What is meant by "real-valued argument" in this context of the convolution operation? Consider the following statement from Deep Learning book (p. 327, chapter 9: Convolutional Networks)

In its most general form, convolution is an operation on two functions
of a real-valued argument.

Suppose $f$ and $g$ are functions on which I want to apply convolution operation. What is meant by two functions of a &quot;real-valued argument&quot; in this context?
Does it mean $f$ and $g$  are real-valued functions? Or does it mean $f$ and $g$  are real functions? or any other?

Real-valued function: Function whose codomain is a subset of real numbers

Real function: Function whose domain and codomain are a subset of real numbers.
In its most raw form, convolution is defined as: $(f*g)(t) = \int_{-\infty}^\infty f(\tau) \cdot g(t-\tau) d\tau$.
Here, t doesn't represent the time domain. Infact, it represents the real valued argument the book is talking about. In this notion, at moment t, convolution can be thought of as a weighted average of the function $f(\tau)$ weighted by $g(–\tau)$, which is simply shifted by amount t.