- #1
AxiomOfChoice
- 533
- 1
I know that the convolution of two functions [itex]f(x)[/itex] and [itex]g(x)[/itex] is given by
[tex]
(f * g)(y) = \int_{\mathbb R} f(x)g(y-x) dx.
[/tex]
But what if I'm trying to convolve a function [itex]f(x)[/itex] with a function [itex]g(x + az)[/itex], where [itex]a[/itex] is some constant? Is it just
[tex]
(f*g)(y) = \int_{\mathbb R} f(x)g(y - x + az) dx.
[/tex]
If so, why? I can't seem to find a definition of the convolution that makes this obvious.
[tex]
(f * g)(y) = \int_{\mathbb R} f(x)g(y-x) dx.
[/tex]
But what if I'm trying to convolve a function [itex]f(x)[/itex] with a function [itex]g(x + az)[/itex], where [itex]a[/itex] is some constant? Is it just
[tex]
(f*g)(y) = \int_{\mathbb R} f(x)g(y - x + az) dx.
[/tex]
If so, why? I can't seem to find a definition of the convolution that makes this obvious.