Rectangle function and integration The Next CEO of Stack OverflowThe value of improper integral $xexp(-lambda x^2), dx$finding intervals for double integrals integrationProbability Density Function (Integration)Integration with probability density functionIntegral for a function with several casesHelp in finding fourier integral representation.Fourier transform of rectWhy is $operatornamerect(frac12-sqrtw) = operatornamerect(w-frac12)$Fourier transformation of $e^-at$ from $0$ to $T$Problem with the fourier transform of sinc
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Rectangle function and integration
The Next CEO of Stack OverflowThe value of improper integral $xexp(-lambda x^2), dx$finding intervals for double integrals integrationProbability Density Function (Integration)Integration with probability density functionIntegral for a function with several casesHelp in finding fourier integral representation.Fourier transform of rectWhy is $operatornamerect(frac12-sqrtw) = operatornamerect(w-frac12)$Fourier transformation of $e^-at$ from $0$ to $T$Problem with the fourier transform of sinc
$begingroup$
There are given:
$$mboxrect(f/2a)=left{beginmatrix
1, & -a<f<a\
0,5 &beginvmatrix
f
endvmatrix=a \
0& beginvmatrix
f
endvmatrix>a
endmatrixright.$$
$V(f,t)$
and I should find:
$$int_infty^-inftyV(f,t) cdot mboxrect(f/2a) e^j pi f t$$
I have started my solution with:
$$int_infty^-inftyV(f,t)cdot mboxrect(f/2a) e^j pi f t=int_a^-aV(f,t) e^j pi f t$$
Is it correct?
integration fourier-transform rectangles
edited Mar 20 at 8:48
postmortes
2,20031422
asked Mar 20 at 8:36
LenaParkLenaPark
83
$endgroup$
add a comment |
$begingroup$
There are given:
$$mboxrect(f/2a)=left{beginmatrix
1, & -a<f<a\
0,5 &beginvmatrix
f
endvmatrix=a \
0& beginvmatrix
f
endvmatrix>a
endmatrixright.$$
$V(f,t)$
and I should find:
$$int_infty^-inftyV(f,t) cdot mboxrect(f/2a) e^j pi f t$$
I have started my solution with:
$$int_infty^-inftyV(f,t)cdot mboxrect(f/2a) e^j pi f t=int_a^-aV(f,t) e^j pi f t$$
Is it correct?
integration fourier-transform rectangles
edited Mar 20 at 8:48
postmortes
2,20031422
asked Mar 20 at 8:36
LenaParkLenaPark
83
$endgroup$
$begingroup$
What is the question? Your step is correct, given the definition of rect, except that the limits of integration are reversed.
$endgroup$
– Chrystomath
Mar 20 at 11:03
$begingroup$
@Chrystomath I am not sure in the changing the interval of integration with such rect function.
$endgroup$
– LenaPark
Mar 20 at 12:21
$begingroup$
@Chrystomath Is my last equation correct?
$endgroup$
– LenaPark
Mar 20 at 12:23
$begingroup$
What are you integrating against exactly? $t$ or $f$?
$endgroup$
– Chrystomath
Mar 20 at 16:19
add a comment |
$begingroup$
There are given:
$$mboxrect(f/2a)=left{beginmatrix
1, & -a<f<a\
0,5 &beginvmatrix
f
endvmatrix=a \
0& beginvmatrix
f
endvmatrix>a
endmatrixright.$$
$V(f,t)$
and I should find:
$$int_infty^-inftyV(f,t) cdot mboxrect(f/2a) e^j pi f t$$
I have started my solution with:
$$int_infty^-inftyV(f,t)cdot mboxrect(f/2a) e^j pi f t=int_a^-aV(f,t) e^j pi f t$$
Is it correct?
integration fourier-transform rectangles
edited Mar 20 at 8:48
postmortes
2,20031422
asked Mar 20 at 8:36
LenaParkLenaPark
83
$endgroup$
There are given:
$$mboxrect(f/2a)=left{beginmatrix
1, & -a<f<a\
0,5 &beginvmatrix
f
endvmatrix=a \
0& beginvmatrix
f
endvmatrix>a
endmatrixright.$$
$V(f,t)$
and I should find:
$$int_infty^-inftyV(f,t) cdot mboxrect(f/2a) e^j pi f t$$
I have started my solution with:
$$int_infty^-inftyV(f,t)cdot mboxrect(f/2a) e^j pi f t=int_a^-aV(f,t) e^j pi f t$$
Is it correct?
integration fourier-transform rectangles
integration fourier-transform rectangles
edited Mar 20 at 8:48
postmortes
2,20031422
asked Mar 20 at 8:36
LenaParkLenaPark
83
edited Mar 20 at 8:48
postmortes
2,20031422
asked Mar 20 at 8:36
LenaParkLenaPark
83
edited Mar 20 at 8:48
postmortes
2,20031422
edited Mar 20 at 8:48
postmortes
2,20031422
edited Mar 20 at 8:48
postmortes
2,20031422
2,20031422
asked Mar 20 at 8:36
LenaParkLenaPark
83
asked Mar 20 at 8:36
LenaParkLenaPark
83
asked Mar 20 at 8:36
LenaParkLenaPark
83
83
$begingroup$
What is the question? Your step is correct, given the definition of rect, except that the limits of integration are reversed.
$endgroup$
– Chrystomath
Mar 20 at 11:03
$begingroup$
@Chrystomath I am not sure in the changing the interval of integration with such rect function.
$endgroup$
– LenaPark
Mar 20 at 12:21
$begingroup$
@Chrystomath Is my last equation correct?
$endgroup$
– LenaPark
Mar 20 at 12:23
$begingroup$
What are you integrating against exactly? $t$ or $f$?
$endgroup$
– Chrystomath
Mar 20 at 16:19
add a comment |
$begingroup$
What is the question? Your step is correct, given the definition of rect, except that the limits of integration are reversed.
$endgroup$
– Chrystomath
Mar 20 at 11:03
$begingroup$
@Chrystomath I am not sure in the changing the interval of integration with such rect function.
$endgroup$
– LenaPark
Mar 20 at 12:21
$begingroup$
@Chrystomath Is my last equation correct?
$endgroup$
– LenaPark
Mar 20 at 12:23
$begingroup$
What are you integrating against exactly? $t$ or $f$?
$endgroup$
– Chrystomath
Mar 20 at 16:19
$begingroup$
What is the question? Your step is correct, given the definition of rect, except that the limits of integration are reversed.
$endgroup$
– Chrystomath
Mar 20 at 11:03
$begingroup$
What is the question? Your step is correct, given the definition of rect, except that the limits of integration are reversed.
$endgroup$
– Chrystomath
Mar 20 at 11:03
$begingroup$
@Chrystomath I am not sure in the changing the interval of integration with such rect function.
$endgroup$
– LenaPark
Mar 20 at 12:21
$begingroup$
@Chrystomath I am not sure in the changing the interval of integration with such rect function.
$endgroup$
– LenaPark
Mar 20 at 12:21
$begingroup$
@Chrystomath Is my last equation correct?
$endgroup$
– LenaPark
Mar 20 at 12:23
$begingroup$
@Chrystomath Is my last equation correct?
$endgroup$
– LenaPark
Mar 20 at 12:23
$begingroup$
What are you integrating against exactly? $t$ or $f$?
$endgroup$
– Chrystomath
Mar 20 at 16:19
$begingroup$
What are you integrating against exactly? $t$ or $f$?
$endgroup$
– Chrystomath
Mar 20 at 16:19
add a comment |
0
active
oldest
votes
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$begingroup$
What is the question? Your step is correct, given the definition of rect, except that the limits of integration are reversed.
$endgroup$
– Chrystomath
Mar 20 at 11:03
$begingroup$
@Chrystomath I am not sure in the changing the interval of integration with such rect function.
$endgroup$
– LenaPark
Mar 20 at 12:21
$begingroup$
@Chrystomath Is my last equation correct?
$endgroup$
– LenaPark
Mar 20 at 12:23
$begingroup$
What are you integrating against exactly? $t$ or $f$?
$endgroup$
– Chrystomath
Mar 20 at 16:19