What is the term used to describe a discrete function which is non-zero at only 1 point, and zero everywhere else? Intended for a spatial domain.

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Please see the image below.



What is the formal term for the type of function shown below.



  • One could describe it as a uniform distribution and the domain being x=5. But this is not elegant

  • One could describe it as a logic signal at x=5, but this is not very accurate.

It is intended for a spatial domain. So if there is a grid, I would like to describe a function which is "a" at only one point in the grid, and "b" everywhere else.



Is a succinct term for this function?



Example image of the type of function referred to in the question




functions signal-processing uniform-distribution discrete-optimization




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  • 1




    The indicator function of $5$ is what I would use.
    – Daniel Mroz
    2 days ago










  • It would improve your Question (and make it more precise!) to specify the domain intended for the function. The image makes it seem that you have in mind a function defined only on integers(?).
    – hardmath
    2 days ago










  • Thank you, I think the Kronecker delta does the job.
    – user5211911
    2 days ago














up vote
0
down vote

favorite












Please see the image below.



What is the formal term for the type of function shown below.



  • One could describe it as a uniform distribution and the domain being x=5. But this is not elegant

  • One could describe it as a logic signal at x=5, but this is not very accurate.

It is intended for a spatial domain. So if there is a grid, I would like to describe a function which is "a" at only one point in the grid, and "b" everywhere else.



Is a succinct term for this function?



Example image of the type of function referred to in the question




functions signal-processing uniform-distribution discrete-optimization




share|cite|improve this question

















  • 1




    The indicator function of $5$ is what I would use.
    – Daniel Mroz
    2 days ago










  • It would improve your Question (and make it more precise!) to specify the domain intended for the function. The image makes it seem that you have in mind a function defined only on integers(?).
    – hardmath
    2 days ago










  • Thank you, I think the Kronecker delta does the job.
    – user5211911
    2 days ago












up vote
0
down vote

favorite









up vote
0
down vote

favorite











Please see the image below.



What is the formal term for the type of function shown below.



  • One could describe it as a uniform distribution and the domain being x=5. But this is not elegant

  • One could describe it as a logic signal at x=5, but this is not very accurate.

It is intended for a spatial domain. So if there is a grid, I would like to describe a function which is "a" at only one point in the grid, and "b" everywhere else.



Is a succinct term for this function?



Example image of the type of function referred to in the question




functions signal-processing uniform-distribution discrete-optimization




share|cite|improve this question













Please see the image below.



What is the formal term for the type of function shown below.



  • One could describe it as a uniform distribution and the domain being x=5. But this is not elegant

  • One could describe it as a logic signal at x=5, but this is not very accurate.

It is intended for a spatial domain. So if there is a grid, I would like to describe a function which is "a" at only one point in the grid, and "b" everywhere else.



Is a succinct term for this function?



Example image of the type of function referred to in the question





functions signal-processing uniform-distribution discrete-optimization





share|cite|improve this question












share|cite|improve this question




share|cite|improve this question








edited 2 days ago
























asked 2 days ago









user5211911

32




32







  • 1




    The indicator function of $5$ is what I would use.
    – Daniel Mroz
    2 days ago










  • It would improve your Question (and make it more precise!) to specify the domain intended for the function. The image makes it seem that you have in mind a function defined only on integers(?).
    – hardmath
    2 days ago










  • Thank you, I think the Kronecker delta does the job.
    – user5211911
    2 days ago












  • 1




    The indicator function of $5$ is what I would use.
    – Daniel Mroz
    2 days ago










  • It would improve your Question (and make it more precise!) to specify the domain intended for the function. The image makes it seem that you have in mind a function defined only on integers(?).
    – hardmath
    2 days ago










  • Thank you, I think the Kronecker delta does the job.
    – user5211911
    2 days ago







1




1




The indicator function of $5$ is what I would use.
– Daniel Mroz
2 days ago




The indicator function of $5$ is what I would use.
– Daniel Mroz
2 days ago












It would improve your Question (and make it more precise!) to specify the domain intended for the function. The image makes it seem that you have in mind a function defined only on integers(?).
– hardmath
2 days ago




It would improve your Question (and make it more precise!) to specify the domain intended for the function. The image makes it seem that you have in mind a function defined only on integers(?).
– hardmath
2 days ago












Thank you, I think the Kronecker delta does the job.
– user5211911
2 days ago




Thank you, I think the Kronecker delta does the job.
– user5211911
2 days ago










1 Answer
1






active

oldest

votes

















up vote
1
down vote



accepted










Perhaps you want the Kronecker delta:
$$
delta_5x = begincases
1 quad x = 5 \
0 quad textotherwise
endcases
$$



Edit in response to an edit in the question.



This will work for a grid: $delta_xy$ makes sense when $x$ and $y$ are elements of any universe $S$ so you can write
$$
f_x(y) = (a-b)delta_xy + b .
$$






share|cite|improve this answer























  • Thank you, this is it.
    – user5211911
    2 days ago










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1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes








up vote
1
down vote



accepted










Perhaps you want the Kronecker delta:
$$
delta_5x = begincases
1 quad x = 5 \
0 quad textotherwise
endcases
$$



Edit in response to an edit in the question.



This will work for a grid: $delta_xy$ makes sense when $x$ and $y$ are elements of any universe $S$ so you can write
$$
f_x(y) = (a-b)delta_xy + b .
$$






share|cite|improve this answer























  • Thank you, this is it.
    – user5211911
    2 days ago














up vote
1
down vote



accepted










Perhaps you want the Kronecker delta:
$$
delta_5x = begincases
1 quad x = 5 \
0 quad textotherwise
endcases
$$



Edit in response to an edit in the question.



This will work for a grid: $delta_xy$ makes sense when $x$ and $y$ are elements of any universe $S$ so you can write
$$
f_x(y) = (a-b)delta_xy + b .
$$






share|cite|improve this answer























  • Thank you, this is it.
    – user5211911
    2 days ago












up vote
1
down vote



accepted







up vote
1
down vote



accepted






Perhaps you want the Kronecker delta:
$$
delta_5x = begincases
1 quad x = 5 \
0 quad textotherwise
endcases
$$



Edit in response to an edit in the question.



This will work for a grid: $delta_xy$ makes sense when $x$ and $y$ are elements of any universe $S$ so you can write
$$
f_x(y) = (a-b)delta_xy + b .
$$






share|cite|improve this answer















Perhaps you want the Kronecker delta:
$$
delta_5x = begincases
1 quad x = 5 \
0 quad textotherwise
endcases
$$



Edit in response to an edit in the question.



This will work for a grid: $delta_xy$ makes sense when $x$ and $y$ are elements of any universe $S$ so you can write
$$
f_x(y) = (a-b)delta_xy + b .
$$







share|cite|improve this answer















share|cite|improve this answer



share|cite|improve this answer








edited 2 days ago


























answered 2 days ago









Ethan Bolker

35.6k54099




35.6k54099











  • Thank you, this is it.
    – user5211911
    2 days ago
















  • Thank you, this is it.
    – user5211911
    2 days ago















Thank you, this is it.
– user5211911
2 days ago




Thank you, this is it.
– user5211911
2 days ago












 

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