Spring 2014 EE 445S Real-Time Digital Signal Processing Laboratory. Homework #0 Solutions on Review of Signals and Systems Material
|
|
- Delphia Phelps
- 6 years ago
- Views:
Transcription
1 Spring 4 EE 445S Real-Time Digital Signal Proceing Laboratory Prof. Evan Homework # Solution on Review of Signal and Sytem Material Problem.. Continuou-Time Sinuoidal Generation. In practice, we cannot generate a two-ided inuoid co( f c, nor can we wait until the end of time to oberve a one-ided inuoid co( f c u(. In the lab, we can turn on a ignal generator for a hort time and oberve the output in the time domain on an ocillocope or in the frequency domain uing a pectrum analyzer. Conider a finite-duration coine that i on from ec to ec given by the equation where f c i the carrier frequency (in Hz). c( = co( f c rect(t ½) Part (a). Uing MATLAB, LabVIEW Mathcript or GNU Octave, plot c( for -.5 < t <.5 for fc = Hz. Turn in your code and plot. You may find the rectpul command ueful. Give a formula for the Fourier tranform of c( for a general value of fc. Solution: Ue MATLAB to plot the ignal c( = co( f rect(t - ½) for -.5 < t <.5. We ll need to pick a ampling rate f o that f > f max to obey the ampling theorem. The value of f max could be computed uing the anwer in part (d) but we know from the modulation property of the Fourier tranform that f max i f plu the bandwidth of rect(t - ½). Let overample: f = Hz. Part (b). Sketch by hand the magnitude of the Fourier tranform of c( for a general value of fc. Uing MATLAB, LabVIEW Mathcript or GNU Octave, plot the magnitude of the Fourier tranform of c( for fc = 8 Hz. Turn in your code and plot. Solution: Taking the Fourier tranform of c( we obtain MATLAB code T =.; t= -.5 : T :.5; f = ; x = co(*pi*f*; h = rectpul(t-.5); c = x.* h; figure plot(t,c) grid title('truncated Coine') xlabel('t') ylabel('c(') Coure Web ite:
2 C( ) F co trect t F co t* F rect t by uing the Fourier tranform property that multiplication in the time domain i convolution in the frequency domain. We then lookup the Fourier tranform of coine and rectangular pule: C ( ) j / π δ π δ * e inc where inc(x) = in( x) / ( x). Then, When plotting by hand, the firt term on the right hand ide of the equation i centered at f = /, and the econd i centered at f =- /. We can then take the abolute value: When plotting in Matlab, we can plot the full formula for the Fourier tranform magnitude. MATLAB code f=8; f=[-:.:]; C =.5*exp(-j*pi*(f-f)).*inc(f-f) +.5*exp(-j*pi*(f+f)).*inc(f+f); plot(f,ab(c)) grid title('plot of Magnitude of Fourier Tranform of c(') xlabel('f (Hz)') ylabel(' C(f) ') A pectrum analyzer would diplay the above magnitude pectrum plu noie. Part (c). Decribe the difference between the magnitude of the Fourier tranform of c( and a twoided coine of the ame frequency. What i the bandwidth of each ignal? Coure Web ite:
3 Solution: Bandwidth i the non-zero extent in poitive frequencie of the ignal' pectrum. Fourier tranform of the two-ided coine x( = co( f i X() = ((+ )+ (- )): () () Each Dirac delta ha width of zero and area of. Bandwidth i zero. From the plot in part (c), the bandwidth of C() i not zero. multiplication of the two-ided coine by rect(t - ½) in the time domain. Thi i becaue of the Each of the following i a valid method to etimate the bandwidth of bandpa ignal C(): Set amplitude threhold of magnitude pectrum at an arbitrary point below which amplitude are treated a if zero. If we ue.5 a the threhold for the plot in part (c), then we can eyeball the etimated bandwidth of C() to be.5 Hz. Meaure width of the mainlobe in the magnitude pectrum between the two zero croing on either ide of the carrier frequency. For the magnitude pectrum in part (c), we can eyeball the etimated bandwidth to be Hz. Etimate the power bandwidth to capture 9% of the area under the power pectrum. With a center frequency of 8 Hz, a bandwidth of Hz would only occupy 55% of the total area. Thi approach doe not work all that well in thi cae. More dicuion next. Firt, we define a function called myfun in file myfun.m to compute C(f) : function mag_c = myfun(f) f=8; mag_c = ab(.5*exp(-j*pi*(f-f)).*inc(f-f) *exp(-j*pi*(f+f)).*inc(f+f)); Next, we can approximate the total area under the magnitude pectrum by uing Hz in place of and uing the numerical integration function quad: area = quad(@myfun,,); Finally, frequencie to Hz only contain 55% of the area: area = quad(@myfun,,); We are better off eyeballing the bandwidth from the plot of the magnitude pectrum. Problem.. Downconverion. A ignal x( i input to a mixer to produce the output y( where y( = x( co( and Coure Web ite:
4 = f and f = khz. A block diagram of the mixer i hown below on the left. The Fourier tranform of x( i hown below on the left. Part (a). Uing Fourier tranform propertie, derive an expreion for Y(f) in term of X(f). Solution: Fourier tranform of y( = x( co( i Y(ω) = Since co(ω Y(f) [co( ]* X(ω) [(ω ω ) + ( ω + ω )], Y ( ) ( X ( ) X ( )) Y f ) f f f f * X ( f ) ( X ( f f ) X ( f In a imilar way, )) Part (b). Sketch Y(f) v. f ( f f(khz) Part (c). What operation would you apply to the ignal y( in part (b) to obtain a baeband ignal? The proce of extracting the baeband ignal from a bandpa ignal i known a downconverion. Solution: Baeband ignal may be obtained by applying a lowpa filter to y( that pae frequencie in [-,] khz and attenuate frequencie at and above 3 khz in abolute value. Problem.3. Sampling in Continuou Time. Sampling the amplitude of an analog, continuou-time ignal f( every T econd can be modeled in continuou time a y( = f( p( where p( i the impule train defined by p( n t nt Coure Web ite:
5 T i known a the ampling duration. The Fourier erie expanion of the impule train i p( co( co(... T where = / T i the ampling rate in unit of radian per econd. Part (a). Plot the impule train. n Solution: Plot of the impule train p( t nt p (t ) () () t -T T The notation (A) mean that the area under the Dirac delta i A. Thi i important becaue the value of the Dirac delta at the origin i undefined. Part (b). Note that in part (a), p( i periodic. What i the period? Solution: A ignal x( i periodic with period T if x( = x(t T) for all t. The mallet value of T for which x( i periodic i called the fundamental period. The impule train p( i periodic with fundamental period T. The fundamental period i ued in the Fourier erie expanion of the impule train where the ampling rate in rad/ i = / T : Part (c). Uing the Fourier erie repreentation of p( given above, pleae give a formula for P(), which i the Fourier tranform of p(. Expre your anwer for P() a an impule train in the Fourier domain. Solution: We apply the Fourier tranform to p( given immediately above to compute P( ) ( ( ) ( ) ( ) ( ) ( )...) T p( co( co(... T by uing the tranform pair co(ω [(ω - ω ) + ( ω + ω )] and (ω) Coure Web ite:
6 Thu n P ( ) ( n ) Part (d). What i the pacing of adjacent impule in the impule train in P() with repect to frequency in rad/? Solution: The pacing of the impule train P() in i, which i the ditance between adjacent impule in the Fourier domain. Problem.4. Dicrete-Time Sinuoidal Generation. Conider a caual dicrete-time linear time-invariant ytem with input x[n] and output y[n] being governed by the following difference equation: y[n] = ( co ) y[n-] - y[n-] + (in ) x[n-] The impule repone of the above ytem i a caual inuoid with dicrete-time frequency in unit of rad/ample. The value of would normally be in the interval [-, ). You will be implementing the above difference equation in C in lab # on a programmable digital ignal proceor for real-time inuoidal generation. Part (a). Draw the block diagram for thi ytem uing add (or ummation), multiplication (or gain), and delay block. Pleae label delay block with the text z -M to denote a delay of M ample. Ue arrowhead to indicate direction of the flow of ignal. Solution: Block diagram of the given filter with input x[n] and output y[n] and with coefficient b = in and a = co : Coure Web ite:
7 Part (b). Pleae tate all initial condition. Pleae give value for the initial condition to atify the tated ytem propertie. Solution: Initial condition can be found by calculating the firt few output value: y[] = ( co ) y[-] - y[-] + (in ) x[-] y[] = ( co ) y[] - y[-] + (in ) x[] Hence, the initial condition are given by y[-], x[-] and y[-]. Thee value correpond to the initial value in the delay-by-one-ample block, which are denoted by z -. The impule repone i given a h[n] = in( n) u[n]. That i, for x[n] = [n], the output i y[n] = h[n], which give y[-] = h[-] = and y[-] = h[-] = and x[-] = [-] =, For the ytem to atify the linearity property, the initial condition mut be zero. Same goe for the ytem property of time-invariance. We will how thi on lide 3- and 3-. Part (c). Find the equation for the tranfer function in the z-domain, including the region of convergence. Solution: y[n] = ( co ) y[n-] - y[n-] + (in ) x[n-] Taking z-tranform of both ide, we get Y(z) = ( co ) z - Y(z) - z - Y(z) + (in ) z - X(z) => Y( z) X ( z) in z co z z => H in z co z z ( z) To find the region of convergence, we need to find the pole of thi tranfer function: - ( co ) z - + z - = By multiplying each ide by z (auming that z ): z - ( co ) z + = Root are located at ½ (-b qrt()). Here, Since <, there are two complex root: 4co 4 4in Coure Web ite:
8 x co j in co j in co j in ; x co j in Both pole have a magnitude of. A a reult, they lie on the unit circle in the z-plane. Since the ytem i caual, the region of convergence will be outide of the circle of radiu equal to the magnitude of the pole with the greatet magnitude, i.e. z >. Part (d). Compute the invere z-tranform of the tranfer function in part (c) to find the impule repone of the ytem. Solution: By uing invere z-tranform table, the above H(z) with the given region of convergence will have an impule repone of h[n] = in( n) u[n]. Part (e). Uing MATLAB, LabVIEW Mathcript or GNU Octave, plot the impule repone obtained in part (d) for equal to, π, and a value in the interval (, π) of your chooing. Turn in your code and plot. Solution: i rad/ample (lef, π rad/ample (center), and π/4 rad/ample (righ: Sample MATLAB code for = π/4: w = pi/4; n = [:5]; u = tepfun(n,); x = in(w*n); h = x.*u; figure, tem(n,h); In the middle plot, which i for = π rad/ample, all amplitude value hould have been zero. Non-zero value are due to numerical error in computing in( n) for n 5 in floating-point arithmetic. The value are on the order of -5, which i very cloe to zero. Coure Web ite:
Chapter 2 Sampling and Quantization. In order to investigate sampling and quantization, the difference between analog
Chapter Sampling and Quantization.1 Analog and Digital Signal In order to invetigate ampling and quantization, the difference between analog and digital ignal mut be undertood. Analog ignal conit of continuou
More informationChapter 2: Problem Solutions
Chapter 2: Solution Dicrete Time Proceing of Continuou Time Signal Sampling à 2.. : Conider a inuoidal ignal and let u ample it at a frequency F 2kHz. xt 3co000t 0. a) Determine and expreion for the ampled
More informationSampling and the Discrete Fourier Transform
Sampling and the Dicrete Fourier Tranform Sampling Method Sampling i mot commonly done with two device, the ample-and-hold (S/H) and the analog-to-digital-converter (ADC) The S/H acquire a CT ignal at
More information( 1) EE 313 Linear Signals & Systems (Fall 2018) Solution Set for Homework #10 on Laplace Transforms
EE 33 Linear Signal & Sytem (Fall 08) Solution Set for Homework #0 on Laplace Tranform By: Mr. Houhang Salimian & Prof. Brian L. Evan Problem. a) xt () = ut () ut ( ) From lecture Lut { ()} = and { } t
More informationDesign of Digital Filters
Deign of Digital Filter Paley-Wiener Theorem [ ] ( ) If h n i a caual energy ignal, then ln H e dω< B where B i a finite upper bound. One implication of the Paley-Wiener theorem i that a tranfer function
More informationDigital Control System
Digital Control Sytem Summary # he -tranform play an important role in digital control and dicrete ignal proceing. he -tranform i defined a F () f(k) k () A. Example Conider the following equence: f(k)
More informationEE 477 Digital Signal Processing. 4 Sampling; Discrete-Time
EE 477 Digital Signal Proceing 4 Sampling; Dicrete-Time Sampling a Continuou Signal Obtain a equence of ignal ample uing a periodic intantaneou ampler: x [ n] = x( nt ) Often plot dicrete ignal a dot or
More informationinto a discrete time function. Recall that the table of Laplace/z-transforms is constructed by (i) selecting to get
Lecture 25 Introduction to Some Matlab c2d Code in Relation to Sampled Sytem here are many way to convert a continuou time function, { h( t) ; t [0, )} into a dicrete time function { h ( k) ; k {0,,, }}
More informationChapter 4: Applications of Fourier Representations. Chih-Wei Liu
Chapter 4: Application of Fourier Repreentation Chih-Wei Liu Outline Introduction Fourier ranform of Periodic Signal Convolution/Multiplication with Non-Periodic Signal Fourier ranform of Dicrete-ime Signal
More informationLecture 10 Filtering: Applied Concepts
Lecture Filtering: Applied Concept In the previou two lecture, you have learned about finite-impule-repone (FIR) and infinite-impule-repone (IIR) filter. In thee lecture, we introduced the concept of filtering
More information5.5 Application of Frequency Response: Signal Filters
44 Dynamic Sytem Second order lowpa filter having tranfer function H()=H ()H () u H () H () y Firt order lowpa filter Figure 5.5: Contruction of a econd order low-pa filter by combining two firt order
More informationDigital Control System
Digital Control Sytem - A D D A Micro ADC DAC Proceor Correction Element Proce Clock Meaurement A: Analog D: Digital Continuou Controller and Digital Control Rt - c Plant yt Continuou Controller Digital
More informationSIMON FRASER UNIVERSITY School of Engineering Science ENSC 320 Electric Circuits II. Solutions to Assignment 3 February 2005.
SIMON FRASER UNIVERSITY School of Engineering Science ENSC 320 Electric Circuit II Solution to Aignment 3 February 2005. Initial Condition Source 0 V battery witch flip at t 0 find i 3 (t) Component value:
More informationLecture 5 Frequency Response of FIR Systems (III)
EE3054 Signal and Sytem Lecture 5 Frequency Repone of FIR Sytem (III Yao Wang Polytechnic Univerity Mot of the lide included are extracted from lecture preentation prepared by McClellan and Schafer Licene
More informationSolutions. Digital Control Systems ( ) 120 minutes examination time + 15 minutes reading time at the beginning of the exam
BSc - Sample Examination Digital Control Sytem (5-588-) Prof. L. Guzzella Solution Exam Duration: Number of Quetion: Rating: Permitted aid: minute examination time + 5 minute reading time at the beginning
More informationR. W. Erickson. Department of Electrical, Computer, and Energy Engineering University of Colorado, Boulder
R. W. Erickon Department of Electrical, Computer, and Energy Engineering Univerity of Colorado, Boulder Cloed-loop buck converter example: Section 9.5.4 In ECEN 5797, we ued the CCM mall ignal model to
More informationRoadmap for Discrete-Time Signal Processing
EE 4G Note: Chapter 8 Continuou-time Signal co(πf Roadmap for Dicrete-ime Signal Proceing.5 -.5 -..4.6.8..4.6.8 Dicrete-time Signal (Section 8.).5 -.5 -..4.6.8..4.6.8 Sampling Period econd (or ampling
More informationProperties of Z-transform Transform 1 Linearity a
Midterm 3 (Fall 6 of EEG:. Thi midterm conit of eight ingle-ided page. The firt three page contain variou table followed by FOUR eam quetion and one etra workheet. You can tear out any page but make ure
More informationECE382/ME482 Spring 2004 Homework 4 Solution November 14,
ECE382/ME482 Spring 2004 Homework 4 Solution November 14, 2005 1 Solution to HW4 AP4.3 Intead of a contant or tep reference input, we are given, in thi problem, a more complicated reference path, r(t)
More information( ) ( ) ω = X x t e dt
The Laplace Tranform The Laplace Tranform generalize the Fourier Traform for the entire complex plane For an ignal x(t) the pectrum, or it Fourier tranform i (if it exit): t X x t e dt ω = For the ame
More informationQuestion 1 Equivalent Circuits
MAE 40 inear ircuit Fall 2007 Final Intruction ) Thi exam i open book You may ue whatever written material you chooe, including your cla note and textbook You may ue a hand calculator with no communication
More informationSAMPLING. Sampling is the acquisition of a continuous signal at discrete time intervals and is a fundamental concept in real-time signal processing.
SAMPLING Sampling i the acquiition of a continuou ignal at dicrete time interval and i a fundamental concept in real-time ignal proceing. he actual ampling operation can alo be defined by the figure belo
More informationDepartment of Mechanical Engineering Massachusetts Institute of Technology Modeling, Dynamics and Control III Spring 2002
Department of Mechanical Engineering Maachuett Intitute of Technology 2.010 Modeling, Dynamic and Control III Spring 2002 SOLUTIONS: Problem Set # 10 Problem 1 Etimating tranfer function from Bode Plot.
More informationDesign By Emulation (Indirect Method)
Deign By Emulation (Indirect Method he baic trategy here i, that Given a continuou tranfer function, it i required to find the bet dicrete equivalent uch that the ignal produced by paing an input ignal
More informationMarch 18, 2014 Academic Year 2013/14
POLITONG - SHANGHAI BASIC AUTOMATIC CONTROL Exam grade March 8, 4 Academic Year 3/4 NAME (Pinyin/Italian)... STUDENT ID Ue only thee page (including the back) for anwer. Do not ue additional heet. Ue of
More informationLTV System Modelling
Helinki Univerit of Technolog S-72.333 Potgraduate Coure in Radiocommunication Fall 2000 LTV Stem Modelling Heikki Lorentz Sonera Entrum O heikki.lorentz@onera.fi Januar 23 rd 200 Content. Introduction
More informationCorrection for Simple System Example and Notes on Laplace Transforms / Deviation Variables ECHE 550 Fall 2002
Correction for Simple Sytem Example and Note on Laplace Tranform / Deviation Variable ECHE 55 Fall 22 Conider a tank draining from an initial height of h o at time t =. With no flow into the tank (F in
More informationIntroduction to Laplace Transform Techniques in Circuit Analysis
Unit 6 Introduction to Laplace Tranform Technique in Circuit Analyi In thi unit we conider the application of Laplace Tranform to circuit analyi. A relevant dicuion of the one-ided Laplace tranform i found
More informationME 375 EXAM #1 Tuesday February 21, 2006
ME 375 EXAM #1 Tueday February 1, 006 Diviion Adam 11:30 / Savran :30 (circle one) Name Intruction (1) Thi i a cloed book examination, but you are allowed one 8.5x11 crib heet. () You have one hour to
More informationEE/ME/AE324: Dynamical Systems. Chapter 8: Transfer Function Analysis
EE/ME/AE34: Dynamical Sytem Chapter 8: Tranfer Function Analyi The Sytem Tranfer Function Conider the ytem decribed by the nth-order I/O eqn.: ( n) ( n 1) ( m) y + a y + + a y = b u + + bu n 1 0 m 0 Taking
More informationHOMEWORK ASSIGNMENT #2
Texa A&M Univerity Electrical Engineering Department ELEN Integrated Active Filter Deign Methodologie Alberto Valde-Garcia TAMU ID# 000 17 September 0, 001 HOMEWORK ASSIGNMENT # PROBLEM 1 Obtain at leat
More informationFRTN10 Exercise 3. Specifications and Disturbance Models
FRTN0 Exercie 3. Specification and Diturbance Model 3. A feedback ytem i hown in Figure 3., in which a firt-order proce if controlled by an I controller. d v r u 2 z C() P() y n Figure 3. Sytem in Problem
More informationMain Topics: The Past, H(s): Poles, zeros, s-plane, and stability; Decomposition of the complete response.
EE202 HOMEWORK PROBLEMS SPRING 18 TO THE STUDENT: ALWAYS CHECK THE ERRATA on the web. Quote for your Parent' Partie: 1. Only with nodal analyi i the ret of the emeter a poibility. Ray DeCarlo 2. (The need
More informationGiven the following circuit with unknown initial capacitor voltage v(0): X(s) Immediately, we know that the transfer function H(s) is
EE 4G Note: Chapter 6 Intructor: Cheung More about ZSR and ZIR. Finding unknown initial condition: Given the following circuit with unknown initial capacitor voltage v0: F v0/ / Input xt 0Ω Output yt -
More informationMathematical modeling of control systems. Laith Batarseh. Mathematical modeling of control systems
Chapter two Laith Batareh Mathematical modeling The dynamic of many ytem, whether they are mechanical, electrical, thermal, economic, biological, and o on, may be decribed in term of differential equation
More informationCHAPTER 4 DESIGN OF STATE FEEDBACK CONTROLLERS AND STATE OBSERVERS USING REDUCED ORDER MODEL
98 CHAPTER DESIGN OF STATE FEEDBACK CONTROLLERS AND STATE OBSERVERS USING REDUCED ORDER MODEL INTRODUCTION The deign of ytem uing tate pace model for the deign i called a modern control deign and it i
More informationThe Laplace Transform
The Laplace Tranform Prof. Siripong Potiuk Pierre Simon De Laplace 749-827 French Atronomer and Mathematician Laplace Tranform An extenion of the CT Fourier tranform to allow analyi of broader cla of CT
More informationME 375 FINAL EXAM Wednesday, May 6, 2009
ME 375 FINAL EXAM Wedneday, May 6, 9 Diviion Meckl :3 / Adam :3 (circle one) Name_ Intruction () Thi i a cloed book examination, but you are allowed three ingle-ided 8.5 crib heet. A calculator i NOT allowed.
More informationMath 273 Solutions to Review Problems for Exam 1
Math 7 Solution to Review Problem for Exam True or Fale? Circle ONE anwer for each Hint: For effective tudy, explain why if true and give a counterexample if fale (a) T or F : If a b and b c, then a c
More informationLecture #9 Continuous time filter
Lecture #9 Continuou time filter Oliver Faut December 5, 2006 Content Review. Motivation......................................... 2 2 Filter pecification 2 2. Low pa..........................................
More informationModule 4: Time Response of discrete time systems Lecture Note 1
Digital Control Module 4 Lecture Module 4: ime Repone of dicrete time ytem Lecture Note ime Repone of dicrete time ytem Abolute tability i a baic requirement of all control ytem. Apart from that, good
More informationECE-320 Linear Control Systems. Spring 2014, Exam 1. No calculators or computers allowed, you may leave your answers as fractions.
ECE-0 Linear Control Sytem Spring 04, Exam No calculator or computer allowed, you may leave your anwer a fraction. All problem are worth point unle noted otherwie. Total /00 Problem - refer to the unit
More informationMAHALAKSHMI ENGINEERING COLLEGE-TRICHY
DIGITAL SIGNAL PROCESSING DEPT./SEM.: CSE /VII DIGITAL FILTER DESIGN-IIR & FIR FILTER DESIGN PART-A. Lit the different type of tructure for realiation of IIR ytem? AUC APR 09 The different type of tructure
More informationEE Control Systems LECTURE 6
Copyright FL Lewi 999 All right reerved EE - Control Sytem LECTURE 6 Updated: Sunday, February, 999 BLOCK DIAGRAM AND MASON'S FORMULA A linear time-invariant (LTI) ytem can be repreented in many way, including:
More informationHomework 7 Solution - AME 30315, Spring s 2 + 2s (s 2 + 2s + 4)(s + 20)
1 Homework 7 Solution - AME 30315, Spring 2015 Problem 1 [10/10 pt] Ue partial fraction expanion to compute x(t) when X 1 () = 4 2 + 2 + 4 Ue partial fraction expanion to compute x(t) when X 2 () = ( )
More informationMassachusetts Institute of Technology Dynamics and Control II
I E Maachuett Intitute of Technology Department of Mechanical Engineering 2.004 Dynamic and Control II Laboratory Seion 5: Elimination of Steady-State Error Uing Integral Control Action 1 Laboratory Objective:
More informationCONTROL SYSTEMS. Chapter 2 : Block Diagram & Signal Flow Graphs GATE Objective & Numerical Type Questions
ONTOL SYSTEMS hapter : Bloc Diagram & Signal Flow Graph GATE Objective & Numerical Type Quetion Quetion 6 [Practice Boo] [GATE E 994 IIT-Kharagpur : 5 Mar] educe the ignal flow graph hown in figure below,
More informationPart A: Signal Processing. Professor E. Ambikairajah UNSW, Australia
Part A: Signal Proceing Chapter 5: Digital Filter Deign 5. Chooing between FIR and IIR filter 5. Deign Technique 5.3 IIR filter Deign 5.3. Impule Invariant Method 5.3. Bilinear Tranformation 5.3.3 Digital
More informationWolfgang Hofle. CERN CAS Darmstadt, October W. Hofle feedback systems
Wolfgang Hofle Wolfgang.Hofle@cern.ch CERN CAS Darmtadt, October 9 Feedback i a mechanim that influence a ytem by looping back an output to the input a concept which i found in abundance in nature and
More informationDYNAMIC MODELS FOR CONTROLLER DESIGN
DYNAMIC MODELS FOR CONTROLLER DESIGN M.T. Tham (996,999) Dept. of Chemical and Proce Engineering Newcatle upon Tyne, NE 7RU, UK.. INTRODUCTION The problem of deigning a good control ytem i baically that
More informationFunction and Impulse Response
Tranfer Function and Impule Repone Solution of Selected Unolved Example. Tranfer Function Q.8 Solution : The -domain network i hown in the Fig... Applying VL to the two loop, R R R I () I () L I () L V()
More informationMidterm Test Nov 10, 2010 Student Number:
Mathematic 265 Section: 03 Verion A Full Name: Midterm Tet Nov 0, 200 Student Number: Intruction: There are 6 page in thi tet (including thi cover page).. Caution: There may (or may not) be more than one
More informationAutomatic Control Systems. Part III: Root Locus Technique
www.pdhcenter.com PDH Coure E40 www.pdhonline.org Automatic Control Sytem Part III: Root Locu Technique By Shih-Min Hu, Ph.D., P.E. Page of 30 www.pdhcenter.com PDH Coure E40 www.pdhonline.org VI. Root
More informationAdvanced Digital Signal Processing. Stationary/nonstationary signals. Time-Frequency Analysis... Some nonstationary signals. Time-Frequency Analysis
Advanced Digital ignal Proceing Prof. Nizamettin AYDIN naydin@yildiz.edu.tr Time-Frequency Analyi http://www.yildiz.edu.tr/~naydin 2 tationary/nontationary ignal Time-Frequency Analyi Fourier Tranform
More informationLRA DSP. Multi-Rate DSP. Applications: Oversampling, Undersampling, Quadrature Mirror Filters. Professor L R Arnaut 1
ulti-rate Application: Overampling, Underampling, Quadrature irror Filter Profeor L R Arnaut ulti-rate Overampling Profeor L R Arnaut Optimal Sampling v. Overampling Sampling at Nyquit rate F =F B Allow
More informationME 375 FINAL EXAM SOLUTIONS Friday December 17, 2004
ME 375 FINAL EXAM SOLUTIONS Friday December 7, 004 Diviion Adam 0:30 / Yao :30 (circle one) Name Intruction () Thi i a cloed book eamination, but you are allowed three 8.5 crib heet. () You have two hour
More informationLinear System Fundamentals
Linear Sytem Fundamental MEM 355 Performance Enhancement of Dynamical Sytem Harry G. Kwatny Department of Mechanical Engineering & Mechanic Drexel Univerity Content Sytem Repreentation Stability Concept
More informatione st t u(t 2) dt = lim t dt = T 2 2 e st = T e st lim + e st
Math 46, Profeor David Levermore Anwer to Quetion for Dicuion Friday, 7 October 7 Firt Set of Quetion ( Ue the definition of the Laplace tranform to compute Lf]( for the function f(t = u(t t, where u i
More informationCOMM 602: Digital Signal Processing. Lecture 8. Digital Filter Design
COMM 60: Digital Signal Proeing Leture 8 Digital Filter Deign Remember: Filter Type Filter Band Pratial Filter peifiation Pratial Filter peifiation H ellipti H Pratial Filter peifiation p p IIR Filter
More informationS_LOOP: SINGLE-LOOP FEEDBACK CONTROL SYSTEM ANALYSIS
S_LOOP: SINGLE-LOOP FEEDBACK CONTROL SYSTEM ANALYSIS by Michelle Gretzinger, Daniel Zyngier and Thoma Marlin INTRODUCTION One of the challenge to the engineer learning proce control i relating theoretical
More informationDetermination of the local contrast of interference fringe patterns using continuous wavelet transform
Determination of the local contrat of interference fringe pattern uing continuou wavelet tranform Jong Kwang Hyok, Kim Chol Su Intitute of Optic, Department of Phyic, Kim Il Sung Univerity, Pyongyang,
More information1. /25 2. /30 3. /25 4. /20 Total /100
Circuit Exam 2 Spring 206. /25 2. /30 3. /25 4. /20 Total /00 Name Pleae write your name at the top of every page! Note: ) If you are tuck on one part of the problem, chooe reaonable value on the following
More informationBogoliubov Transformation in Classical Mechanics
Bogoliubov Tranformation in Claical Mechanic Canonical Tranformation Suppoe we have a et of complex canonical variable, {a j }, and would like to conider another et of variable, {b }, b b ({a j }). How
More informationControl Systems Engineering ( Chapter 7. Steady-State Errors ) Prof. Kwang-Chun Ho Tel: Fax:
Control Sytem Engineering ( Chapter 7. Steady-State Error Prof. Kwang-Chun Ho kwangho@hanung.ac.kr Tel: 0-760-453 Fax:0-760-4435 Introduction In thi leon, you will learn the following : How to find the
More informationChapter #4 EEE8013. Linear Controller Design and State Space Analysis. Design of control system in state space using Matlab
EEE83 hapter #4 EEE83 Linear ontroller Deign and State Space nalyi Deign of control ytem in tate pace uing Matlab. ontrollabilty and Obervability.... State Feedback ontrol... 5 3. Linear Quadratic Regulator
More informationHomework #7 Solution. Solutions: ΔP L Δω. Fig. 1
Homework #7 Solution Aignment:. through.6 Bergen & Vittal. M Solution: Modified Equation.6 becaue gen. peed not fed back * M (.0rad / MW ec)(00mw) rad /ec peed ( ) (60) 9.55r. p. m. 3600 ( 9.55) 3590.45r.
More informationEE Control Systems LECTURE 14
Updated: Tueday, March 3, 999 EE 434 - Control Sytem LECTURE 4 Copyright FL Lewi 999 All right reerved ROOT LOCUS DESIGN TECHNIQUE Suppoe the cloed-loop tranfer function depend on a deign parameter k We
More informationMAE140 Linear Circuits Fall 2012 Final, December 13th
MAE40 Linear Circuit Fall 202 Final, December 3th Intruction. Thi exam i open book. You may ue whatever written material you chooe, including your cla note and textbook. You may ue a hand calculator with
More informationNCAAPMT Calculus Challenge Challenge #3 Due: October 26, 2011
NCAAPMT Calculu Challenge 011 01 Challenge #3 Due: October 6, 011 A Model of Traffic Flow Everyone ha at ome time been on a multi-lane highway and encountered road contruction that required the traffic
More information1 Routh Array: 15 points
EE C28 / ME34 Problem Set 3 Solution Fall 2 Routh Array: 5 point Conider the ytem below, with D() k(+), w(t), G() +2, and H y() 2 ++2 2(+). Find the cloed loop tranfer function Y () R(), and range of k
More informationμ + = σ = D 4 σ = D 3 σ = σ = All units in parts (a) and (b) are in V. (1) x chart: Center = μ = 0.75 UCL =
Our online Tutor are available 4*7 to provide Help with Proce control ytem Homework/Aignment or a long term Graduate/Undergraduate Proce control ytem Project. Our Tutor being experienced and proficient
More informationWeek 3 Statistics for bioinformatics and escience
Week 3 Statitic for bioinformatic and escience Line Skotte 28. november 2008 2.9.3-4) In thi eercie we conider microrna data from Human and Moue. The data et repreent 685 independent realiation of the
More information5.5 Sampling. The Connection Between: Continuous Time & Discrete Time
5.5 Sampling he Connection Between: Continuou ime & Dicrete ime Warning: I don t really like how the book cover thi! It i not that it i wrong it jut ail to make the correct connection between the mathematic
More informationLinearteam tech paper. The analysis of fourth-order state variable filter and it s application to Linkwitz- Riley filters
Linearteam tech paper The analyi of fourth-order tate variable filter and it application to Linkwitz- iley filter Janne honen 5.. TBLE OF CONTENTS. NTOCTON.... FOTH-OE LNWTZ-LEY (L TNSFE FNCTON.... TNSFE
More informationEECE 301 Signals & Systems Prof. Mark Fowler
EECE 31 Signal & Syem Prof. Mark Fowler Noe Se #27 C-T Syem: Laplace Tranform Power Tool for yem analyi Reading Aignmen: Secion 6.1 6.3 of Kamen and Heck 1/18 Coure Flow Diagram The arrow here how concepual
More informationSolutions to homework #10
Solution to homework #0 Problem 7..3 Compute 6 e 3 t t t 8. The firt tep i to ue the linearity of the Laplace tranform to ditribute the tranform over the um and pull the contant factor outide the tranform.
More informationEE 508 Lecture 16. Filter Transformations. Lowpass to Bandpass Lowpass to Highpass Lowpass to Band-reject
EE 508 Lecture 6 Filter Tranformation Lowpa to Bandpa Lowpa to Highpa Lowpa to Band-reject Review from Lat Time Theorem: If the perimeter variation and contact reitance are neglected, the tandard deviation
More informationLecture 17: Analytic Functions and Integrals (See Chapter 14 in Boas)
Lecture 7: Analytic Function and Integral (See Chapter 4 in Boa) Thi i a good point to take a brief detour and expand on our previou dicuion of complex variable and complex function of complex variable.
More informationQ.1 to Q.30 carry one mark each
1 Q.1 to Q. carry one mark each Q.1 Conider the network graph hown in figure below. Which one of the following i NOT a tree of thi graph? Q. The equivalent inductance meaured between the terminal 1 and
More information9 Lorentz Invariant phase-space
9 Lorentz Invariant phae-space 9. Cro-ection The cattering amplitude M q,q 2,out p, p 2,in i the amplitude for a tate p, p 2 to make a tranition into the tate q,q 2. The tranition probability i the quare
More informationFourier Series And Transforms
Chapter Fourier Serie And ranform. Fourier Serie A function that i defined and quare-integrable over an interval, [,], and i then periodically extended over the entire real line can be expreed a an infinite
More informationFourier Transforms of Functions on the Continuous Domain
Chapter Fourier Tranform of Function on the Continuou Domain. Introduction The baic concept of pectral analyi through Fourier tranform typically are developed for function on a one-dimenional domain where
More informationLecture 8: Period Finding: Simon s Problem over Z N
Quantum Computation (CMU 8-859BB, Fall 205) Lecture 8: Period Finding: Simon Problem over Z October 5, 205 Lecturer: John Wright Scribe: icola Rech Problem A mentioned previouly, period finding i a rephraing
More informationMODERN CONTROL SYSTEMS
MODERN CONTROL SYSTEMS Lecture 1 Root Locu Emam Fathy Department of Electrical and Control Engineering email: emfmz@aat.edu http://www.aat.edu/cv.php?dip_unit=346&er=68525 1 Introduction What i root locu?
More informationR. W. Erickson. Department of Electrical, Computer, and Energy Engineering University of Colorado, Boulder
R. W. Erickon Department of Electrical, Computer, and Energy Engineering Univerity of Colorado, Boulder ZOH: Sampled Data Sytem Example v T Sampler v* H Zero-order hold H v o e = 1 T 1 v *( ) = v( jkω
More informationRoot Locus Contents. Root locus, sketching algorithm. Root locus, examples. Root locus, proofs. Root locus, control examples
Root Locu Content Root locu, ketching algorithm Root locu, example Root locu, proof Root locu, control example Root locu, influence of zero and pole Root locu, lead lag controller deign 9 Spring ME45 -
More informationPhysics 218: Exam 1. Class of 2:20pm. February 14th, You have the full class period to complete the exam.
Phyic 218: Exam 1 Cla of 2:20pm February 14th, 2012. Rule of the exam: 1. You have the full cla period to complete the exam. 2. Formulae are provided on the lat page. You may NOT ue any other formula heet.
More informationSource slideplayer.com/fundamentals of Analytical Chemistry, F.J. Holler, S.R.Crouch. Chapter 6: Random Errors in Chemical Analysis
Source lideplayer.com/fundamental of Analytical Chemitry, F.J. Holler, S.R.Crouch Chapter 6: Random Error in Chemical Analyi Random error are preent in every meaurement no matter how careful the experimenter.
More informationAn estimation approach for autotuning of event-based PI control systems
Acta de la XXXIX Jornada de Automática, Badajoz, 5-7 de Septiembre de 08 An etimation approach for autotuning of event-baed PI control ytem Joé Sánchez Moreno, María Guinaldo Loada, Sebatián Dormido Departamento
More informationCumulative Review of Calculus
Cumulative Review of Calculu. Uing the limit definition of the lope of a tangent, determine the lope of the tangent to each curve at the given point. a. f 5,, 5 f,, f, f 5,,,. The poition, in metre, of
More informationA Simple Approach to Synthesizing Naïve Quantized Control for Reference Tracking
A Simple Approach to Syntheizing Naïve Quantized Control for Reference Tracking SHIANG-HUA YU Department of Electrical Engineering National Sun Yat-Sen Univerity 70 Lien-Hai Road, Kaohiung 804 TAIAN Abtract:
More information0 of the same magnitude. If we don t use an OA and ignore any damping, the CTF is
1 4. Image Simulation Influence of C Spherical aberration break the ymmetry that would otherwie exit between overfocu and underfocu. One reult i that the fringe in the FT of the CTF are generally farther
More informationSuggested Answers To Exercises. estimates variability in a sampling distribution of random means. About 68% of means fall
Beyond Significance Teting ( nd Edition), Rex B. Kline Suggeted Anwer To Exercie Chapter. The tatitic meaure variability among core at the cae level. In a normal ditribution, about 68% of the core fall
More informationLecture 2: The z-transform
5-59- Control Sytem II FS 28 Lecture 2: The -Tranform From the Laplace Tranform to the tranform The Laplace tranform i an integral tranform which take a function of a real variable t to a function of a
More informationNAME (pinyin/italian)... MATRICULATION NUMBER... SIGNATURE
POLITONG SHANGHAI BASIC AUTOMATIC CONTROL June Academic Year / Exam grade NAME (pinyin/italian)... MATRICULATION NUMBER... SIGNATURE Ue only thee page (including the bac) for anwer. Do not ue additional
More informationCHAPTER 8 OBSERVER BASED REDUCED ORDER CONTROLLER DESIGN FOR LARGE SCALE LINEAR DISCRETE-TIME CONTROL SYSTEMS
CHAPTER 8 OBSERVER BASED REDUCED ORDER CONTROLLER DESIGN FOR LARGE SCALE LINEAR DISCRETE-TIME CONTROL SYSTEMS 8.1 INTRODUCTION 8.2 REDUCED ORDER MODEL DESIGN FOR LINEAR DISCRETE-TIME CONTROL SYSTEMS 8.3
More informationThermal Σ- Modulator: Anemometer Performance Analysis
Intrumentation and Meaurement Technology Conference IMTC 007 Waraw, Poland, May 1-3, 007 Thermal Σ- Modulator: Anemometer Performance Analyi Will R. M. Almeida 1, Georgina M. Freita 1, Lígia S. Palma 3,
More informationSocial Studies 201 Notes for March 18, 2005
1 Social Studie 201 Note for March 18, 2005 Etimation of a mean, mall ample ize Section 8.4, p. 501. When a reearcher ha only a mall ample ize available, the central limit theorem doe not apply to the
More informationHomework 12 Solution - AME30315, Spring 2013
Homework 2 Solution - AME335, Spring 23 Problem :[2 pt] The Aerotech AGS 5 i a linear motor driven XY poitioning ytem (ee attached product heet). A friend of mine, through careful experimentation, identified
More informationMedical Imaging. Transmission Measurement
Medical Imaging Image Recontruction from Projection Prof Ed X. Wu Tranmiion Meaurement ( meaurable unknown attenuation, aborption cro-ection hadowgram ) I(ϕ,ξ) µ(x,) I = I o exp A(x, )dl L X-ra ource X-Ra
More information