Answers.Body: <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>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2021-04-28T06:08:43.713Z
Answers.Text: Oh, the domains for both f and g are a subset of real numbers... t is continuous...
Answers.UserDisplayName: hanugm
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2021-04-28T06:03:24.217Z
Answers.LastActivityDate: 2021-04-28T06:03:24.217Z
Answers.UserDisplayName: user529295
Body: <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>
  
Tags: <deep-learning><convolutional-neural-networks><terminology><convolution><books>
Title: What is meant by "real-valued argument" in this context of the convolution operation?
UserDisplayName: hanugm
ThreadText: # 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
  
  ---
  
  ## 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...  
  
  ---
  
  