# what symbol should we encourage peeps to use for convolution? for “equal to by definition”?

of course the traditional symbol is the six-pointed asterisk $*$ or $\ast$. of course, the problem with that is that all of these programming languages use the asterisk for multiplication.

MattL likes to use the five-pointed $\star$. dunno if i have seen it anywhere else.

http://web.mit.edu/2.14/www/Handouts/Convolution.pdf uses $\otimes$ which i really do not recommend.

my preference is to extend the idea of $\otimes$ but put inside the circle the traditional six-pointed asterisk. LaTeX has a symbol for this $\circledast$. it is sufficiently different from the naked asterisk, to mean something different, yet recognizable.

what do you folks think? we could be establishing a new standard for the lit (hope so).

another symbol i have seen used is $\triangleq$ (an equal sign with a little triangle on top) for "equal by definition to". it's better than that three-line equal sign $\equiv$ which means "logical equivalence". should we encourage usage of that symbol for definitions?

• For the mention, around the $\triangleq$ tex.stackexchange.com/questions/163829/delta-equal-to-symbol – Laurent Duval May 19 '16 at 23:32
• But at the same time the linear and circular convolution signs be distinct? I suppose the circle conventionally is preserved for the circular convolution? – Fat32 Jun 3 '16 at 23:38
• ya know, i wasn't thinking that, but it's a pretty good idea. my problem with the asterisk "$*$" is that it's use is a little ambiguous since, in most computer languages, it's used for multiplication. @MattL. uses $\star$ for convolution. maybe we should use that for linear convolution and the circled star (dunno the LaTeX for it) for circular convolution. – robert bristow-johnson Jun 4 '16 at 2:42
• I have recently seen a post regarding an SE math-symbol-compatible search engine. Such a question could possibly be thought about in this context – Laurent Duval Sep 17 '16 at 9:51