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# ELECTRIC CURCUIT ANALYS III ECE 223

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This 97 page Class Notes was uploaded by Miss Chadrick Doyle on Tuesday September 1, 2015. The Class Notes belongs to ECE 223 at Portland State University taught by Staff in Fall. Since its upload, it has received 29 views. For similar materials see /class/168241/ece-223-portland-state-university in ELECTRICAL AND COMPUTER ENGINEERING at Portland State University.

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ECE 223 Signals and Systems ll httpwwwecepdxed uprasads Dr Shalini Prasad Electrical and Computer Engineering sprasadpdxedu Pr 39tltTLitf gl l 1 STATE U Wiznam39 1 S Prasad Portland State University ECE 223 Fall 2007 Lecture 20 Final Exam December 6th Thursday Time 100 minutes Location EB 103 No calculators One page front and back of handwritten notes Time 730 pm920 pm 2 S Prasad Portland State University ECE 223 Fall 2007 Lecture 20 Exam 2 Topics Comprehensive Signals overview Complex Sinusoids DTFS CTFS DTFT CTFT Fourier Properties FFT Sampling 3 S Prasad Portland State University ECE 223 Fall 2007 Lecture 20 Final Exam 4 questions Max score 60 points 1 from FFT 1 from Sampling 2 from rest of syllabus 4 S Prasad Portland State University ECE 223 Fall 2007 Lecture 20 Final Exam Prep Lecture notes Online lectures Old exams HW 5 S Prasad Portland State University ECE 223 Fall 2007 Lecture 20 Lecture Overview Last Time Sampling Exam 2 Back This Time Sampling Questions on Exam 2 grading ti Dec 6th 6 S Prasad Portland State University ECE 223 Fall 2007 Lecture 20 ECE 223 Signals and Systems ll httpwwwecepdxed uprasads Dr Shalini Prasad Electrical and Computer Engineering sprasadpdxedu Pr 39tltTLitf gl l 1 STATE U Wiznam39 1 S Prasad Portland State University ECE 223 Fall 2007 Lecture 3 Archived Lectures Lectures were taped in Spring 2007 Is available as archived Lectures available online at httpwwwmediapdxedu Lecture Password ece223s07 2 S Prasad Portland State University ECE 223 Fall 2007 Lecture 3 Lab TA and coordinator Lab Section Fri 300 550 pm Sean Pearson seanbodxedu Office Hours M and F 200 pm300 pm FAB 6001Tektronix Lab Lab coordinator Dan Korpenfelt Contact drdancecsodxedu Office Hours FAB 6002 MF 800 am 400pm 3 S Prasad Portland State University ECE 223 Fall 2007 Lecture 3 Instructor Office Hours Instructor Office Hours Th and F 100 200 pm FAB 16011 4 S Prasad Portland State University ECE 223 Fall 2007 Lecture 3 6 digit codes 6 digit codes will be used for displaying grades and test marks Email me the code this week Can be any character sent via plain text email Remember it for exams and homework pickup Homework assignment tables xAssignment number First letter of your last name 6 digit code 5 S Prasad Portland State University ECE 223 Fall 2007 Lecture 3 Homework Assignment Email me 6 digit code Homework 1 October 12th Friday Email 6digit code Read Review Chapters 1 amp 2 Required Chapter 3 Sections 14 Ch 3 48a 48 b 49a 49b 50d Solutions have been posted 6 S Prasad Portland State University ECE 223 Fall 2007 Lecture 3 Lecture Overview Last Time Fundamentals of Signals Complex Sinusoids This Time Complex Sinusoids Discrete Time Fourier Series 7 S Prasad Portland State University ECE 223 Fall 2007 Lecture 3 Overview of DiscreteTime Filters Ideal filters Firstorder filters Practical filters 0 Frequencyselective filter specifications Ripple versus filter order tradeoff Application example Portland State University ECE 223 DT Filters Ver 105 DiscreteTime Filters Overview N M ZakyM k Zbkxm k 160 k0 M 39 k yejw Zk0 bke 3w N jwk Zk0 ake Discretetime filters are divided into two categories Finite impulse response FIR Mn 0 for n lt a and ngtbsuchthat ooltaltnltbltoo Infinite impulse response IIR not FIR Xejw o Filters that can be described with differenceequations FIR N 0 IIR N gt 0 o A simple FIR filter is the moving average filter A simple IIR filter is the firstorder lowpass filter Portland State University ECE 223 DT Filters Ver 105 Example 1 FirstOrder Filters Consider the following filter yin ayin 1 1 awn 1 Solve for the filter39s transfer function 2 Find the cutoff frequency as a function of a Portland State University ECE 223 DT Filters Ver 105 Example 1 Workspace Portland State University ECE 223 DT Filters Ver 105 35 Dc radsample Example 1 20 versus a Portland State University ECE 223 DT Filters Ver 105 Example 1 Hejw for various a Hej l 1 Has 0 Frequency radssample 105 Portland State University ECE 223 DT Filters Ver Example 1 Filtered Signals 36 Int 1ClosingDaily Price Over 1Year xn y01n y06n Raw signal Cutoff056 Cutoff011 0 50 00 150 200 Time day Portland State University ECE 223 DT Filters Ver 105 Example 1 MATLAB Code qunction FirstOrderApplied close all d load InteltXt Z Closing daily price nd lengthd X dnd 11 Reorder so first element is oldest data n Ozndl Discrete time index Plot the relationship between cutoff frequency and a a 00000l00l1 wc acos14aa 22a figure FigureSet1 LTX h plotawc LineWidth 10 ylabel omegac radsample Xlabel a grid on box off AXisSet8 print depsc FUCutoff Plot the relationship between cutoff frequency and a Portland State University ECE 223 DT Filters Ver 105 a O1O1O9 w pi001pi H zeros1engtha1engthw for out 1zlengtha hw freqz1acnt1 acntw Hcnt h end figure FigureSet1 LTX subplot211 h plotwabsH xlimpi p11 ylim0 1051 legend a01 aO2 aOS aO4 aO5 aO6 aO7 aO8 aO9 2 ylabel lHe j0mega grid on box off subplot212 h plotwremangleH180pi180 X1impi pi ylim 70 70 ylabel angle He jomega o x1abel Frequency radssample grid on box off AXisSet8 print depsc FOTransferFunctions Portland State University ECE 223 DT Filters Ver 105 Filter amp Plot a 058 K cutoff frequency approximately 01 W1 acos14aa 22a y1 zerosnd1 for cnt 2nd y1cnt ay1cnt1 1axcnt end a 090 cutoff frequency approximately 01 W2 acos14aa 2 2a y2 zerosnd1 for cnt 2nd y2cnt ay2cnt1 1axcnt end figure FigureSet1 LTX h plotnx b ny1 r ny2 g seth LineWidth 06 ylabel xn y01n y06n Xlabel Time day title Intel Closing Daily Price Over 1 Year xlim0 nd1 ylim19 56 box off grid on AXisSet8 legend Raw signal sprintf Cutoff42f w1sprintf Cutoff42f w24 print depsc FUSignalFiltered Portland State University ECE 223 DT Filters Ver 105 Ideal Filters A Lowpass Highpass A Notch 1 IT I 1 20 E 39 20 f2 20 E2 Bandpass Bandstop I 901 902 E I 901 902 E o MATLAB can be used to design standard frequency selective filters that meet userspecified requirements 0 These filters include lowpass highpass bandpass and bandstop 0 Unlike continuoustime filters these must have cutoff frequencies that range between 0 and 7r Portland State University ECE 223 DT Filters Ver 105 11 Practical Filters 0 Practical filters are usually designed to meet a set of specifications 0 Lowpass and highpass filters usually have the following requirements Passband range Stopband range Maximum ripple in the passband Minimum attenuation in the stopband o If we know the specifications we can ask MATLAB to generate the filter for us 0 There are four popular types of standard filters Butterworth Chebyshev Type Chebyshev Type II Elliptic Portland State University ECE 223 DT Filters Ver 105 12 Ripple Tradeoff Filter Order Passband Stopband Butterworth Largest Smooth Smooth Chebyshev Type Moderate Ripple Smooth Chebyshev Type II Moderate Smooth Ripple Elliptic Lowest Ripple Ripple o The four popular filter types differ in how they satisfy the specifications 0 In the passband and stopband each filter is either smooth or contains ripple o Elliptic filters are also called equiripple filters and Cauer filters Portland State University ECE 223 DT Filters Ver 105 13 Example 2 Lowpass Filter Specifications Design a lowpass filter that meets the following specifications 0 The passband ripple is no more than 04455 dB 095 g lHejwl g 1 o The stopband attenuation is at least 2602 dB lHejwl g 005 o The passband ranges from 0 027r radsample o The stopband ranges from 037r 7r radsample Plot the magnitude of the resulting transfer function on a linearlinear plot the impulse response and the step response Try the Butterworth Chebyshev l Chebyshev II and elliptic filters Portland State University ECE 223 DT Filters Ver 105 14 Example 3 Butterworth Lowpass Butterworth Low ass Filter Transfer Function Order 10 08 X 06 E 3 E 04 02 0 0 05 1 15 2 25 3 Frequency radsample ECE 223 DT Filters Ver 105 15 Portland State University Example 3 Butterworth Lowpass 025 02 015 01 hn 005 l Butterworth Lowpass Filter Impulse Response Order 10 TU 33 005 l l 111 w w w 0l 39 40 50 90 100 Time n 80 Portland State University ECE 223 DT Filters Ver 105 Example 3 Butterworth Lowpass Butterworth Lowpass Filter Step Response Order 10 08 quot hn 06 0 10 20 30 40 50 60 70 80 90 100 Time n Portland State University ECE 223 DT Filters Ver 105 Example 3 Chebyshevl Lowpass Cheb shev I Low ass Filter Transfer Function Order 5 l 1 5 2 Frequency radsample Portland State University ECE 223 DT Filters Ver 105 Example 3 Chebyshevl Lowpass Chebyshev I Lowpass Filter Impulse Response Order5 02 0 015 01 hn 005 I I I I I I I I I 100 Portland State University ECE 223 DT Filters Ver 105 Example 3 Chebyshevl Lowpass 14 12 08 MM 06 04 02 Ti Chebyshev I Lowpass Filter Step Response Order5 20 30 40 50 60 70 80 90 Time n 100 Portland State University ECE 223 DT Filters Ver 105 20 Example 3 Chebyshev ll Lowpass Cheb shev II Low ass Filter Transfer Function Order 5 1 5 2 Frequency radsample Portland State University ECE 223 DT Filters Ver 105 21 Example 3 Chebyshevll Lowpass 0 25 Chebyshev II Lowpass Filter Impulse Response Order5 02 015 01 hn 005 0 T TNT m 7 1 all u 005 I I I I I I I I I I 0 10 20 30 40 50 60 70 80 90 100 Time n Portland State University ECE 223 DT Filters Ver 105 22 Example 3 Chebyshevll Lowpass 12 Chebyshev II Lowpass Filter Step Response Order5 08 hn 30 40 50 60 70 80 90 Time n 100 Portland State University ECE 223 DT Filters Ver 105 23 Example 3 Elliptic Lowpass Elli tic Low ass Filter Transfer Function Order 4 1 5 2 Frequency radsample Portland State University ECE 223 DT Filters Ver 105 24 Example 3 Elliptic Lowpass Elliptic Lowpass Filter Impulse Response Order4 02 015 01 hn 005 005 I I I I I I I I I I 0 10 20 30 40 50 60 70 80 90 100 Time n Portland State University ECE 223 DT Filters Ver 105 25 08 hln 06 Example 3 Elliptic Lowpass Elliptic Lowpass Filter Step Response Order4 20 30 40 50 60 70 80 90 100 Time n Portland State University ECE 223 DT Filters Ver 105 26 Example 3 MATLAB Code qunction Lowpass clear all close all Wp 020 K Passband ends Ws 080 Stopband begins Rp 20log10095 Maximum deviation from 1 in the passband dB Rs 20log10005 Minimum attenuation in the stopband dB for cnt 14 if cnt 0dwn buttordWpWsRpRs BA butterodwn stFilter Butterworth elseif cnt 0dwn ellipordWpWsRpRs BA ellipodRpRswn stFilter Elliptic elseif cnt S 0dwn cheb10rdWpWsRpRs BA cheby1odRpwn stFilter ChebyshevI elseif cnt 0dwn cheb2ordWpWsRpRs BA cheby2odRswn stFilter ChebyshevII else Portland State University ECE 223 DT Filters Ver 105 break end sys tfBA1 wp Wppi ws Wspi Plot Magnitude on Linear Scale ymax 105 pbmax 1 pbmin 10 Rp20 sbmax 10 Rs20 wmax pi O0001wmax Hw freqzBAw mag absH phs ang1eH W figure FigureSet1 LTX h patch0 wp wp OO O pbmin pbmin051 1 1 seth LineWidth 00001 hold on h patch0 ws ws wmax wmax Opbmax pbmax sbmax sbmax ymax ymax051 1 1 seth LineWidth 00001 h plotwmag r seth LineWidth 10 hold off ylimO ymax xlimO wmaXJ Portland State University ECE 223 DT Filters Ver 105 grid on ylabel lHe jOmega titlesprintf s Lowpass Filter Transfer Function Order xlabel Frequency radsample box off AXisSet8 st sprintf print depsc Lowpasss stFilter evalst Zd stFilterod Impulse Response figure FigureSet1 LTX n 0100 Xt impulsesysn h stemtx b seth1 MarkerFaceColor b seth1 MarkerSize 2 ylabel hn Xlabel Time n titlesprintf s Lowpass Filter Impulse Response box off hold on h plotXlim0 0 k hold off AXisSet8 st sprintf print depsc LowpassZsImpulse stFilter evalst Urderd stFilterod Portland State University ECE 223 DT Filters Ver 105 29 Step Response figure FigureSet1 LTX n 0100 Xt stepsysn h stemtx b seth1 MarkerFaceColor b seth1 MarkerSize 2 ylabe1 hn X1abe1 Time n tit1esprintf s Lowpass Filter Step Response box off hold on h plotxlim1 1 k hold off AXisSet8 Urderd stFilterod st sprintf print depsc LowpasssStep stFilter eva1st end Portland State University ECE 223 DT Filters Ver 105 30 Practical Filter Tradeoffs o Butterworth Highest order Hejw l No passband or stopband ripple o Chebyshev Type l No stopband ripple Chebyshev Type H l No passband ripple Elliptic l Lowest order Hejw Passband and stopband ripple Portland State University ECE 223 DT Filters Ver 105 31 Application Example 1 Microelectrode Recording Filter An engineer wishes to detect action potentials in a microelectrode recording with a simple threshold detector The signal contains significant baseline drift Action potentials typically last about 1ms o What type of filter should the engineer use 0 What should the filter specifications be c What should the cutoff frequencyies be Portland State University ECE 223 DT Filters Ver 105 32 Application Example 1 FrequencySelective Filters Microelectrode Recording 08 06 04 02 02 l 04 06 1 12 14 16 18 2 22 24 26 28 Time sec Portland State University ECE 223 DT Filters Ver 105 33 Application Example 1 FrequencySelective Filters 40 30 FT Magnitude 10 0 500 1000 1500 500 400 300 200 FT Magnitude MA AAA AIA AAA I AAA 2000 4 L 250 300 Portland State University ECE 223 DT Filters Ver 105 34 Application Example 1 FrequencySelective Filters Microelectrode Recording 05 0 39 05 0 02 0 4 06 08 1 12 14 16 18 2 Time sec 05 0 05 0 02 0 4 06 08 1 12 14 16 18 2 Time sec Portland State University ECE 223 DT Filters Ver 105 35 Application Example 1 FrequencySelective Filters FT Magnitude 0 500 1000 1500 2000 FT Magnitude Filtered Portland State University ECE 223 DT Filters Ver 105 36 Application Example 1 MATLAB Code qunction MER close all xfsnbits wavread Henderson2wav X decimatex2 fs fs2 k roundfs1roundfs5 Look at only 5 s X Xk nx lengthx figure FigureSet1 LTX t k1fs h plottx b seth LineWidth O6 xrng maxxminx Xlimmint maxt ylimminx00lxrng maxx001xrng AXisLines Xlabel Time sec ylabel title Microelectrode Recording box off AXisSet8 print depsc MERSignal Portland State University ECE 223 DT Filters Ver 105 37 1zfloor1engthX12 k 1fs nX1 X fftx2 12 nX 1engthX k f figure FigureSet1 LTX subplot211 h plotfabsXk r seth LineWidth 06 X1imminf maxf ylim0 50 setgca XTick 015001maxf box off ylabe1 FT Magnitude subplot212 h plotfabsXk r seth LineWidth 06 x1im0 500 ylim0 500 setgca XTick 0z500zmaxf S box off ylabe1 FT Magnitude AXisSet6 print w 210fs2 Ws 190fs2 Rp 201og100 Rs 20log100 95 05 depsc MERSpectralDensity Passband ends Stopband begins Maximum deviation from 1 in the passband dB Minimum attenuation in the stopband dB Portland State University ECE 223 DT Filters Ver 105 38 0dwn ellipordWpWsRpRs BA ellipodRpRswn high stFilter Elliptic y filtfiltBAX figure FigureSet1 LTX k izlengthx t k1fs subplot211 t k1fs h plottx b seth LineWidth O6 xrng maxxminx Xlimmint maxt ylimminx00lxrng maxx001xrng AXisLines X1abel Time sec ylabel title Microelectrode Recording box off subplot212 h plotty g seth LineWidth O6 Xlimmint maxt ylimminx00lxrng maxx001xrng AXisLines X1abel Time sec ylabel box off Portland State University ECE 223 DT Filters Ver 105 39 AXisSet8 print depsc MERSignalFiltered Y ffty2 12 nY 1engthY k 1zfloor1engthY12 f k1fsnY1 figure FigureSet1 LTX subplot211 h plotfabsXk r seth LineWidth O6 X1imminf maxf ylimO 50 setgca XTick OzSOOzmaxf box off ylabe1 FT Magnitude subplot212 h plotfabsYk g seth LineWidth O6 X1imminf maxf ylimO 50 setgca XTick OzSOOzmaxf box off ylabe1 FT Magnitude Filtered AXisSet6 print depsc MERSpectralDensityFiltered Portland State University ECE 223 DT Filters Ver 105 40 Summary 0 DT filters are much like the CT filters that we discussed in ECE 222 The filters are broadly characterized by the same types The primary design tradeoffs are the same presence of ripple versus filter order 0 Unlike analog circuits DT filters can be noncausal May have finite impulse response FIR 0 Many applications Portland State University ECE 223 DT Filters Ver 105 41 ECE 223 Signals and Systems ll httpwwwecepdxed uprasads Dr Shalini Prasad Electrical and Computer Engineering sprasadpdxedu Pr 39tltTLitf gl l 1 STATE U Wiznam39 1 S Prasad Portland State University ECE 223 Fall 2007 Lecture 19 Homework Assignment IV Problems 416 a 417a 418a 425a 426a Due Fri NOV 30 Read Chapter 3 Sections 311312 314320 Chapter 4 Section 4 and 5 FFT and Sampling 2 S Prasad Portland State University ECE 223 Fall 2007 Lecture 19 Final Exam December 6th Thursday Time 100 minutes Location EB 103 No calculators One page front and back of handwritten notes Time 730 pm920 pm 3 S Prasad Portland State University ECE 223 Fall 2007 Lecture 19 Exam 2 Topics Comprehensive Signals overview Complex Sinusoids DTFS CTFS DTFT CTFT Fourier Properties FFT Sampling 4 S Prasad Portland State University ECE 223 Fall 2007 Lecture 19 Final Exam 4 questions Max score 60 points 1 from FFT 1 from Sampling 2 from rest of syllabus 5 S Prasad Portland State University ECE 223 Fall 2007 Lecture 19 Final Exam Prep Lecture notes Online lectures Old exams HW e S Prasad Portland State University ECE 223 Fall 2007 Lecture 19 Lab Presentations Nov 30th Tomorrow Project Demo Philip Wong new Labcoordinator okwonoeceodxedu All of you need to be signed up No extensions to ensure timely grading 7 S Prasad Portland State University ECE 223 Fall 2007 Lecture 19 Exam 2 Exam2 Number of Students O k 0 00h 01 O l 00 Number of Students 24 Mean 4285 8 S Prasad Portland State University ECE 223 Fall 2007 Lecture 19 Comments on Exam 2 Approx 80 gt80 score Qt Transform Mapping Approx 60 gt80 score Q2 CTFT Approx 95 gt80 score Q3 Properties of FFT Approx 85 gt80 score Q4 Interpretation of Transforms 9 S Prasad Portland State University ECE 223 Fall 2007 Lecture 19 Lecture Overview Last Time Fast Fourier Transform This Time Sampling Exam 2 Back Questions on Exam 2 grading till Dec 6th 10 S Prasad Portland State University ECE 223 Fall 2007 Lecture 19 ECE 223 Signals and Systems ll httpwwwecepdxed uprasads Dr Shalini Prasad Electrical and Computer Engineering sprasadpdxedu Pr 39tltTLitf gl l 1 STATE U Wiznam39 1 S Prasad Portland State University ECE 223 Fall 2007 Lecture 7 Homework Assignment Homework 1 October 26th Friday 0 Read Chapter 3 Section 56 CTFS and DTFT Problems 38 CTFS 312 313 solutions in textDTFT 350 d and e CTFS Solutions have been posted 2 S Prasad Portland State University ECE 223 Fall 2007 Lecture 7 Exam 1 Reading for Exam1 Chapter 1 and Chapter 3135 Complements Lecture Notes Should be able to do example problems in the text book Draft topics for exam posted in HW section of website Up through CT Fourier Series 3 S Prasad Portland State University ECE 223 Fall 2007 Lecture 7 Exam 1 You are allowed one single page hand written letter size notes Study Aids for exam Lecture notes Recorded Lectures Homework Old HW and exams 4 S Prasad Portland State University ECE 223 Fall 2007 Lecture 7 Exam 1 DateOctober 19th Friday Time 100 minutes Number of questions 4 Total Score 60 Overview of signals 1 Complex Sinusoids1 Discrete Time Fourier Series1 Continuous Time Fourier Series 1 5 S Prasad Portland State University ECE 223 Fall 2007 Lecture 7 Exam 1 Topics Signals overviewenergy and power signals Eigen Functionsvalues Periodic Signals Fundamental Period Frequency Euler ldentity Fourier Series Representation Effect of Linear Systems of Fourier Series Symmetry and Periodicity of Coefficients Various Formats of Fourier Series DC Component 6 S Prasad Portland State University ECE 223 Fall 2007 Lecture 7 Lecture Overview Last Time Continuous Time Fourier Series This Time Continuous Time Fourier Series Discrete Time Fourier Transform 7 S Prasad Portland State University ECE 223 Fall 2007 Lecture 7 ECE 223 Signals and Systems ll httpwwwecepdxed uprasads Dr Shalini Prasad Electrical and Computer Engineering sprasadpdxedu Pr 39tltTLitf gl l 1 STATE U Wiznam39 1 S Prasad Portland State University ECE 223 Fall 2007 Lecture 6 Homework Assignment Homework 1 October 26th Friday Read Chapter 3 Section 56 CTFS and DTFT Problems 38 CTFS 312 313 solutions in textDTFT 350 d and e CTFS Solutions have been posted 2 S Prasad Portland State University ECE 223 Fall 2007 Lecture 6 Exam 1 Reading for Exam1 Chapter 1 and Chapter 3135 Complements Lecture Notes Should be able to do example problems in the text book Draft topics for exam posted in HW section of website Up through CT Fourier Series 3 S Prasad Portland State University ECE 223 Fall 2007 Lecture 6 Exam 1 You are allowed one single page hand written letter size notes Study Aids for exam Lecture notes Recorded Lectures Homework Old HW and exams 4 S Prasad Portland State University ECE 223 Fall 2007 Lecture 6 Exam 1 DateOctober 19th Friday Time 100 minutes Number of questions 4 Overview of signals 1 Complex Sinusoids1 Discrete Time Fourier Series1 Continuous Time Fourier Series 1 5 S Prasad Portland State University ECE 223 Fall 2007 Lecture 6 Exam 1 Topics Eigen Functionsvalues Periodic Signals Fundamental Period Frequency Euler ldentity Fourier Series Representation Effect of Linear Systems of Fourier Series Symmetry and Periodicity of Coefficients Various Formats of Fourier Series DC Component 6 S Prasad Portland State University ECE 223 Fall 2007 Lecture 6 Lecture Overview Last Time Continuous Time Fourier Series This Time Continuous Time Fourier Series 7 S Prasad Portland State University ECE 223 Fall 2007 Lecture 6 ECE 223 Signals and Systems ll httpwwwecepdxed uprasads Dr Shalini Prasad Electrical and Computer Engineering sprasadpdxedu Pr 39tltTLitf gl l 1 STATE U Wiznam39 1 S Prasad Portland State University ECE 223 Fall 2007 Lecture 14 Homework Assignment IV Problems 416 a 417a 418a 425a 426a Due Fri NOV 30 Read Chapter 3 Sections 311312 314320 Chapter 4 Section 4 and 5 FFT and Sampling 2 S Prasad Portland State University ECE 223 Fall 2007 Lecture 14 Exam 2 November 16th FridayTomorrow Time 100 minutes Location EB 103 No calculators One page front and back of handwritten notes 3 S Prasad Portland State University ECE 223 Fall 2007 Lecture 14 Exam 2 Topics DTFT CTFT Properties of FT and applications of FT Interpretation of FT Total Score 60 points 4 questiOHS problem 1 20 pts Problem 2 1O pts PrOb39em 31 19 pts Problem 4 11 pts 4 S Prasad Portland State University ECE 223 Fall 2007 Lecture 14 Discrete Time Fourier Transform DTFT Low frequency and high frequency discretetime signals Determine transforms of most simple signals by applying the definition Find the inverse transform Sufficient conditions for convergence and inverse transform convergence Relationship of symmetry and periodicity of the transform to properties of the signal The relationship of the output of an LTl system to the Fourier transforms of the input signal and the impulse response of the system 5 S Prasad Portland State University ECE 223 Fall 2007 Lecture 14 Continuous Time Fourier Transform CTFT Transform of simple signals by applying the definition Inverse transform by applying the definition Sufficient conditions for convergence and how the transform can be applied when it does not converge by the use of impulse functions symmetry of the transform and relationship to properties of the signal How the transform relates to LTI systems and transfer functions calculated by the Laplace transform 6 S Prasad Portland State University ECE 223 Fall 2007 Lecture 14 Continuous Time FOUI IeI Transform QTFT The tradeoffs of using the Fourier transform versus the Laplace transform How the DTFT of a periodic signal is related to the DTFS coefficients 7 S Prasad Portland State University ECE 223 Fall 2007 Lecture 14 FOUI IeI Transform amp Series Properties Properties of the four transforms Effect of windowing on the magnitude spectrum How to identify the magnitude spectrum of basic timedomain signals that have been windowed How each of the properties is relevant to practical applications and design as discussed in class 8 S Prasad Portland State University ECE 223 Fall 2007 Lecture 14 Lecture Overview Last Time Properties of Fourier Transform This Time Fast Fourier Transform Sampling 9 S Prasad Portland State University ECE 223 Fall 2007 Lecture 14 ECE 223 Signals and Systems ll httpwwwecepdxed uprasads Dr Shalini Prasad Electrical and Computer Engineering sprasadpdxedu Pr 39tltTLitf gl l 1 STATE U Wiznam39 1 S Prasad Portland State University ECE 223 Fall 2007 Lecture 5 Homework Assignment Email me 6 digit code Homework 1 October 12th Friday Email 6digit code Read Review Chapters 1 amp 2 Required Chapter 3 Sections 14 Ch 3 48a 48 b 49a 49b Ch3 50d HW2 section 35 CTFS Solutions have been posted 2 S Prasad Portland State University ECE 223 Fall 2007 Lecture 5 Exam 1 Reading forExam1 Chapter 1 and Chapter 3135 Complements Lecture Notes Should be able to do example problems in the text book Draft topics for exam posted in HW section of website Up through CT Fourier Series 3 S Prasad Portland State University ECE 223 Fall 2007 Lecture 5 Exam 1 You are allowed one single page hand written letter size notes Study Aids for exam Lecture notes Recorded Lectures Homework Old HW and exams 4 S Prasad Portland State University ECE 223 Fall 2007 Lecture 5 Lecture Overview Last Time Discrete Time Fourier Series This Time Discrete Time Fourier Series Continuous Time Fourier Series 5 S Prasad Portland State University ECE 223 Fall 2007 Lecture 5 ECE 223 Signals and Systems ll httpwwwecepdxed uprasads Dr Shalini Prasad Electrical and Computer Engineering sprasadpdxedu Pr 39tltTLitf gl l 1 STATE U Wiznam39 1 S Prasad Portland State University ECE 223 Fall 2007 Lecture 13 Homework Assignment lll Homework 3 Due Friday Nov 9 Problems on DTFT CTFT and Properties of FT Read Chapter 3 Sections 610 Problems 352 b 353 b 3540 and 355 c 356 a 357a 358 a 2 S Prasad Portland State University ECE 223 Fall 2007 Lecture 13 Exam 2 November 16th Friday Time 100 minutes Location EB 103 No calculators One page front and back of handwritten notes 3 S Prasad Portland State University ECE 223 Fall 2007 Lecture 13 Exam 2 Topics DTFT 1 CTFT 1 Properties of FT 1 Total Score 60 points 4 S Prasad Portland State University ECE 223 Fall 2007 Lecture 13 Lecture Overview Last Time Start Properties of Fourier Transform This Time Properties of Fourier Transform 5 S Prasad Portland State University ECE 223 Fall 2007 Lecture 13

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