- #1
mnb96
- 715
- 5
Hello,
given two functions f and g the operation of convolution [itex]f\ast g[/itex] finds many applications in many different branches of science. However, in such applications, it is typically assumed that one of the two functions (the convolution kernel) is a real scalar field, although the mathematical definition does not impose such constraint.
My question is: does the convolution of, say, two complex-valued functions has any known application? For instance when f,g are of the kind:
[itex]f:\mathbb{R}^2 \rightarrow \mathbb{C}[/itex], and
[itex]g:\mathbb{R}^2 \rightarrow \mathbb{C}[/itex] ?
Note that such functions could represent, for instance, vector fields on the Cartesian plane.
given two functions f and g the operation of convolution [itex]f\ast g[/itex] finds many applications in many different branches of science. However, in such applications, it is typically assumed that one of the two functions (the convolution kernel) is a real scalar field, although the mathematical definition does not impose such constraint.
My question is: does the convolution of, say, two complex-valued functions has any known application? For instance when f,g are of the kind:
[itex]f:\mathbb{R}^2 \rightarrow \mathbb{C}[/itex], and
[itex]g:\mathbb{R}^2 \rightarrow \mathbb{C}[/itex] ?
Note that such functions could represent, for instance, vector fields on the Cartesian plane.