10krunner said:I'm trying to plot the function f(x,y) = DiracDelta[y-x tan (theta)] and then take the 2D Fourier transform.
A 2-D Delta function, also known as a 2-D Dirac delta function, is a mathematical function that represents a point mass or impulse at the origin in two-dimensional space. It is often used in physics and engineering to model point sources or to simplify calculations involving point masses.
The main difference between a 2-D Delta function and a regular Delta function is the dimensionality. A regular Delta function is one-dimensional, meaning it only has one independent variable, while a 2-D Delta function is two-dimensional, with two independent variables. Additionally, the 2-D Delta function has a different mathematical expression and properties compared to the regular Delta function.
2-D Delta functions have many applications in various fields, including physics, engineering, and signal processing. They are commonly used to represent point sources in electric and magnetic fields, as well as in fluid dynamics to model vortices. They are also used in image processing and computer graphics to represent sharp edges and perform convolutions.
A 2-D Delta function is typically represented by the symbol δ(x,y) or δx,y. It has the following mathematical properties:
- δ(x,y) = 0 for all points (x,y) ≠ (0,0)
- ∫∫δ(x,y) dx dy = 1
- ∫∫f(x,y) δ(x,y) dx dy = f(0,0)
Where f(x,y) is any continuous function.
Yes, a 2-D Delta function can be generalized to any number of dimensions. For example, a 3-D Delta function, also known as a 3-D Dirac delta function, represents a point mass at the origin in three-dimensional space. Higher dimensional Delta functions have similar mathematical properties and applications, but they become increasingly complex in higher dimensions.