...MEEN 260 Introduction to Engineering Experimentation Homework 10: Laplace Transform, and Frequency Response Solution Assigned: Thursday, 9 Apr. 2009 Due: Thursday, 16 Apr. 2009, 5:00pm Learning Objectives: After completing this homework assignment, you should be able to: 1) 2) 3) 4) 5) Determine the Laplace Transform of a signal using the definition, tables, or properties of the Laplace Transform Utilize the Laplace Transform to find the Transfer Function of a dynamic system represented by a system of differential equations Utilize the Laplace Transform to solve for the transient response of a dynamic system Discuss the difference between the Laplace and Fourier Transforms and their respective uses Using the Transfer Function of a system, determine and plot the associated frequency response, and determine the steady state response of a system to a harmonic input signal Homework Problems: Problem 1) Definition of Laplace Transform Using the mathematical definition, compute the Laplace transform for the function: f (t ) = 3t + t cos(2t ) Solution: From the mathematical definition, we split the function into two pieces: 3 3 · We use u-v substitution (u=3t, dv=e-st) to get: ∞ 3 ∞ 3 3 0 0 The second piece of the function is more complicated. Recall that: · So we find: cos 2 We use u-v substitution (u=e-st, dv=cos(2t)) and get: sin 2 2 This does not give us a useful answer, so we perform a u-v substitution to the right hand side of the equation to obtain: cos 2 By rearranging...
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...2007-2008 JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY, HYDERABAD B.TECH. ELECTRONICS AND COMMUNICATION ENGINEERING I YEAR COURSE STRUCTURE |Code |Subject |T |P/D |C | | |English |2+1 |- |4 | | |Mathematics - I |3+1 |- |6 | | |Mathematical Methods |3+1 |- |6 | | |Applied Physics |2+1 |- |4 | | |C Programming and Data Structures |3+1 |- |6 | | |Network Analysis |2+1 |- |4 | | |Electronic Devices and Circuits |3+1 |- |6 | | |Engineering Drawing |- |3 |4 | | |Computer Programming Lab. |- |3 |4 | | |IT Workshop |- |3 |4 | | |Electronic Devices and Circuits Lab |- |3...
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...in textbooks on Fourier theory. It seems that there is little that can be done with wavelets that cannot be done with traditional Fourier analysis. Stephane Mallat was not the father of wavelet theory, but he is certainly an evangelist. His textbook on the subject, A Wavelet Tour of Signal Processing [1], contains proofs about the theory of wavelets, and a summation about what is known about them with applications to signal processing. One of his many papers, Characterization of Signals from Multiscale Edges [2], is frequently cited as a link between wavelets and edge detection. Mallat’s method not only finds edges, but classifies them into different types as well. Mallat goes on to describe a method of recovering complete images using only the edges, but we will not implement it in this project. In this project, we study this paper, and implement the method of Mallat to multiscale edge detection and analysis. We will first present a short background on wavelet theory. Then we will describe the different types of edges that exist in images, and how they can be characterized using a Lipschitz constant. Next, we describe the algorithm for the wavelet transform, from the Mallat paper. Finally, we show the results of applying the algorithm to a test image, and a real image. wave with the signal. When the results high valued, the coefficients of the Fourier transform will be high. Where the signal or the wave is close to zero, the coefficients will be low. Fourier analysis has a...
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...UNIVERSITY OF MIAMI TONALITY ESTIMATION USING WAVELET PACKET ANALYSIS By Vaibhav Chhabra A Research Project Submitted to the Faculty of the University of Miami in partial fulfillment of the requirements for the degree of Master of Science Coral Gables, Florida May 2005 UNIVERSITY OF MIAMI A research project submitted in partial fulfillment of the requirements for the degree of Master of Science TONALITY ESTIMATION USING WAVELET PACKET ANALYSIS Vaibhav Chhabra Approved: ________________ Ken Pohlmann Professor of Music Engineering _________________ Dr. Edward Asmus Associate Dean of Graduate Studies ________________ Colby Leider Assistant Professor of Music Engineering _________________ Dr. Paul Mermelstein Professor of Electrical Engineering DEDICATION They say that one’s experience is what defines an individual. After all, you are what you are because of your experiences. On that note I would like to dedicate this work to all those who have contributed to my experience in this journey. For what I have learned has laid the foundation for what I will learn. I would also like to thank my family who has always been supportive of me, my brother Ruchir who is a natural send-master, Papa and Ma thanks for keeping the faith. All the Chacha’s, Chachi’s and cousins, thank you all for the support. Next on my thank you list are my Tae Kwon Do buddies. Sensei Jeff thanks for all of your advice, some day I’ll be teacher like you. Rico, training...
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...SOLUTIONS MANUAL Communication Systems Engineering Second Edition John G. Proakis Masoud Salehi Prepared by Evangelos Zervas Upper Saddle River, New Jersey 07458 Publisher: Tom Robbins Editorial Assistant: Jody McDonnell Executive Managing Editor: Vince O’Brien Managing Editor: David A. George Production Editor: Barbara A. Till Composition: PreTEX, Inc. Supplement Cover Manager: Paul Gourhan Supplement Cover Design: PM Workshop Inc. Manufacturing Buyer: Ilene Kahn c 2002 Prentice Hall by Prentice-Hall, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. No part of this book may be reproduced in any form or by any means, without permission in writing from the publisher. The author and publisher of this book have used their best efforts in preparing this book. These efforts include the development, research, and testing of the theories and programs to determine their effectiveness. The author and publisher make no warranty of any kind, expressed or implied, with regard to these programs or the documentation contained in this book. The author and publisher shall not be liable in any event for incidental or consequential damages in connection with, or arising out of, the furnishing, performance, or use of these programs. Printed in the United States of America 10 9 8 7 6 5 4 3 2 1 ISBN Pearson Pearson Pearson Pearson Pearson Pearson Pearson Pearson Pearson 0-13-061974-6 Education Ltd., London Education Australia Pty. Ltd., Sydney Education Singapore...
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...GITAM UNIVERSTIY (Declared as Deemed to be University U/S 3 of UGC Act, 1956) [pic] REGULATIONS & SYLLABUS Of B.Tech. (Electrical & Electronics & Engineering) (W.e.f 2012-13 admitted batch) Gandhi Nagar Campus, Rushikonda VISAKHAPATNAM – 530 045 Website: www.gitam.edu REGULATIONS (W.e.f. 2012-013 admitted batch) 1. ADMISSIONS 1. Admissions into B.Tech (Electrical & Electronics Engineering) programme of GITAM University are governed by GITAM University admission regulations. 2. ELIGIBILTY CRITERIA 1. A pass in 10+2 or equivalent examination approved by GITAM University with Physics, Chemistry and Mathematics. 2. Admissions into B.Tech will be based on an All India Entrance Test (GAT) conducted by GITAM University and the rule of reservation, wherever applicable. 3. STRUCTURE OF THE B.Tech. PROGRAMME 3.1 The Programme of instruction consists of: i) A general core programme comprising Basic Sciences, Basic Engineering, Humanities & Social Sciences and Mathematics. ii) An engineering core programme imparting to the student the fundamentals of engineering in the branch concerned. iii) An elective programme enabling the students to take up a group of departmental / interdepartmental courses of interest to him/her. In addition, a student has to i)...
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...Digital Image Processing: PIKS Inside, Third Edition. William K. Pratt Copyright © 2001 John Wiley & Sons, Inc. ISBNs: 0-471-37407-5 (Hardback); 0-471-22132-5 (Electronic) DIGITAL IMAGE PROCESSING DIGITAL IMAGE PROCESSING PIKS Inside Third Edition WILLIAM K. PRATT PixelSoft, Inc. Los Altos, California A Wiley-Interscience Publication JOHN WILEY & SONS, INC. New York • Chichester • Weinheim • Brisbane • Singapore • Toronto Designations used by companies to distinguish their products are often claimed as trademarks. In all instances where John Wiley & Sons, Inc., is aware of a claim, the product names appear in initial capital or all capital letters. Readers, however, should contact the appropriate companies for more complete information regarding trademarks and registration. Copyright 2001 by John Wiley and Sons, Inc., New York. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic or mechanical, including uploading, downloading, printing, decompiling, recording or otherwise, except as permitted under Sections 107 or 108 of the 1976 United States Copyright Act, without the prior written permission of the Publisher. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 605 Third Avenue, New York, NY 10158-0012, (212) 850-6011, fax (212) 850-6008, E-Mail: PERMREQ @ WILEY.COM. This publication is designed...
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...PE, etc. Bio-composite materials that can be decomposed naturally will be a solution to solve these problems. The aim of this study was to utilize the waste shredded coconut after the coconut milk was extracted, and used as reinforcing agent bio-composite material with matrix of Polylacticacid(PLA) that can decompose naturally. During this time, grated coconut is simply discarded without further exploited. Alkalization chemical treatment with 5% NaOH 1 hour to Grated Coconut Milk Residue (GCMR) was done to improve compatibility with PLA matrix. Bio-composite material was made with a fraction of 0%, 15%, 30% w/w using compression molding technique. The chemical structure of GCMR before and after chemical treatment was observed with Fourier Transform Infrared. The mechanical property of bio-composite material was observed with tensile test. Whereas the morphological characteristics of GCMR and fracture on the surface of bio-composite observed using Field Emission Scanning Electron Microscope. Then, thermal properties of bio-composite observed with Simultaneous Thermal Analysis. Result showed the addition of grated coconut fibers improve the mechanical properties, thermal stability, speed recrystallization PLA and PLA interfacial bonding between the filler GCMR. Thus, this material has the potential to reduce the environmental crisis caused by non-biodegradable material and non-renewable. Kata Kunci—Instruksi; Poly(latic acid)(PLA), Reinforcing Agent, Grated Coconut Residue, Bio-composites...
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...this has been properly acknowledged and referenced in accordance with departmental requirements. 3. I have not used work previously produced by another student or any other person to hand in as my own. 4. I have not allowed, and will not allow, anyone to copy my work with the intention of passing it off as his or her own work. Name | Student number | Signature | | | | Date | | Contents Table of Figures 3 Acronyms Used 3 PART 1 Filtering in the Frequency Domain 3 Introduction 3 Review of Prior Knowledge 4 Complex Numbers 4 Fourier series 4 Fourier Transform 4 Convolution Theorem 5 Overview 5 2-D FFT 6 DFT 6 IDFT 7 2-D FFT 7 Comparison with 1-D FFT 8 2-D FFT and Image Processing 8 Image Smoothing and Sharpening 9 Smoothing 9 Sharpening 11 Conclusion 13 PART 2 Application of Filtering in the Frequency Domain 13 Introduction 13 Gaussian Filter Theoretical Analysis 13 Gaussian Low Pass Filter 14 Gaussian High Pass Filter 14 Gaussian Filter Design 15 Practical Results 16 Conclusion 17 References 18 Table of Figures Figure 1: Input Signal Transformed to Frequency Domain 5 Figure 2: Flow Diagram of Filtering in the Frequency Domain 5 Figure 3: Spatial VS Frequency Domain 5 Figure 4: 2-D Sinusoidal Wave 7 Figure 5: Flow Diagram of Filtering in the Frequency Domain 9 Figure 6: Graphical Representation of an Ideal Low Pass Filter 10 Figure 7: Image that was smoothed 11 Figure 8: Graphical...
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...Lovely Professional University, Punjab Course Code MTH251 Course Category Course Title FUNCTION OF COMPLEX VARIABLE AND TRANSFORM Courses with Numerical focus Course Planner 16423::Harsimran Kaur Lectures 3.0 Tutorials Practicals Credits 2.0 0.0 4.0 TextBooks Sr No T-1 Title Advanced Engineering Mathematics Reference Books Sr No R-1 R-2 Other Reading Sr No OR-1 Journals articles as Compulsary reading (specific articles, complete reference) Journals atricles as compulsory readings (specific articles, Complete reference) , Title Higher Engineering Mathematics Advanced Modern Engineering Mathematics Author Grewal, B. S. Glyn James Edition 40th 3rd Year 2007 2011 Publisher Name Khanna Publishers Pearson Author Jain R. K. and Iyenger S. R. K. Edition 3rd Year 2007 Publisher Name Narosa Relevant Websites Sr No RW-1 RW-2 (Web address) (only if relevant to the course) www2.latech.edu/~schroder/comp_var_videos.htm freescienceonline.blogspot.com/2010_04_01_archive.html Salient Features Topic videos available Complex Analysis Reference Material Available LTP week distribution: (LTP Weeks) Weeks before MTE Weeks After MTE Spill Over 7 6 2 Detailed Plan For Lectures Week Number Lecture Number Broad Topic(Sub Topic) Chapters/Sections of Text/reference books Other Readings, Lecture Description Relevant Websites, Audio Visual Aids, software and Virtual Labs Introduction Functions of a Complex Variable Learning Outcomes Pedagogical Tool Demonstration/ Case Study...
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...March 2008, 1{22 RESEARCH ARTICLE Laplace transform approach to the rigorous upscaling of the in¯nite adsorption rate reactive °ow under dominant Peclet number through a pore z Catherine Choquet a and Andro Mikeli¶c b ¤ aUniversit¶e P. C¶ezanne, LATP UMR 6632, Facult¶e des Sciences et Techniques de Saint-J¶er^ome, 13397 Marseille Cedex 20, FRANCE bUniversit¶e de Lyon, Lyon, F-69003, FRANCE; Universit¶e Lyon 1, Institut Camille Jordan, UFR Math¶ematiques, Site de Gerland, B^at. A, 50, avenue Tony Garnier 69367 Lyon Cedex 07, FRANCE (submitted on March 31, 2008) In this paper we undertake a rigorous derivation of the upscaled model for reactive °ow through a narrow and long two-dimensional pore. The transported and di®used solute par- ticles undergo the in¯nite adsorption rate reactions at the lateral tube boundary. At the inlet boundary we suppose Danckwerts' boundary conditions. The transport and reaction pa- rameters are such that we have dominant Peclet number. Our analysis uses the anisotropic singular perturbation technique, the small characteristic parameter " being the ratio between the thickness and the longitudinal observation length. Our goal is to obtain error estimates for the approximation of the physical solution by the upscaled one. They are presented in the energy norm. They give the approximation error as a power of " and guarantee the validity of the upscaled model. We use the Laplace transform in time to get better estimates than in our...
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...Fourier Transform and its applications Jatin Kumar Murray State University Abstract It has been widely recognized that waveforms are an integral part of the various universe phenomenon. Waveforms can be used to represent almost everything in the world. Therefore it is understandable that concepts related to waveforms or signals are extremely important as their applications exist in a broad variety of fields. The processes and ideas related to waveforms play a vital role in different areas of science and technology such as communications, optics, quantum mechanics, aeronautics, image processing to name a few. Even though the physical nature of signals might be completely different in various disciplines, all waveforms follow one fundamental principle; they can be represented by functions of one or more independent variables. This paper would focus on the concept of Fourier Transform, the technique through which signals can be deconstructed and represented as sum of various elementary signals. It briefly describes Linear Time Invariant systems and their response to superimposed signals. Fourier transform has many applications in physics and Engineering. This paper would also cover some of Fourier Transform applications in telecommunication and its impact on society. Introduction Some of the basic signals that exist in the world and are useful in various technology fields are continuous and discrete time...
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...f ( t ) = L -1 {F ( s )} 1. 3. 5. 7. 9. 11. 1 t n , n = 1, 2,3,K t sin ( at ) t sin ( at ) sin ( at ) - at cos ( at ) cos ( at ) - at sin ( at ) sin ( at + b ) sinh ( at ) e at sin ( bt ) e at sinh ( bt ) t ne at , n = 1, 2,3,K uc ( t ) = u ( t - c ) Heaviside Function F ( s ) = L { f ( t )} 1 s n! s n +1 Table of Laplace Transforms f ( t ) = L -1 {F ( s )} F ( s ) = L { f ( t )} 1 s-a G ( p + 1) s p +1 1 × 3 × 5L ( 2n - 1) p 2n s 2 s 2 s + a2 s2 - a2 2 n+ 1 2. 4. 6. 8. 2 e at t p , p > -1 t n- 1 2 p 2s a 2 s + a2 2as 2 3 2 , n = 1, 2,3,K cos ( at ) t cos ( at ) sin ( at ) + at cos ( at ) cos ( at ) + at sin ( at ) cos ( at + b ) cosh ( at ) e at cos ( bt ) e at cosh ( bt ) f ( ct ) (s + a2 ) 10. 12. (s + a2 ) 2 13. 15. 17. 19. 21. 23. 25. 27. 29. 31. 33. 35. 37. (s + a ) s(s - a ) (s + a ) 2 2 2 2 2 2 2 2 2a 3 14. 16. 18. 20. 22. 24. 26. 28. 30. 32. 34. 36. (s + a ) s ( s + 3a ) (s + a ) 2 2 2 2 2 2 2 2 2as 2 s sin ( b ) + a cos ( b ) s2 + a2 a 2 s - a2 b s cos ( b ) - a sin ( b ) s2 + a2 s 2 s - a2 s-a (s - a) 2 + b2 -b n +1 2 (s - a) 2 + b2 - b2 b s-a (s - a) 2 (s - a) 2 n! (s - a) 1 æsö Fç ÷ c ècø e - cs e - cs L { g ( t + c )} uc ( t ) f ( t - c ) ect f ( t ) 1 f (t ) t e - cs s - cs e F (s) F ( s - c) ¥ s d (t - c ) Dirac Delta Function uc ( t ) g ( t ) t t n f ( t ) , n = 1, 2,3,K ( -1) T 0 n F ( n) ( s ) ò F ( u )...
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...student version of MATLAB 7.x available under general software in the UCCS bookstore. Other specific programming tools will be discussed in class. 1.) 2.) 3.) 4.) 5.) 6.) Graded homework worth 20%. Quizzes worth 15% total Laboratory assignments worth 20% total. Mid-term exam worth 15%. Final MATLAB project worth 10%. Final exam worth 20%. Topics Text 1.1–1.4 2.1–2.9 3.1–3.9 4.1–4.6 5.1–5.9 6.1–6.9 7.1–7.10 8.1–8.12 9.1–9.10 10.1–10.6 11.1–11.11 12.1–12.4 Weeks 0.5 1.0 1.0 1.0 1.5 1.5 (exam) 1.0 2.0 1.5? 0.5? 1.5? 1.5 (project) 1. Course Overview and Introduction 2. Sinusoids 3. Spectrum Representation 4. Sampling and Aliasing 5. FIR filters 6. Frequency response of FIR filters 7. z-Transforms 8. IIR Filters 9. Continuous-Time Signals and Systems 10. Frequency Response 11. Continuous-Time Fourier Transform 12. Filtering, Modulation, and Sampling Note: that topics 9–12 will most likely only be overviewed at the end of the semester....
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...Electric Circuits and Fields: Network graph, KCL, KVL, node and mesh analysis, transient response of dc and ac networks; sinusoidal steady-state analysis, resonance, basic filter concepts; ideal current and voltage sources. The venin's, Norton's and Superposition and Maximum Power Transfer theorems, two-port networks, three phase circuits; Gauss Theorem, electric field and potential due to point, line, plane and spherical charge distributions; Ampere's and Biot-Savart's laws; inductance; dielectrics; capacitance. Signals and Systems: Representation of continuous and discrete-time signals; shifting and scaling operations; linear, time-invariant and causal systems. Fourier series representation of continuous periodic signals; sampling theorem; Fourier, Laplace and Z transforms. Electrical Machines: Single phase transformer - equivalent circuit, phasor diagram, tests, regulation and efficiency; three phase transformers - connections, parallel operation; auto-transformer; energy conversion principles. DC machines - types, windings, generator characteristics, armature reaction and commutation, starting and speed control of motors; three phase induction motors - principles, types, performance characteristics, starting and speed control; single phase induction motors; synchronous machines - performance, regulation and parallel operation of generators, motor starting, characteristics and applications; servo and stepper motors. Power Systems: Basic power generation concepts;...
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