Efficient way to do a Fourrier Transform like operation
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Suppose we have two functions $f,g:[0,infty) rightarrow [0,infty)$. Then one can use Fast Fourrier Transforms to quickly compute $int_0^t f(t-s) g(s) , ds$ for $t$ in some range of values $[0,T]$ this can be done for example in Matlab using ifft(fft(f).*fft(g)).
Now let $M in [0,infty)$ be some number and assume we want to compute the integral $int_0^M f(t-s) g(s) , ds$ for $t$ in some range $[M,T]$. Is there something similar we can do?
real-analysis calculus matlab fast-fourier-transform
asked Dec 5 '18 at 16:38
DarkwizieDarkwizie
14811
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add a comment |
$begingroup$
Suppose we have two functions $f,g:[0,infty) rightarrow [0,infty)$. Then one can use Fast Fourrier Transforms to quickly compute $int_0^t f(t-s) g(s) , ds$ for $t$ in some range of values $[0,T]$ this can be done for example in Matlab using ifft(fft(f).*fft(g)).
Now let $M in [0,infty)$ be some number and assume we want to compute the integral $int_0^M f(t-s) g(s) , ds$ for $t$ in some range $[M,T]$. Is there something similar we can do?
real-analysis calculus matlab fast-fourier-transform
asked Dec 5 '18 at 16:38
DarkwizieDarkwizie
14811
$endgroup$
$begingroup$
can't you just define $g$ to be $0$ on the range $[M,T]$ so that the integral is equal to the integral over the range $[0,T]$ and then you can apply the method you mentioned first?
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– mathworker21
Dec 5 '18 at 16:41
$begingroup$
That is completely correct! Thanks, you can formulate this as a proper answer, thank you.
$endgroup$
– Darkwizie
Dec 5 '18 at 19:28
add a comment |
$begingroup$
Suppose we have two functions $f,g:[0,infty) rightarrow [0,infty)$. Then one can use Fast Fourrier Transforms to quickly compute $int_0^t f(t-s) g(s) , ds$ for $t$ in some range of values $[0,T]$ this can be done for example in Matlab using ifft(fft(f).*fft(g)).
Now let $M in [0,infty)$ be some number and assume we want to compute the integral $int_0^M f(t-s) g(s) , ds$ for $t$ in some range $[M,T]$. Is there something similar we can do?
real-analysis calculus matlab fast-fourier-transform
asked Dec 5 '18 at 16:38
DarkwizieDarkwizie
14811
$endgroup$
Suppose we have two functions $f,g:[0,infty) rightarrow [0,infty)$. Then one can use Fast Fourrier Transforms to quickly compute $int_0^t f(t-s) g(s) , ds$ for $t$ in some range of values $[0,T]$ this can be done for example in Matlab using ifft(fft(f).*fft(g)).
Now let $M in [0,infty)$ be some number and assume we want to compute the integral $int_0^M f(t-s) g(s) , ds$ for $t$ in some range $[M,T]$. Is there something similar we can do?
real-analysis calculus matlab fast-fourier-transform
real-analysis calculus matlab fast-fourier-transform
asked Dec 5 '18 at 16:38
DarkwizieDarkwizie
14811
asked Dec 5 '18 at 16:38
DarkwizieDarkwizie
14811
asked Dec 5 '18 at 16:38
DarkwizieDarkwizie
14811
asked Dec 5 '18 at 16:38
DarkwizieDarkwizie
14811
asked Dec 5 '18 at 16:38
DarkwizieDarkwizie
14811
14811
$begingroup$
can't you just define $g$ to be $0$ on the range $[M,T]$ so that the integral is equal to the integral over the range $[0,T]$ and then you can apply the method you mentioned first?
$endgroup$
– mathworker21
Dec 5 '18 at 16:41
$begingroup$
That is completely correct! Thanks, you can formulate this as a proper answer, thank you.
$endgroup$
– Darkwizie
Dec 5 '18 at 19:28
add a comment |
$begingroup$
can't you just define $g$ to be $0$ on the range $[M,T]$ so that the integral is equal to the integral over the range $[0,T]$ and then you can apply the method you mentioned first?
$endgroup$
– mathworker21
Dec 5 '18 at 16:41
$begingroup$
That is completely correct! Thanks, you can formulate this as a proper answer, thank you.
$endgroup$
– Darkwizie
Dec 5 '18 at 19:28
$begingroup$
can't you just define $g$ to be $0$ on the range $[M,T]$ so that the integral is equal to the integral over the range $[0,T]$ and then you can apply the method you mentioned first?
$endgroup$
– mathworker21
Dec 5 '18 at 16:41
$begingroup$
can't you just define $g$ to be $0$ on the range $[M,T]$ so that the integral is equal to the integral over the range $[0,T]$ and then you can apply the method you mentioned first?
$endgroup$
– mathworker21
Dec 5 '18 at 16:41
$begingroup$
That is completely correct! Thanks, you can formulate this as a proper answer, thank you.
$endgroup$
– Darkwizie
Dec 5 '18 at 19:28
$begingroup$
That is completely correct! Thanks, you can formulate this as a proper answer, thank you.
$endgroup$
– Darkwizie
Dec 5 '18 at 19:28
add a comment |
1 Answer
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You can just define g to be $0$ on the range $[M,T]$ so that the integral is equal to the integral over the range $[0,T]$ and then you can apply the method you mentioned first.
answered Dec 5 '18 at 21:49
mathworker21mathworker21
8,9421928
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$begingroup$
You can just define g to be $0$ on the range $[M,T]$ so that the integral is equal to the integral over the range $[0,T]$ and then you can apply the method you mentioned first.
answered Dec 5 '18 at 21:49
mathworker21mathworker21
8,9421928
$endgroup$
add a comment |
$begingroup$
You can just define g to be $0$ on the range $[M,T]$ so that the integral is equal to the integral over the range $[0,T]$ and then you can apply the method you mentioned first.
answered Dec 5 '18 at 21:49
mathworker21mathworker21
8,9421928
$endgroup$
add a comment |
$begingroup$
You can just define g to be $0$ on the range $[M,T]$ so that the integral is equal to the integral over the range $[0,T]$ and then you can apply the method you mentioned first.
answered Dec 5 '18 at 21:49
mathworker21mathworker21
8,9421928
$endgroup$
You can just define g to be $0$ on the range $[M,T]$ so that the integral is equal to the integral over the range $[0,T]$ and then you can apply the method you mentioned first.
answered Dec 5 '18 at 21:49
mathworker21mathworker21
8,9421928
answered Dec 5 '18 at 21:49
mathworker21mathworker21
8,9421928
answered Dec 5 '18 at 21:49
mathworker21mathworker21
8,9421928
answered Dec 5 '18 at 21:49
mathworker21mathworker21
8,9421928
8,9421928
add a comment |
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can't you just define $g$ to be $0$ on the range $[M,T]$ so that the integral is equal to the integral over the range $[0,T]$ and then you can apply the method you mentioned first?
$endgroup$
– mathworker21
Dec 5 '18 at 16:41
$begingroup$
That is completely correct! Thanks, you can formulate this as a proper answer, thank you.
$endgroup$
– Darkwizie
Dec 5 '18 at 19:28