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Fourier Analysis

Forurier Series and Coefficients

1.(a) Evaluate the Fourier coefficients ao, an, bn and the exponential coefficient Dn for the waveform shown below; do not use MATLAB or a calculator for integrations. (b) Plot 2 or 3 cycles of the Fourier series using MATLAB and verify whether the plot matches the given waveform. (c) Find C0 and Cn from the answer to part (a)

This is a Heat Equation Problem

Can someone please solve this heat equations with details on how to arrive at the solution.? Solve the heat equation: u_t = 3*u_xx with the following I.C/B.C: u(0,t) = u(L,t) = 0 u(x,0)=L*[1-cos(2*Pi*x/L)]

Find Fourier Series

Find Fourier series for f(x) = {-4 for x greater than/= -pi, and x less than/= 0 { 4 for x greater than/= 0, and less than/= pi

Fourier Transform

See attachment. Please use the Fourier transform tables rather than a direct computation. Cheers.

Fourier Series

Find the nth Fourier coefficient (in terms of the an's) of the signal y(t) defined by: y(t) = x(t+1) + x(1-t), for all t in <R>. Please see attachment for more readable form of question.

Dirichlet's theorem

For of the periodic functions , I need to find the value to which the Fourier series converges at x= 0 , Pi/2 , - Pi/2 , Pi , -Pi , 2Pi , - 2Pi Using Dirichlet's theorem --- (See attached files for full problem description)

Fourier Series

Please help ... what is the Fourier series expansion of f(t). It is a multiple answer question. (See attached file for full problem description)

Fourier Cosine Transform

The problem is from Fourier Cosine and Sine Transforms, and Passage from Fourier Integral to Laplace Transform: Solve using a cosine or sine transform. u'' - 9u =50e^-3x (0<x<infinty) u'(0) = 0, u(infinity)bounded

The problem is from Fourier Series in Undergraduate 400 level.

Please show each step of your solution. When you use theorems, definitions, etc., please include in your answer. Fourier Cosine and Sine Transforms, and Passage from Fourier Integral to Laplace Transform: Given the rectangular pulse.. Please see attached.

Calculate Fourier Transforms Using a Table

Evaluate the following using Appendix D (Fourier Tranform Table). You may need to use more than one entry. Cite, by number, any entrie that you use. a)F{4x^2e^(-3|x|)} c) F{cos 3x/(x^2 + 2)} Please see the attached file for the fully formatted problems.

Sturm-Liouville expansion

Please show each step of your solution. When you use theorems, definitions, etc., please include in your answer. 3. Expand... in terms of the eigenfunctions of the Sturm-Liouville problem. Please see attached.

Eigenfunctions - Expand the function

Please show each step of your solution. When you use theorems, definitions, etc., please include in your answer. Expand the function f(x) = {x^4, 0 <= x < 2 {0, 2 <= x <= pi in terms of the eigenfunctions of the given eigenvalue problem. Use computer software, such as the Maple int command, to evaluate the expan

Sturm Liouville problem

4. Use the results of Exercise 3 to recast each of the following differential equations in the Sturm-Liouville form (1a). Identify p(x), q(x), and w(x). (a) xy" + 5y' + lambda xy = 0 (b) y" + 2y' + xy + lambda x^2y = 0 (c) y" + y' + lambda y = 0 (d) y" - y' + lambda xy = 0 (e) x^2y" + xy' + lambda x^2y = 0 (f) y" + (cot

Eigenvalues and eigenfunctions

1. Identify p(x), q(x), w(x) alpha, beta, gamma, delta, solve for the eigenvalues and eigenfunctions, and work out the eigenfunction expansion of the given function f. If the characteristic equation is too difficult to solve analytically, state that and proceed with the rest of the problem as though the lambda_n's were known.

Partial Sums of Fourier Series

The problems are from Fourier Series, Fourier Integral, and Fourier Transform. Please show each step of your solution. Obtain a computer plot of the partial sums of the Fourier series (19) of the periodic function shown in the attached figure, for (a) n =2 (b) n = 5 (c) n = 10 (d) n = 20 (e) n = 30 (f) n = 50 Ple

Fourier Series of a Periodic Fuction : Convergence

Work out the Fourier series of f, given over one period as follows. At which values of x does the series fail to converge to f(x)? To what values does it converge at those points? (h) |cos x| for all x (k) x on 0<x<1, 1<x<2

Fourier Transform

Find the Fourier transfrom of the following function: f(t) = te^(-2t), for t > 0

Fourier Series help

Find the complex Fourier series coefficients for the function x(t) depicted in the below figure Please see

Fourier Coefficients

Here, we have to find f(t) from the given value of Cn. I am not able to arrive at f(t)={3/[5-4cos(pit+pi/20)} despite many attempts. Please show me how to arrive at the final expected f(t) value.

Fourier Cosine Series and Fourier Series Expansion

In the interval (-pi, pi), &#948;n(x) = (n/x^1/2) e ^(-n^2 x^2) a) Expand &#948;n(x) as a Fourier Cosine Series. b) Show that your Fourier Series agrees with a Fourier expansion of &#948;n(x) in the limit as n--> infinity. Please see the attached file for the fully formatted problems.

Signal Function : Fourier Transform and Coefficients

A signal function f(t) of period 2 pi is given by: (See attached file) As required by my question I have drawn the above signal in the interval -4pi < t < 4pi which I beleive to be a sawtooth signal. I also need to find if f(t) is odd, even or neither, hence state which coefficients, if any, are zero. If there

Fourier Transformation : Even Function

A function h(x) is positive or zero for all values of x. Assume h(x) is even. If the Fourier transformation of h(x) is H(u) show that... (See attachment for full question)

Sum of Series using Fourier Series

Use the Fourier series of the function f(x) and the properties of Fourier series to obtain the Fourier series of... (aee attachment for full question)

Note to YINON

Yinon, If you do not wish to work on the Laplace diffusion problem anymore, I would like to see the solution you have formulated thus far and will pay you some credits even though it is not entirely correct. Please leave me a note. Thank you!

Laplace/Fourier Transforms

Please see the attached file for the fully formatted problems. The problem is number 8 on page 989 of the 2nd Edition of Greenberg's Advanced Engineering Mathematics book, PART C ONLY. This is in section 18.4 (Chapter 18 is the Diffusion Equation), in the exercises at the end of the section. PLEASE NOTE: I have scanned th