Fourier series

Lesson/Chapter Name Engineering Mathematics Fourier Series Author(s) Reviewer(s) Name Ms.ShwetaDua College/Department: Bhaskaracharya College of Applied Sciences Contact No: 9650875992 e-mail id: shwetadua8@gmail.com Date of Submission: 12-07-2013 Date of Final Submission (after revisions if any): 17-08-2013 Contact No: Table of Contents Chapter 1:Fourier Series 1.1 Introduction 1.1.1 Fourier Series 1.1.2Advantage and Use of Fourier Series 1.1.3 Periodic Function

FOURIER SERIES AND ITS SOME APPLICATIONS P. Sathyabama Assistant professor, Department of Mathematics, Bharath collage of science and management, Thanjavur- 5 Abstract The Fourier Series, the founding principle behind the field of Fourier Analysis, is an infinite expansion of a function in terms of sines and cosines.In physics and engineering,expanding functions in terms of sines and cosines is useful because it allows one to more easily manipulate functions.In particular, the fields of electronics

factor in signal processing as it causes overshoot, ringing artifacts, and is considered as the convolution of the cardinal sine function (represented as sin (x)/ x or sinc (x)) and the Heaviside step function that corresponds to shortening the Fourier series, which causes the Gibbs

Joseph Fourier was born in a modest family at Auxerre, France. Orphaned at an early age, Joseph acquired his initial education from Pallais’s school, which was run by the music teacher from the cathedral. Thereafter he proceeded to the École Royale Militaire of Auxerre. While he showed an aptitude and flair for literature, by the age of thirteen, this was overshadowed by mathematics a subject he found himself really interested in. Joseph completed a study of the six volumes of Bezout's Cours de mathématiques

Chapter 3 METHODOLOGY 3.1 Method of Separation of Variable (developed by J. Fourier) The method of separation is based on the expansion of an arbitrary function in terms of the Fourier series. This method is applied by assuming that the dependent variable is a product of a number of functions and each function being a function of a single independent variable. This reduces the partial differential equation to a system of ordinary differential equations, each being a function of a single independent

Let a_0 = 0. Using equations 2 and 3, after canceling terms, ∫_"0" ^"T" ▒〖"f" ("x" )" " "sin" ⁡〖"πkx" /"T" 〗 " dx= " 〗 "b" _"k" "T" "b" _"k" "= " "1" /"T" ∫_"0" ^"T" ▒〖"f" ("x" ) "sin" ⁡〖"(" "πkx" ⁄"T" ")" 〗 "dx" 〗 The process to derive "a" _"k" was much simpler than deriving "b" _"k" , since I simply multiplied the original equation by "cos" ⁡〖"πmx" /"T" 〗 and then used the orthogonality conditions. "f" ("x" )"=" "a" _"0" "+" ∑_"k=1" ^"∞" ▒("a" _"k" "cos" ⁡〖"πkx" /"T" 〗 "+" "b" _"k"

The core aim of the present work is to completely analyze precise electronic structure of the five different doped BaTiO3 systems and the bonding interactions between the constituent atoms. This aim is achieved successfully by adopting maximum entropy method (MEM). In this section, the importance of electron density studies in structure analysis, the formalism of MEM method, the principle, MEM methodology followed in this work to elucidate the electron density are given elaborately. 1.9.2.1 Electron

The rapid invention going in internet usage has resulted in the media ownership and attention towards intellectual property rights among internet users. In this paper, a Multiwavelet Transform (MWT) based video encoding is proposed. Video watermarking is the practice of inserting an encode information known as the watermark, into an original video in an imperceptible approach. The watermark converts or represents information that can protect the watermarked video, typically identifying the source

International Journal of Computational Engineering Research||Vol, 03||Issue, 6|| www.ijceronline.com ||June ||2013|| Page 57 Detection System of Illegal Logging Image Using Matching Process With Discrete Cosine Transform Syafruddin Syarif1, Nadjamuddin Harun2, M. Tola3, M. Wihardi Tjaronge4 1 Student of Doctoral Program Civil Engineering Hasanuddin University, Makassar Indonesia 1,2,3 Department of Electrical Engineering, Hasanuddin University, Makassar, Indonesia 4 Department of Civil Engineering

Music, in one way or another, is a part of everyone’s life, whether it is listening to music when travelling or learning how to play a musical instrument (Stutz). Beginning piano lessons at the age of 6, I have developed a passion for music and find it to be a way to escape from a hectic life. A requirement of the Royal Conservatory of Music, a corporation that runs exams to test the ability of music students, is to learn music history, and during the course, I was amazed at the fact that when two