1
$\begingroup$

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 "real-valued argument" 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.

$\endgroup$
1
$\begingroup$

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.

$\endgroup$
1
  • $\begingroup$ Oh, the domains for both f and g are a subset of real numbers... t is continuous... $\endgroup$ – hanugm Apr 28 at 6:08

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.