Fourier Transform

The Fourier transform and its inverse transform are respectively defined as:

%5Ctilde%7Bf%7D(%5Comega)%20%3D%20%5Cfrac%7B1%7D%7B%5Csqrt%7B2%5Cpi%7D%7D%20%5Cint_%7B-%5Cinfty%7D%5E%7B%2B%5Cinfty%7D%20f(x)%20e%5E%7Bi%20%5Comega%20x%7D%20dx

and

f(x)%20%3D%20%5Cfrac%7B1%7D%7B%5Csqrt%7B2%5Cpi%7D%7D%20%5Cint_%7B-%5Cinfty%7D%5E%7B%2B%5Cinfty%7D%20%5Ctilde%7Bf%7D(%5Comega)%20e%5E%7B-i%20%5Comega%20x%7D%20d%5Comega

Consider two functions

f

and

g

. Another function

f%20*%20g

is defined as:

(f%20*%20g)(x)%20%3D%20%5Cfrac%7B1%7D%7B%5Csqrt%7B2%5Cpi%7D%7D%20%5Cint_%7B-%5Cinfty%7D%5E%7B%2B%5Cinfty%7D%20f(y)%20g(x%20-%20y)%20dy

Which of the following relation is/are true?Note: Tilde (~) denotes the Fourier transform.

Chapter Questions
1 MCQs