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Convolution Notation: The difference between (f*g)(x) and f(x)*g(x)
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What is the difference between (f*g)(x) and f(x)*g(x) [1] for convolutions? Are they the same? I ask this because I have been asked to prove the Reflection of Convolution property for my course in the Theory of Distributions,
i.e that f(-x)g(-x)=(fg)(-x). But if there is no difference between [1], then surely the proof follows from [1] and nothing actually needs to be proven.
notation convolution reflection
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up vote
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down vote
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What is the difference between (f*g)(x) and f(x)*g(x) [1] for convolutions? Are they the same? I ask this because I have been asked to prove the Reflection of Convolution property for my course in the Theory of Distributions,
i.e that f(-x)g(-x)=(fg)(-x). But if there is no difference between [1], then surely the proof follows from [1] and nothing actually needs to be proven.
notation convolution reflection
asked yesterday
user617486
1
New contributor
user617486 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
What is the difference between (f*g)(x) and f(x)*g(x) [1] for convolutions? Are they the same? I ask this because I have been asked to prove the Reflection of Convolution property for my course in the Theory of Distributions,
i.e that f(-x)g(-x)=(fg)(-x). But if there is no difference between [1], then surely the proof follows from [1] and nothing actually needs to be proven.
notation convolution reflection
asked yesterday
user617486
1
New contributor
user617486 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
What is the difference between (f*g)(x) and f(x)*g(x) [1] for convolutions? Are they the same? I ask this because I have been asked to prove the Reflection of Convolution property for my course in the Theory of Distributions,
i.e that f(-x)g(-x)=(fg)(-x). But if there is no difference between [1], then surely the proof follows from [1] and nothing actually needs to be proven.
notation convolution reflection
notation convolution reflection
asked yesterday
user617486
1
New contributor
user617486 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked yesterday
user617486
1
New contributor
user617486 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked yesterday
user617486
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user617486 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked yesterday
user617486
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asked yesterday
user617486
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user617486 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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user617486 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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1 Answer
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$f*g$ means that $*$ is defined on the space of functions. The notation $f(x)*g(x)$ makes it look as though $*$ is defined on the space of real numbers (if the functions are real that is), and hence isn't great. It's the same solecism as talking about 'the function $f(x)$'---it's $f$ that is the function, not $f(x)$.
answered yesterday
Richard Martin
1,3238
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
2
down vote
$f*g$ means that $*$ is defined on the space of functions. The notation $f(x)*g(x)$ makes it look as though $*$ is defined on the space of real numbers (if the functions are real that is), and hence isn't great. It's the same solecism as talking about 'the function $f(x)$'---it's $f$ that is the function, not $f(x)$.
answered yesterday
Richard Martin
1,3238
add a comment |
up vote
2
down vote
$f*g$ means that $*$ is defined on the space of functions. The notation $f(x)*g(x)$ makes it look as though $*$ is defined on the space of real numbers (if the functions are real that is), and hence isn't great. It's the same solecism as talking about 'the function $f(x)$'---it's $f$ that is the function, not $f(x)$.
answered yesterday
Richard Martin
1,3238
add a comment |
up vote
2
down vote
up vote
2
down vote
$f*g$ means that $*$ is defined on the space of functions. The notation $f(x)*g(x)$ makes it look as though $*$ is defined on the space of real numbers (if the functions are real that is), and hence isn't great. It's the same solecism as talking about 'the function $f(x)$'---it's $f$ that is the function, not $f(x)$.
answered yesterday
Richard Martin
1,3238
$f*g$ means that $*$ is defined on the space of functions. The notation $f(x)*g(x)$ makes it look as though $*$ is defined on the space of real numbers (if the functions are real that is), and hence isn't great. It's the same solecism as talking about 'the function $f(x)$'---it's $f$ that is the function, not $f(x)$.
answered yesterday
Richard Martin
1,3238
answered yesterday
Richard Martin
1,3238
answered yesterday
Richard Martin
1,3238
answered yesterday
Richard Martin
1,3238
1,3238
add a comment |
add a comment |
user617486 is a new contributor. Be nice, and check out our Code of Conduct.
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