Purchase Solution

# Convolution of Fourier transforms : Associativity Law

Not what you're looking for?

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.
(a)Is it true that f*g = g*f? Why?
(b) If F(k) = (i//) f°° exp (?ikx) f(x) dx and G(k) = (i//) f°° exp (?ikx) g(x) dx are the Fourier transforms of f(x) and g(x), FIND the Fourier transform of h(x) = f *g (x).
(c) Is it true that (f * g) * h (x) = f * (g * h) (x)? If yes, can this Associativity Law be validated with the help of (b)'?

##### Solution Summary

A convolution of Fourier transfors is investigated. The solution is detailed and well presented.

##### Graphs and Functions

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

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.

##### Probability Quiz

Some questions on probability