Purchase Solution

Periodic Functions via Convolution

Not what you're looking for?

Ask Custom Question

Please see the attached file for the fully formatted problems.

"Periodic Function via Convolution"
Consider the periodic train of Dirac delta "functions"
f(x) =....
with real period ....
(a) FIND and DESCRIBE its Fourier transform F(k). What happens to F if c gets doubled?
(b) Let p(x + c) = p(x) be a periodic function.
Prove or disprove: p(x) is the convolution (i.e. f * g (x) E f(x ? t)g(t) dt) of a periodic train of Dirac delta functions with a non-periodic function, say g(x) in L2 (?co, oo). What is g(x)?
(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. Relate your answer to the Fourier series coefficients of the periodic function p(x)

Attachments
Purchase this Solution
Solution Summary

A periodic train of Dirac functions are investigated via convolution. The solution is detailed and well presented.

Purchase this Solution
Free BrainMass Quizzes
Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Exponential Expressions

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

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.

Multiplying Complex Numbers

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

Graphs and Functions

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

View More Free Quizzes
Related BrainMass Solutions

  • Fourier Analysis and Series : Periodic Functions and Convolution

    157761 Fourier Analysis and Series : Periodic Functions and Convolution Please see the attached file for the fully formatted problems. Please see the attachment.

  • Writing the signals as rect(t) convolutions

    Write an algebraic expression for the negative going pressure pulses as a convolution between a rect() function and a sum of delta functions.

  • Laplace Transform of a periodic function

    24736 Laplace Transform of a Periodic Function See the attached file. Let f be a piecewise continuous function on [0,T]. Define f on the whole of [0,inf) by f(t+nT) for all t and all integer n.

  • Partial differential equations - convolution of functions

    180967 Partial Differential Equations - Convolution of Functions See attached problem (convolution of two functions). Please find the solution in the attached file. The solution provides a problem about the convolution of two functions.

  • Discrete signals and systems problems

    Determine if each of the following signals is periodic. If a signal is periodic, what is its period? x[n] = 3sin(100n) x[n] = 4cos(1.5πn) 3.

  • Applications of Fourier transform

    • By the convolution theorem , Fourier transforms turn the complicated convolution operation into simple multiplication, which means that they provide an efficient way to compute convolution-based operations such as polynomial multiplication and multiplying

  • MATLAB Convolution Simulation

    Test with the following signals: (Plot all results -> use the stem command) Case 1: h(n)=1 for 1functions equal zero in regions not defined above.

  • Convolution of Fourier transforms : Associativity Law

    17173 Convolution of Fourier Transforms: Associativity Law Please see the attached file for the fully formatted problems. The convolution of two functions f and g is defined to be the new function f * g. whenever the integral converges.

  • Laplace transform : Solve an I.V.P.

    of convolution of functions transform into the multiplication of the individual functions.

View More Related Solutions