency response of this system H 6 b Is the system LPF HPF BPF ESP Verify your method The right answer without reasons will be considered as the wrong answer Using matlab plot the impulse response for 200 input samples Also plot the step response for 200 input samples 0 V ENGR 361 Digital Signal Processing Midterm 1 Friday September 21 2007 Open books notes computer Name SOLUTION 1 10 points Determine if the discrete time signal is periodic If it is find its period a A continuous signal x10 sin27rflt where f1 500 Hz is sampled at the sampling frequency F 10000 Hz xn X nT sin M F 27r500n 111 10000 27m 111 7 20 To find the period 27rk 2 k 1 20 N 20 b x2n 0763 cos 0324 cos 532 2m 2 k 5 V1 6 3 27rk 3 k 3 N2 10 N 30 2 10 points Determine and show whether or not the system is 1 causal 2 stable 3 time invariant 4 linear and 5 memoryless a yn1xn3 0 Obviously it is causal stable memoryless and time invariant Not linear since ax1nbxn3 2 axln3 bxn3 2 b yn 01 2 xn k where dis a non constant 0 Obviously it is stable causal and time invariant but not memoryless 0 Not linear since 2 2 2 2 2 a2x1n kab2x2n k 2 aaZx1n kb2x2n k k0 k0 k0 k0 3 For LTI system we are given a signal xn 6n 2 6n 6n 2 a If the system hn can be described by the following differential equation yn xn 2xn 1 3xn 2 xn 3 draw the discrete time signal of hn with appropriate indexing hn 6n 26n 1 36n 2 6n 3 Mn b Find the output yn and draw the figure with appropriate indexing Wt xn Mn 1 0 1 0 11 2 3 1 1 2 4 3 4 3 3 1 WV clear allclcclose all x l 0 71 0 1 h l 2 3 1 y convxh stem25ly axis 76 6 76 6 4 An LTI system is describe by the differential equation yn 05yn l 025yn 2 xn 2xn l xn 3 a What is the frequency response of this system H 6 1 267 6713 b Is the system LPF HPF BPF ESP Verify your method The right answer without reasons will be considered as the wrong answer Lowpass lter by looking at magnitude response clear allclcclose all B l 2 0 1 A l 705 025 freqzBA t E Eltn E E K g ewx k 0 01 09 1 Normalized Frequency X1 radsample Phase degrees 0 01 02 09 1 0 0 0 7 Normalized Frequency X1 radsample c Using matlab plot the impulse response for 200 input samples Also plot the step response for 200 input samples clear allclcclose all B l 2 0 l A 1 705 025 x1 zerosl200xll 1 x2 onesl200 yl filterBAxl y2 filterBAx2 subplot21lstemyl subplot212stemy2 o 20 40 so so 100 120 140 160 180 200 5 You are given a causal LTI unknown system If the input to the system is xn l un 2 2un 1 4 2 the system generates the output and its z transform is o zwozw i z 11 2z 113z 1 a Determine XzYz and Hz Yz 1 1 Ezl 1liz1lzl YZ717z71172z71l3z71 WNW 165 sz 17z 1172z71l3z71 1iz 11z391 1amp6 lgz ljhmz gtl Xz 1 MlH Hz b Draw ROC for X Y and H H KOCA 1W 1 Guml i 5 W 2 39 ROCX l 54 0 7g 2 0 WC W13 Rochng j 7f 0393 2 5 c Find the impulse response of the system hn Is the system stable ROC does not include a unit circle so it is not stable

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