Does $(xw)$ denote the resulting composite function, given $$ denotes the convolution operation?

Question

Chapter 9.1 of the Deep Learning book gives this formula

$s(t)=(x*w)(t) \tag{(9.2)}$

where the operator $*$ denotes the convolution operation.

I'm conscious what the convolution operation is, I just have difficulty understanding the notation.

Does $(x*w)$ denote the resulting composite function which takes $t$ as its independent variable?

Here is the page in question

score 1 · Accepted Answer · answered Aug 23 '21 at 03:26

1

$x * w$ denotes the function that is the convolution of the functions $x$ and $w$. You can choose any letter for the independent variable. If you choose $t$, then it is written $(x * w)(t)$.

answered Aug 23 '21 at 03:26

Ted

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Thank you. Does the original $x$ denote a function or a set of numbers? – JakeMZ Aug 23 '21 at 03:39
1

@JakeMZ It's apparently a real-valued function. It might be confusing when the author says $x, t$ are real-valued. – justadzr Aug 23 '21 at 03:50

Does $(xw)$ denote the resulting composite function, given $$ denotes the convolution operation?

1 Answers1

Linked

Does $(x*w)$ denote the resulting composite function, given $*$ denotes the convolution operation?

1 Answers1

Linked

Does $(xw)$ denote the resulting composite function, given $$ denotes the convolution operation?