<p>In its most raw form, convolution is defined as: <span class="math-container">$(f*g)(t) = \int_{-\infty}^\infty f(\tau) \cdot g(t-\tau) d\tau$</span>.</p>
<p>Here, <em>t</em> doesn't represent the time domain. Infact, it represents the real valued argument the book is talking about. In this notion, at moment <em>t</em>, convolution can be thought of as a weighted average of the function <span class="math-container">$f(\tau)$</span> weighted by <span class="math-container">$g(–\tau)$</span>, which is simply shifted by amount <em>t</em>.</p>

CC BY-SA 4.0
2021-04-28T06:08:43.713Z
Oh, the domains for both f and g are a subset of real numbers... t is continuous...
hanugm
CC BY-SA 4.0
2021-04-28T06:03:24.217Z
2021-04-28T06:03:24.217Z
user529295
<p>Consider the following statement from <a href="https://www.deeplearningbook.org/contents/convnets.html" rel="nofollow noreferrer">Deep Learning book (p. 327, chapter 9: Convolutional Networks)</a></p>
<blockquote>
<p>In its most general form, convolution is an operation on two functions
<strong>of a real-valued argument</strong>.</p>
</blockquote>
<p>Suppose <span class="math-container">$f$</span> and <span class="math-container">$g$</span> 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?</p>
<p>Does it mean <span class="math-container">$f$</span> and <span class="math-container">$g$</span>  are real-valued functions? Or does it mean <span class="math-container">$f$</span> and <span class="math-container">$g$</span>  are real functions? or any other?</p>
<ul>
<li><p><em>Real-valued function:</em> Function whose codomain is a subset of real numbers</p>
</li>
<li><p><em>Real function:</em> Function whose domain and codomain are a subset of real numbers.</p>
</li>
</ul>

<deep-learning><convolutional-neural-networks><terminology><convolution><books>
What is meant by "real-valued argument" in this context of the convolution operation?
hanugm
# What is meant by "real-valued argument" in this context of the convolution operation?

(Asked by: username_0 on 2021-04-28)

Consider the following statement from [Deep Learning book (p. 327, chapter 9: Convolutional Networks)](https://www.deeplearningbook.org/contents/convnets.html)

> 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.

**Tags:** deep-learning, convolutional-neural-networks, terminology, convolution, books


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## 1 answers

### Answer by username_1 on 2021-04-28. Score: 1

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*.

> **Comments:**
> **username_0**: Oh, the domains for both f and g are a subset of real numbers... t is continuous...  

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