EECS 206 Solutions to Midterm Exam 2 July 12, Problems 1 to 10 are multiple-choice. Each has 7 points. No partial credit will be given.
|
|
- Lynette Harrington
- 7 years ago
- Views:
Transcription
1 EECS 06 Solutions to Midterm Exam July, 00 Instructions: Answer on this questionnaire Print your name Sign the pledge below Closed book and notes One 8 / x sheet of paper allowed Calculators allowed Read the questions carefully. Problems to 0 are multiple-choice. Each has 7 points. No partial credit will be given. In Problems and, partial credit will be given. You must show your derivations/calculations to get full credit. Name: PLEDGE: I have neither given nor received any aid on this exam, nor have I concealed any violations of the Honor Code. SIGNATURE: DO NOT TURN THIS PAGE OVER UNTIL TOLD TO DO SO! Good Luck!
2 Mark your answers for Problems ( (0 ( (a (b (c (d (e ( (a (b (c (d (e (3 (a (b (c (d (e ( (a (b (c (d (e (5 (a (b (c (d (e (6 (a (b (c (d (e (7 (a (b (c (d (e (8 (a (b (c (d (e (9 (a (b (c (d (e (0 (a (b (c (d (e Subtotal ( ( Total
3 ( The fundamental period of the following discrete-time signal is (a 8 (b (c 8 (d (e None of the above Answer: (e cos( π n cos(3π 7 n The signal consists of two sinusoids. The component signals are periodic: Let N and N denote their respective periods (they ust be positive integers. π N = πm, 3π 7 N = πl, where m and l are positive integers. This implies that Since N and N are positive integers, N = 8m, N = l/3. N = 8, 6,..., N =, 8,.... Therefore, common multiples of 8 and will be periods of the given signal: 56,,.... ( A real discrete-time signal x[n] is periodic with the fundamental period 8 and some of its 8-point DFT coefficients are given below. X 0 = 0, X =, X = j, X 3 = + j. Then X 6 is (a 0 (b (c + j (d j (e Not enough information is given Answer: (c A real signal has the complex conjugate property: X N k = X k. Then X 6 = X 8 = X = + j. (3 A real discrete-time signal x[n] is periodic with the fundamental period n 3
4 Let X k be the DFT coefficients of the 8-point DFT of x[n]. Then the value of (a (b (c (d (e None of the above Answer: (b Parseval s theorem states that Note that for the given signal Therefore, By evaluation, we get x[n] = n=0 7 x[n] = n=0 X 0 = X k. k=0 7 x[n] = 0. k=0 7 X k = X 0 + }{{} 0 k=0 7 x[n] =. n=0 7 X k. k= 7 X k equals k= ( The signal 0 cos ( π5t + π, when sampled at f s = 0 samples/sec, will alias to (a 0 cos ( π5t π (b 0 cos ( π5t + π (c 0 cos ( π5t π (d 0 cos ( π5t + π (e None of the above Answer: (b Aliases of 0 cos ( π5t + π 0 cos ( π(5 + f s lt + π or 0 cos ( π(f s m 5t π, where l and m are integers. Among these candidates the answer is the one with frequency less than half the sampling frequency, f s / = 0. Therefore, from the following candidates, l =, 0,,... = f = 5, 5, 5,..., m =, 3,,... = f = 5, 35, 55,.... the frequncy that is less than f s / = 0 is obtained when l = and the corresponding signal is 0 cos ( π5t + π.
5 (5 The ideal interpolation of cos( π n cos(7π n 0. using the sampling period T s = /f s = 0.0 will produce (a cos( π 00t cos( 7π 00t 0. (b cos( π 00t + 0. cos( 7π 00t + 0. (c cos( π 00t + 0. (d cos( π 00t 0. (e None of the above Answer: (c We note that if 0 ˆω < π. Since the second term of the given signal the given signal is, in effect, cos(ˆωn + φ = cos(ˆωf s t + φ cos( 7π n 0. = cos((7π πn 0. = cos( π n 0. = cos(π n + 0., Therefore, the ideal reconstruction will be cos( π n cos(7π n 0. = cos(π n cos( π n + 0. = cos(π 00t (6 The system whose input/output relationship is given by is y[n] = n x[n] x[n] y[n] n (a (b (c (d (e linear and time-invariant nonlinear and time-invariant linear and time-varying noninear and time-varying Not enough information is given Answer: (c The system is linear and time-varying. 5
6 (i Linearity T {αx [n] + βx [n]} = n ( αx [n] + βx [n] = αnx [n] + βn x [n] = αt {x [n]} + βt {x [n]}. (ii Time-varying (7 The condition for the system to be linear and time-invariant is (a ABC 0. (b A = B = 0 and C 0. (c A 0 and B = C = 0. (d C = 0. (e A = C = 0. Answer: (e T {x[n n 0 ]} = n x[n n 0 ] (n n 0 x[n n 0 ] = y[n n 0 ]. y[n] = Ax [n] + Bx[n 3] + C A must be zero, because otherwise the system will create a cross term, making it nonliner. Also C must be zero, because a nonzero constant term violate linearity. (8 The convolution of the following two signals x[n] = ( nu[n] and y[n] = u[n] x[n] y[n] n n is given by, for n 0, (a ( n (b + ( n (c ( n+ (d + ( n+ (e None of the above Answer: (a 6
7 x[n] y[n] = = = n k=0 x[k]y[n k] ( k u[k] }{{} =,k 0 ( k n 0 = (/n+ / (9 An LTI filter is described by the following difference equation: Which of the following statements is incorrect? u[n k] }{{} =,n k = ( n. y[n] = x[n + ] + x[n] + x[n ]. (a Its order is 3. (b It is noncausal. (c Its impulse response h[n] is given by h[n] = δ[n + ] + δ[n] + δ[n ]. (d y[n] is periodic whenever x[n] is periodic. (e y[n] is sinusoidal whenever x[n] is sinusoidal. Answer: (a The order is. (0 The overall impulse response h[n] of the following two cascaded LTI filters x[n] Unit Delay + h [n] = δ[n] + δ[n ] +... y[n] is (a δ[n] δ[n ]. (b δ[n] + δ[n ]. (c δ[n] δ[n ]. (d (δ[n] (δ[n ]. (e None of the above. Answer: (c (Also (d is acceptable. 7
8 Two LI filters are cascaded. So, h[n] = h [n] h [n] = (δ[n] δ[n ] (δ[n] + δ[n ] = δ[n] δ[n ]. Choice (d happens to give the same answer: in general δ[n k] = (δ[n k] m, for m =,,.... ( (5 points The following continuous-time signal is to be sampled and reconstructed. x(t = cos ( π0t + π ( π ( + cos π0t + + cos π60t. Let the sampling frequency f s = 00 samples/sec and x[n] = x(nt s = x(n/f s. (a Plot the double-sided spectrum of x(t as a functon of f Hz. x(t = cos ( π0t + π ( π ( + cos π0t + + cos π60t = e j π e jπ0t + e j π e jπ0t + e j π e jπ0t + e j π e jπ0t + e jπ60t + e jπ60t. e jπ/ e jπ/ e jπ/ e jπ/ f (b Determine whether x(t can be perfectly reconstructed from x[n] using the ideal interpolation. Justify your answer. No, because aliasing occurs due to the fact that f s = 00 < f max = 60 = 0. (c Find and simplify the reconstruction x(t from x[n] using the ideal interpolation. When sampled at f s = 00 (T s = 0.0, we get x[n] = cos ( π0 0.0n + π ( π ( + cos π0 0.0n + + cos π60 0.0n = cos ( 0.πn + π ( π ( + cos 0.8πn + + cos.πn }{{} = cos ( 0.8πn = cos ( 0.πn + π ( π ( + cos 0.8πn + + cos 0.8πn } {{} combine these = cos ( 0.πn + π +.7 cos ( 0.8πn Note that each of frequencies in the last expression is less than π. reconstruct x(t = cos ( 0.π00t + π +.7 cos ( 0.8π00t = cos ( π0t + π +.7 cos ( π0t This reconstructed waveform differs from x(t due to undersampling and hence aliasing. Then the ideal interpolation will 8
9 ( (0 points Answer for the LTI filter whose input/output relationship is given by y[n] = 3x[n] + x[n ] + x[n ]. (a Find and plot the impulse response h[n]. h[n] = 3δ[n] + δ[n ] + δ[n ] n (b Draw the block diagram implementation in the direct form. x[n] Unit Delay Unit Delay y[n] (c Find the response of the filter to input x[n] = e j( π n 0. and simplify it. y[n] = h[k]x[n k] = h[k]e j0. e j π (n k = e j0. e j π n h[k]e j π k = e j0. e j π n( 3 + e j π + e j π = e j0. e j π n 5.033e j = 5.033e j( π n
UNIVERSITY OF CALIFORNIA, SAN DIEGO Electrical & Computer Engineering Department ECE 101 - Fall 2009 Linear Systems Fundamentals
UNIVERSITY OF CALIFORNIA, SAN DIEGO Electrical & Computer Engineering Department ECE 101 - Fall 2009 Linear Systems Fundamentals MIDTERM EXAM You are allowed one 2-sided sheet of notes. No books, no other
More information3 Signals and Systems: Part II
3 Signals and Systems: Part II Recommended Problems P3.1 Sketch each of the following signals. (a) x[n] = b[n] + 3[n - 3] (b) x[n] = u[n] - u[n - 5] (c) x[n] = 6[n] + 1n + (i)2 [n - 2] + (i)ag[n - 3] (d)
More informationUNIVERSITY OF CALIFORNIA, SAN DIEGO Electrical & Computer Engineering Department ECE 101 - Fall 2010 Linear Systems Fundamentals
UNIVERSITY OF CALIFORNIA, SAN DIEGO Electrical & Computer Engineering Department ECE 101 - Fall 2010 Linear Systems Fundamentals FINAL EXAM WITH SOLUTIONS (YOURS!) You are allowed one 2-sided sheet of
More informationSGN-1158 Introduction to Signal Processing Test. Solutions
SGN-1158 Introduction to Signal Processing Test. Solutions 1. Convolve the function ( ) with itself and show that the Fourier transform of the result is the square of the Fourier transform of ( ). (Hints:
More informationFrequency Response of FIR Filters
Frequency Response of FIR Filters Chapter 6 This chapter continues the study of FIR filters from Chapter 5, but the emphasis is frequency response, which relates to how the filter responds to an input
More informationDiscrete-Time Signals and Systems
2 Discrete-Time Signals and Systems 2.0 INTRODUCTION The term signal is generally applied to something that conveys information. Signals may, for example, convey information about the state or behavior
More informationClass Note for Signals and Systems. Stanley Chan University of California, San Diego
Class Note for Signals and Systems Stanley Chan University of California, San Diego 2 Acknowledgement This class note is prepared for ECE 101: Linear Systems Fundamentals at the University of California,
More informationThe Z transform (3) 1
The Z transform (3) 1 Today Analysis of stability and causality of LTI systems in the Z domain The inverse Z Transform Section 3.3 (read class notes first) Examples 3.9, 3.11 Properties of the Z Transform
More informationSampling and Interpolation. Yao Wang Polytechnic University, Brooklyn, NY11201
Sampling and Interpolation Yao Wang Polytechnic University, Brooklyn, NY1121 http://eeweb.poly.edu/~yao Outline Basics of sampling and quantization A/D and D/A converters Sampling Nyquist sampling theorem
More information1.1 Discrete-Time Fourier Transform
1.1 Discrete-Time Fourier Transform The discrete-time Fourier transform has essentially the same properties as the continuous-time Fourier transform, and these properties play parallel roles in continuous
More informationTTT4120 Digital Signal Processing Suggested Solution to Exam Fall 2008
Norwegian University of Science and Technology Department of Electronics and Telecommunications TTT40 Digital Signal Processing Suggested Solution to Exam Fall 008 Problem (a) The input and the input-output
More informationSAMPLE SOLUTIONS DIGITAL SIGNAL PROCESSING: Signals, Systems, and Filters Andreas Antoniou
SAMPLE SOLUTIONS DIGITAL SIGNAL PROCESSING: Signals, Systems, and Filters Andreas Antoniou (Revision date: February 7, 7) SA. A periodic signal can be represented by the equation x(t) k A k sin(ω k t +
More information(Refer Slide Time: 01:11-01:27)
Digital Signal Processing Prof. S. C. Dutta Roy Department of Electrical Engineering Indian Institute of Technology, Delhi Lecture - 6 Digital systems (contd.); inverse systems, stability, FIR and IIR,
More information6 Systems Represented by Differential and Difference Equations
6 Systems Represented by ifferential and ifference Equations An important class of linear, time-invariant systems consists of systems represented by linear constant-coefficient differential equations in
More informationAnalysis/resynthesis with the short time Fourier transform
Analysis/resynthesis with the short time Fourier transform summer 2006 lecture on analysis, modeling and transformation of audio signals Axel Röbel Institute of communication science TU-Berlin IRCAM Analysis/Synthesis
More informationT = 10-' s. p(t)= ( (t-nt), T= 3. n=-oo. Figure P16.2
16 Sampling Recommended Problems P16.1 The sequence x[n] = (-1)' is obtained by sampling the continuous-time sinusoidal signal x(t) = cos oot at 1-ms intervals, i.e., cos(oont) = (-1)", Determine three
More informationDigital Transmission of Analog Data: PCM and Delta Modulation
Digital Transmission of Analog Data: PCM and Delta Modulation Required reading: Garcia 3.3.2 and 3.3.3 CSE 323, Fall 200 Instructor: N. Vlajic Digital Transmission of Analog Data 2 Digitization process
More informationLecture 8 ELE 301: Signals and Systems
Lecture 8 ELE 3: Signals and Systems Prof. Paul Cuff Princeton University Fall 2-2 Cuff (Lecture 7) ELE 3: Signals and Systems Fall 2-2 / 37 Properties of the Fourier Transform Properties of the Fourier
More informationChapter 8 - Power Density Spectrum
EE385 Class Notes 8/8/03 John Stensby Chapter 8 - Power Density Spectrum Let X(t) be a WSS random process. X(t) has an average power, given in watts, of E[X(t) ], a constant. his total average power is
More information10 Discrete-Time Fourier Series
10 Discrete-Time Fourier Series In this and the next lecture we parallel for discrete time the discussion of the last three lectures for continuous time. Specifically, we consider the representation of
More informationmin ǫ = E{e 2 [n]}. (11.2)
C H A P T E R 11 Wiener Filtering INTRODUCTION In this chapter we will consider the use of LTI systems in order to perform minimum mean-square-error (MMSE) estimation of a WSS random process of interest,
More informationPYKC Jan-7-10. Lecture 1 Slide 1
Aims and Objectives E 2.5 Signals & Linear Systems Peter Cheung Department of Electrical & Electronic Engineering Imperial College London! By the end of the course, you would have understood: Basic signal
More informationHow To Understand The Nyquist Sampling Theorem
Nyquist Sampling Theorem By: Arnold Evia Table of Contents What is the Nyquist Sampling Theorem? Bandwidth Sampling Impulse Response Train Fourier Transform of Impulse Response Train Sampling in the Fourier
More informationchapter Introduction to Digital Signal Processing and Digital Filtering 1.1 Introduction 1.2 Historical Perspective
Introduction to Digital Signal Processing and Digital Filtering chapter 1 Introduction to Digital Signal Processing and Digital Filtering 1.1 Introduction Digital signal processing (DSP) refers to anything
More informationDigital Signal Processing IIR Filter Design via Impulse Invariance
Digital Signal Processing IIR Filter Design via Impulse Invariance D. Richard Brown III D. Richard Brown III 1 / 11 Basic Procedure We assume here that we ve already decided to use an IIR filter. The basic
More information1.4 Fast Fourier Transform (FFT) Algorithm
74 CHAPTER AALYSIS OF DISCRETE-TIME LIEAR TIME-IVARIAT SYSTEMS 4 Fast Fourier Transform (FFT Algorithm Fast Fourier Transform, or FFT, is any algorithm for computing the -point DFT with a computational
More informationSan José State University Department of Electrical Engineering EE 112, Linear Systems, Spring 2010
San José State University Department of Electrical Engineering EE 112, Linear Systems, Spring 2010 Instructor: Robert H. Morelos-Zaragoza Office Location: ENGR 373 Telephone: (408) 924-3879 Email: robert.morelos-zaragoza@sjsu.edu
More information9 Fourier Transform Properties
9 Fourier Transform Properties The Fourier transform is a major cornerstone in the analysis and representation of signals and linear, time-invariant systems, and its elegance and importance cannot be overemphasized.
More informationCourse overview Processamento de sinais 2009/10 LEA
Course overview Processamento de sinais 2009/10 LEA João Pedro Gomes jpg@isr.ist.utl.pt Instituto Superior Técnico Processamento de sinais MEAer (IST) Course overview 1 / 19 Course overview Motivation:
More informationSignals and Systems. Richard Baraniuk NONRETURNABLE NO REFUNDS, EXCHANGES, OR CREDIT ON ANY COURSE PACKETS
Signals and Systems Richard Baraniuk NONRETURNABLE NO REFUNDS, EXCHANGES, OR CREDIT ON ANY COURSE PACKETS Signals and Systems Course Authors: Richard Baraniuk Contributing Authors: Thanos Antoulas Richard
More informationTCOM 370 NOTES 99-4 BANDWIDTH, FREQUENCY RESPONSE, AND CAPACITY OF COMMUNICATION LINKS
TCOM 370 NOTES 99-4 BANDWIDTH, FREQUENCY RESPONSE, AND CAPACITY OF COMMUNICATION LINKS 1. Bandwidth: The bandwidth of a communication link, or in general any system, was loosely defined as the width of
More informationLecture 18: The Time-Bandwidth Product
WAVELETS AND MULTIRATE DIGITAL SIGNAL PROCESSING Lecture 18: The Time-Bandwih Product Prof.Prof.V.M.Gadre, EE, IIT Bombay 1 Introduction In this lecture, our aim is to define the time Bandwih Product,
More informationTime Series Analysis: Introduction to Signal Processing Concepts. Liam Kilmartin Discipline of Electrical & Electronic Engineering, NUI, Galway
Time Series Analysis: Introduction to Signal Processing Concepts Liam Kilmartin Discipline of Electrical & Electronic Engineering, NUI, Galway Aims of Course To introduce some of the basic concepts of
More informationReview of Fourier series formulas. Representation of nonperiodic functions. ECE 3640 Lecture 5 Fourier Transforms and their properties
ECE 3640 Lecture 5 Fourier Transforms and their properties Objective: To learn about Fourier transforms, which are a representation of nonperiodic functions in terms of trigonometric functions. Also, to
More informationMAT 200, Midterm Exam Solution. a. (5 points) Compute the determinant of the matrix A =
MAT 200, Midterm Exam Solution. (0 points total) a. (5 points) Compute the determinant of the matrix 2 2 0 A = 0 3 0 3 0 Answer: det A = 3. The most efficient way is to develop the determinant along the
More informationAutomatic Detection of Emergency Vehicles for Hearing Impaired Drivers
Automatic Detection of Emergency Vehicles for Hearing Impaired Drivers Sung-won ark and Jose Trevino Texas A&M University-Kingsville, EE/CS Department, MSC 92, Kingsville, TX 78363 TEL (36) 593-2638, FAX
More informationLinear Equations and Inequalities
Linear Equations and Inequalities Section 1.1 Prof. Wodarz Math 109 - Fall 2008 Contents 1 Linear Equations 2 1.1 Standard Form of a Linear Equation................ 2 1.2 Solving Linear Equations......................
More information4F7 Adaptive Filters (and Spectrum Estimation) Least Mean Square (LMS) Algorithm Sumeetpal Singh Engineering Department Email : sss40@eng.cam.ac.
4F7 Adaptive Filters (and Spectrum Estimation) Least Mean Square (LMS) Algorithm Sumeetpal Singh Engineering Department Email : sss40@eng.cam.ac.uk 1 1 Outline The LMS algorithm Overview of LMS issues
More informationSection 1.1 Linear Equations: Slope and Equations of Lines
Section. Linear Equations: Slope and Equations of Lines Slope The measure of the steepness of a line is called the slope of the line. It is the amount of change in y, the rise, divided by the amount of
More informationMarch 29, 2011. 171S4.4 Theorems about Zeros of Polynomial Functions
MAT 171 Precalculus Algebra Dr. Claude Moore Cape Fear Community College CHAPTER 4: Polynomial and Rational Functions 4.1 Polynomial Functions and Models 4.2 Graphing Polynomial Functions 4.3 Polynomial
More informationPower Spectral Density
C H A P E R 0 Power Spectral Density INRODUCION Understanding how the strength of a signal is distributed in the frequency domain, relative to the strengths of other ambient signals, is central to the
More informationModulation and Demodulation
MIT 6.02 DRAFT Lecture Notes Last update: April 11, 2012 Comments, questions or bug reports? Please contact {hari, verghese} at mit.edu CHAPTER 14 Modulation and Demodulation This chapter describes the
More informationAdding Sinusoids of the Same Frequency. Additive Synthesis. Spectrum. Music 270a: Modulation
Adding Sinusoids of the Same Frequency Music 7a: Modulation Tamara Smyth, trsmyth@ucsd.edu Department of Music, University of California, San Diego (UCSD) February 9, 5 Recall, that adding sinusoids of
More informationSignal Detection C H A P T E R 14 14.1 SIGNAL DETECTION AS HYPOTHESIS TESTING
C H A P T E R 4 Signal Detection 4. SIGNAL DETECTION AS HYPOTHESIS TESTING In Chapter 3 we considered hypothesis testing in the context of random variables. The detector resulting in the minimum probability
More informationTTT4110 Information and Signal Theory Solution to exam
Norwegian University of Science and Technology Department of Electronics and Telecommunications TTT4 Information and Signal Theory Solution to exam Problem I (a The frequency response is found by taking
More informationDesign of FIR Filters
Design of FIR Filters Elena Punskaya www-sigproc.eng.cam.ac.uk/~op205 Some material adapted from courses by Prof. Simon Godsill, Dr. Arnaud Doucet, Dr. Malcolm Macleod and Prof. Peter Rayner 68 FIR as
More information2 Signals and Systems: Part I
2 Signals and Systems: Part I In this lecture, we consider a number of basic signals that will be important building blocks later in the course. Specifically, we discuss both continuoustime and discrete-time
More informationZeros of a Polynomial Function
Zeros of a Polynomial Function An important consequence of the Factor Theorem is that finding the zeros of a polynomial is really the same thing as factoring it into linear factors. In this section we
More informationLuigi Piroddi Active Noise Control course notes (January 2015)
Active Noise Control course notes (January 2015) 9. On-line secondary path modeling techniques Luigi Piroddi piroddi@elet.polimi.it Introduction In the feedforward ANC scheme the primary noise is canceled
More informationThe continuous and discrete Fourier transforms
FYSA21 Mathematical Tools in Science The continuous and discrete Fourier transforms Lennart Lindegren Lund Observatory (Department of Astronomy, Lund University) 1 The continuous Fourier transform 1.1
More informationALGEBRA 2/TRIGONOMETRY
ALGEBRA /TRIGONOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION ALGEBRA /TRIGONOMETRY Tuesday, June 1, 011 1:15 to 4:15 p.m., only Student Name: School Name: Print your name
More information4ECE 320 Signals and Systems II Department of Electrical and Computer Engineering George Mason University Fall, 2015
ECE 320 1 Fall, 2015 4ECE 320 Signals and Systems II Department of Electrical and Computer Engineering George Mason University Fall, 2015 Class Meeting Information Day and Time: Tuesday and Thursday, 4:30
More informationProbability and Random Variables. Generation of random variables (r.v.)
Probability and Random Variables Method for generating random variables with a specified probability distribution function. Gaussian And Markov Processes Characterization of Stationary Random Process Linearly
More informationArithmetic and Algebra of Matrices
Arithmetic and Algebra of Matrices Math 572: Algebra for Middle School Teachers The University of Montana 1 The Real Numbers 2 Classroom Connection: Systems of Linear Equations 3 Rational Numbers 4 Irrational
More informationThroughout this text we will be considering various classes of signals and systems, developing models for them and studying their properties.
C H A P T E R 2 Signals and Systems This text assumes a basic background in the representation of linear, time-invariant systems and the associated continuous-time and discrete-time signals, through convolution,
More informationIntroduction to the Z-transform
ECE 3640 Lecture 2 Z Transforms Objective: Z-transforms are to difference equations what Laplace transforms are to differential equations. In this lecture we are introduced to Z-transforms, their inverses,
More informationTime series analysis Matlab tutorial. Joachim Gross
Time series analysis Matlab tutorial Joachim Gross Outline Terminology Sampling theorem Plotting Baseline correction Detrending Smoothing Filtering Decimation Remarks Focus on practical aspects, exercises,
More informationSYSTEMS AND SIGNALS ONLINE QUESTIONS AND GRADING
In proceedings of ETFA 2005, the 10th IEEE International Conference on Emerging Technologies and Factory Automation Catania, Italy, 19-22 September 2005, pp. 41-47 SYSTEMS AND SIGNALS ONLINE QUESTIONS
More informationSECTION 0.6: POLYNOMIAL, RATIONAL, AND ALGEBRAIC EXPRESSIONS
(Section 0.6: Polynomial, Rational, and Algebraic Expressions) 0.6.1 SECTION 0.6: POLYNOMIAL, RATIONAL, AND ALGEBRAIC EXPRESSIONS LEARNING OBJECTIVES Be able to identify polynomial, rational, and algebraic
More information2.2/2.3 - Solving Systems of Linear Equations
c Kathryn Bollinger, August 28, 2011 1 2.2/2.3 - Solving Systems of Linear Equations A Brief Introduction to Matrices Matrices are used to organize data efficiently and will help us to solve systems of
More informationSECTION 6 DIGITAL FILTERS
SECTION 6 DIGITAL FILTERS Finite Impulse Response (FIR) Filters Infinite Impulse Response (IIR) Filters Multirate Filters Adaptive Filters 6.a 6.b SECTION 6 DIGITAL FILTERS Walt Kester INTRODUCTION Digital
More informationThe Fourier Analysis Tool in Microsoft Excel
The Fourier Analysis Tool in Microsoft Excel Douglas A. Kerr Issue March 4, 2009 ABSTRACT AD ITRODUCTIO The spreadsheet application Microsoft Excel includes a tool that will calculate the discrete Fourier
More informationECE 5520: Digital Communications Lecture Notes Fall 2009
ECE 5520: Digital Communications Lecture Notes Fall 2009 Dr. Neal Patwari University of Utah Department of Electrical and Computer Engineering c 2006 ECE 5520 Fall 2009 2 Contents 1 Class Organization
More information1.3 LINEAR EQUATIONS IN TWO VARIABLES. Copyright Cengage Learning. All rights reserved.
1.3 LINEAR EQUATIONS IN TWO VARIABLES Copyright Cengage Learning. All rights reserved. What You Should Learn Use slope to graph linear equations in two variables. Find the slope of a line given two points
More informationFinal Year Project Progress Report. Frequency-Domain Adaptive Filtering. Myles Friel. Supervisor: Dr.Edward Jones
Final Year Project Progress Report Frequency-Domain Adaptive Filtering Myles Friel 01510401 Supervisor: Dr.Edward Jones Abstract The Final Year Project is an important part of the final year of the Electronic
More informationFFT Algorithms. Chapter 6. Contents 6.1
Chapter 6 FFT Algorithms Contents Efficient computation of the DFT............................................ 6.2 Applications of FFT................................................... 6.6 Computing DFT
More informationAngle Modulation, II. Lecture topics FM bandwidth and Carson s rule. Spectral analysis of FM. Narrowband FM Modulation. Wideband FM Modulation
Angle Modulation, II EE 179, Lecture 12, Handout #19 Lecture topics FM bandwidth and Carson s rule Spectral analysis of FM Narrowband FM Modulation Wideband FM Modulation EE 179, April 25, 2014 Lecture
More information3.3. Solving Polynomial Equations. Introduction. Prerequisites. Learning Outcomes
Solving Polynomial Equations 3.3 Introduction Linear and quadratic equations, dealt within Sections 3.1 and 3.2, are members of a class of equations, called polynomial equations. These have the general
More informationEE 179 April 21, 2014 Digital and Analog Communication Systems Handout #16 Homework #2 Solutions
EE 79 April, 04 Digital and Analog Communication Systems Handout #6 Homework # Solutions. Operations on signals (Lathi& Ding.3-3). For the signal g(t) shown below, sketch: a. g(t 4); b. g(t/.5); c. g(t
More informationELECTRICAL ENGINEERING
EE ELECTRICAL ENGINEERING See beginning of Section H for abbreviations, course numbers and coding. The * denotes labs which are held on alternate weeks. A minimum grade of C is required for all prerequisite
More informationElectronic Communications Committee (ECC) within the European Conference of Postal and Telecommunications Administrations (CEPT)
Page 1 Electronic Communications Committee (ECC) within the European Conference of Postal and Telecommunications Administrations (CEPT) ECC RECOMMENDATION (06)01 Bandwidth measurements using FFT techniques
More informationUnderstanding CIC Compensation Filters
Understanding CIC Compensation Filters April 2007, ver. 1.0 Application Note 455 Introduction f The cascaded integrator-comb (CIC) filter is a class of hardware-efficient linear phase finite impulse response
More information3.5.1 CORRELATION MODELS FOR FREQUENCY SELECTIVE FADING
Environment Spread Flat Rural.5 µs Urban 5 µs Hilly 2 µs Mall.3 µs Indoors.1 µs able 3.1: ypical delay spreads for various environments. If W > 1 τ ds, then the fading is said to be frequency selective,
More informationEECS 556 Image Processing W 09. Interpolation. Interpolation techniques B splines
EECS 556 Image Processing W 09 Interpolation Interpolation techniques B splines What is image processing? Image processing is the application of 2D signal processing methods to images Image representation
More informationIntroduction to IQ-demodulation of RF-data
Introduction to IQ-demodulation of RF-data by Johan Kirkhorn, IFBT, NTNU September 15, 1999 Table of Contents 1 INTRODUCTION...3 1.1 Abstract...3 1.2 Definitions/Abbreviations/Nomenclature...3 1.3 Referenced
More informationMATHEMATICAL SURVEY AND APPLICATION OF THE CROSS-AMBIGUITY FUNCTION
MATHEMATICAL SURVEY AND APPLICATION OF THE CROSS-AMBIGUITY FUNCTION Dennis Vandenberg Department of Mathematical Sciences Indiana University South Bend E-mail Address: djvanden@iusb.edu Submitted to the
More informationBy choosing to view this document, you agree to all provisions of the copyright laws protecting it.
This material is posted here with permission of the IEEE Such permission of the IEEE does not in any way imply IEEE endorsement of any of Helsinki University of Technology's products or services Internal
More informationMotorola Digital Signal Processors
Motorola Digital Signal Processors Principles of Sigma-Delta Modulation for Analog-to- Digital Converters by Sangil Park, Ph. D. Strategic Applications Digital Signal Processor Operation MOTOROLA APR8
More information1 The Concept of a Mapping
Arkansas Tech University MATH 4033: Elementary Modern Algebra Dr. Marcel B. Finan 1 The Concept of a Mapping The concept of a mapping (aka function) is important throughout mathematics. We have been dealing
More informationSIGNAL PROCESSING & SIMULATION NEWSLETTER
1 of 10 1/25/2008 3:38 AM SIGNAL PROCESSING & SIMULATION NEWSLETTER Note: This is not a particularly interesting topic for anyone other than those who ar e involved in simulation. So if you have difficulty
More informationSimulation of Wireless Fading Channels
Blekinge Institute of Technology Research Report No 2003:02 Simulation of Wireless Fading Channels Ronnie Gustafsson Abbas Mohammed Department of Telecommunications and Signal Processing Blekinge Institute
More informationTables of Common Transform Pairs
ble of Common rnform Pir 0 by Mrc Ph. Stoecklin mrc toecklin.net http://www.toecklin.net/ 0--0 verion v.5.3 Engineer nd tudent in communiction nd mthemtic re confronted with tion uch the -rnform, the ourier,
More informationUnderstanding Digital Signal Processing. Third Edition
Understanding Digital Signal Processing Third Edition This page intentionally left blank Understanding Digital Signal Processing Third Edition Richard G. Lyons Upper Saddle River, NJ Boston Indianapolis
More informationConvolution. The Delta Function and Impulse Response
CHAPTER 6 Convolution Convolution is a mathematical way of combining two signals to form a third signal. It is the single most important technique in Digital Signal Processing. Using the strategy of impulse
More informationPaper Reference. Edexcel GCSE Mathematics (Linear) 1380 Paper 3 (Non-Calculator) Monday 6 June 2011 Afternoon Time: 1 hour 45 minutes
Centre No. Candidate No. Paper Reference 1 3 8 0 3 H Paper Reference(s) 1380/3H Edexcel GCSE Mathematics (Linear) 1380 Paper 3 (Non-Calculator) Higher Tier Monday 6 June 2011 Afternoon Time: 1 hour 45
More informationManual for SOA Exam MLC.
Chapter 4. Life Insurance. c 29. Miguel A. Arcones. All rights reserved. Extract from: Arcones Manual for the SOA Exam MLC. Fall 29 Edition. available at http://www.actexmadriver.com/ c 29. Miguel A. Arcones.
More informationIntroduction to Modem Design. Paolo Prandoni, LCAV - EPFL
Introduction to Modem Design Paolo Prandoni, LCAV - EPFL January 26, 2004 2 Part 1 Modulation In order to transmit a signal over a given physical medium we need to adapt the characteristics of the signal
More informationAVR223: Digital Filters with AVR. 8-bit Microcontrollers. Application Note. Features. 1 Introduction
AVR223: Digital Filters with AVR Features Implementation of Digital Filters Coefficient and Data scaling Fast Implementation of 4 th Order FIR Filter Fast Implementation of 2 nd Order IIR Filter Methods
More informationby the matrix A results in a vector which is a reflection of the given
Eigenvalues & Eigenvectors Example Suppose Then So, geometrically, multiplying a vector in by the matrix A results in a vector which is a reflection of the given vector about the y-axis We observe that
More informationThe Calculation of G rms
The Calculation of G rms QualMark Corp. Neill Doertenbach The metric of G rms is typically used to specify and compare the energy in repetitive shock vibration systems. However, the method of arriving
More informationTMA4213/4215 Matematikk 4M/N Vår 2013
Norges teknisk naturvitenskapelige universitet Institutt for matematiske fag TMA43/45 Matematikk 4M/N Vår 3 Løsningsforslag Øving a) The Fourier series of the signal is f(x) =.4 cos ( 4 L x) +cos ( 5 L
More informationLecture - 4 Diode Rectifier Circuits
Basic Electronics (Module 1 Semiconductor Diodes) Dr. Chitralekha Mahanta Department of Electronics and Communication Engineering Indian Institute of Technology, Guwahati Lecture - 4 Diode Rectifier Circuits
More informationDesign of Efficient Digital Interpolation Filters for Integer Upsampling. Daniel B. Turek
Design of Efficient Digital Interpolation Filters for Integer Upsampling by Daniel B. Turek Submitted to the Department of Electrical Engineering and Computer Science in partial fulfillment of the requirements
More informationDSP First Laboratory Exercise #9 Sampling and Zooming of Images In this lab we study the application of FIR ltering to the image zooming problem, where lowpass lters are used to do the interpolation needed
More informationTrend and Seasonal Components
Chapter 2 Trend and Seasonal Components If the plot of a TS reveals an increase of the seasonal and noise fluctuations with the level of the process then some transformation may be necessary before doing
More information8. Linear least-squares
8. Linear least-squares EE13 (Fall 211-12) definition examples and applications solution of a least-squares problem, normal equations 8-1 Definition overdetermined linear equations if b range(a), cannot
More informationCROSSING THE BRIDGE: TAKING AUDIO DSP FROM THE TEXTBOOK TO THE DSP DESIGN ENGINEER S BENCH. Robert C. Maher
CROSSING THE BRIDGE: TAKING AUDIO DSP FROM THE TEXTBOOK TO THE DSP DESIGN ENGINEER S BENCH Robert C. Maher Department of Electrical and Computer Engineering, Montana State University, Bozeman MT 59717
More informationNRZ Bandwidth - HF Cutoff vs. SNR
Application Note: HFAN-09.0. Rev.2; 04/08 NRZ Bandwidth - HF Cutoff vs. SNR Functional Diagrams Pin Configurations appear at end of data sheet. Functional Diagrams continued at end of data sheet. UCSP
More informationFrom Fundamentals of Digital Communication Copyright by Upamanyu Madhow, 2003-2006
Chapter Introduction to Modulation From Fundamentals of Digital Communication Copyright by Upamanyu Madhow, 003-006 Modulation refers to the representation of digital information in terms of analog waveforms
More informationMATH 423 Linear Algebra II Lecture 38: Generalized eigenvectors. Jordan canonical form (continued).
MATH 423 Linear Algebra II Lecture 38: Generalized eigenvectors Jordan canonical form (continued) Jordan canonical form A Jordan block is a square matrix of the form λ 1 0 0 0 0 λ 1 0 0 0 0 λ 0 0 J = 0
More information