Purchase Solution

Real Analysis : Fourier Transform for L1R

Not what you're looking for?

Ask Custom Question

Proof regarding a Fourier Transform for L1R.

Show 1/2pi ∫-1 -->1 (1 -|y|)e^(iyx) dy = 1/2pi [(sin x/2)/(x/2)]^2

Please see the attached file.

Attachments
Purchase this Solution
Solution Summary

An equality is proven using Fourier transforms.

Solution Preview

Please see the attached file for the complete solution.
Thanks for using BrainMass.

Text: An Introduction to Harmoni c Analysis (Fourier Series)
by Yitzhak Katznelson

The following problem is a portion of the proof about Fourier Transforms for .

Problem 1.8: Show

The first fact we need is that ei = cos  + i sin 

(If you aren't familiar with this, check out any complex analysis introductory text - I recommend Schaum's, but whatever you or your library may have.)

Second, dealing with absolute ...

Purchase this Solution
Free BrainMass Quizzes
Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

View More Free Quizzes
Related BrainMass Solutions

  • Find the fourier transform of x^k, where k is a positive integer and x is a single real variable.

    76817 Find the fourier transform of a positive integer Find the fourier transform of x^k, where k is a positive integer and x is a single real variable. Please see the attached file for the complete solution. Thanks for using BrainMass.

  • Fourier Transforms and Convolution Theorem

    (1) Since given equation is Now taking Fourier Transform Both sides We get (b) Now taking inverse Fourier transform Inverse Fourier transform of g(x) = = g(x) And inverse Fourier transform of = We have to

  • Fourier Series and Fourier Transform

    579494 Fourier Series and Fourier Transform Please show all steps. 1. Let f(x) be a 2pi- periodic function such that f(x) = x^2 −x for x ∈ [−pi,pi]. Find the Fourier series for f(x). 2.

  • Waveforms : Fourier and Laplace Transforms

    b.Derive the Laplace transform for this signal. c.Use Laplace transform analysis to derive the Fourier transform in its simplest form. All details in the attached sheet. Please see the attached file for the complete solution.

  • Periodic Functions via Convolution

    (c) Find the Fourier transform 5(k) FpJ(k) = * f ep(x) dx of p(x) in terms of the Fourier transform (k) of that nonperiodic function.

  • Fourier transform problems

    A continuous time signal x(t) has the Fourier transform X(ω) = 1/(jω+b) where b is a constant. Determine the Fourier transform for v(t) = x(t) * x(t). 3. Compute the Fourier transform for x(t) = te^-t u(t) 4.

  • DSP related problems solved in Matlab

    Cheers, Your OTA This solution describes the DSP problems related to sampling, fourier transform and z-transform solved in Matlab.

  • Fourier transform of functions

    By applying the frequency shifting property of Fourier transform , the following Fourier transform pair can be obtained So for can be treated as .

  • Fourier Analysis of Time domain waveform using Excel and THD

    See attachments for questions. The Fourier Analysis tool solves problems in linear systems and analyzes periodic data by using the Fast Fourier Transform (FFT) method to transform data.

View More Related Solutions