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Is it possible to fourier analyze a hill function?
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In mathematical models of genetic transcriptional circuits, you get a lot of differential equations of the form:
$$ fracdp(t)dt = k frac a(t) 1 + a(t)$$
Is there any way to fourier analyze this differential equation in $a(t)$ and $p(t)$ - without linearizing? I'd like to examine $P(omega)$ as a response of $A(omega)$.
There doesn't seem to be a way.
$$ frac12pi int_-infty^infty iomega P(omega)e^iomega t domega = k fracfrac12piint_-infty^infty A(omega)e^iomega t domega1 + frac12pi int_-infty^inftyA(omega) e^iomega t domega $$
Is there some kind of Fourier Analysis chain rule I could use?
fourier-analysis
asked Jul 20 at 20:40
Mike Flynn
5611517
add a comment |Â
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0
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In mathematical models of genetic transcriptional circuits, you get a lot of differential equations of the form:
$$ fracdp(t)dt = k frac a(t) 1 + a(t)$$
Is there any way to fourier analyze this differential equation in $a(t)$ and $p(t)$ - without linearizing? I'd like to examine $P(omega)$ as a response of $A(omega)$.
There doesn't seem to be a way.
$$ frac12pi int_-infty^infty iomega P(omega)e^iomega t domega = k fracfrac12piint_-infty^infty A(omega)e^iomega t domega1 + frac12pi int_-infty^inftyA(omega) e^iomega t domega $$
Is there some kind of Fourier Analysis chain rule I could use?
fourier-analysis
asked Jul 20 at 20:40
Mike Flynn
5611517
You seem to believe that the Fourier transform of $a/(1+a)$ is $A/(1+A)$. This is wrong.
– Julián Aguirre
Jul 24 at 16:39
Well there is a difference between $A/(1 + A)$ and $int A e^iomega d omega/ left [ 2pi + int A e^iomega t d omega right ]$ right? I'm trying to substitute in the inverse Fourier transform. Though I agree that the forward direction is probably better.
– Mike Flynn
Jul 24 at 18:31
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
In mathematical models of genetic transcriptional circuits, you get a lot of differential equations of the form:
$$ fracdp(t)dt = k frac a(t) 1 + a(t)$$
Is there any way to fourier analyze this differential equation in $a(t)$ and $p(t)$ - without linearizing? I'd like to examine $P(omega)$ as a response of $A(omega)$.
There doesn't seem to be a way.
$$ frac12pi int_-infty^infty iomega P(omega)e^iomega t domega = k fracfrac12piint_-infty^infty A(omega)e^iomega t domega1 + frac12pi int_-infty^inftyA(omega) e^iomega t domega $$
Is there some kind of Fourier Analysis chain rule I could use?
fourier-analysis
asked Jul 20 at 20:40
Mike Flynn
5611517
In mathematical models of genetic transcriptional circuits, you get a lot of differential equations of the form:
$$ fracdp(t)dt = k frac a(t) 1 + a(t)$$
Is there any way to fourier analyze this differential equation in $a(t)$ and $p(t)$ - without linearizing? I'd like to examine $P(omega)$ as a response of $A(omega)$.
There doesn't seem to be a way.
$$ frac12pi int_-infty^infty iomega P(omega)e^iomega t domega = k fracfrac12piint_-infty^infty A(omega)e^iomega t domega1 + frac12pi int_-infty^inftyA(omega) e^iomega t domega $$
Is there some kind of Fourier Analysis chain rule I could use?
fourier-analysis
asked Jul 20 at 20:40
Mike Flynn
5611517
asked Jul 20 at 20:40
Mike Flynn
5611517
asked Jul 20 at 20:40
Mike Flynn
5611517
asked Jul 20 at 20:40
Mike Flynn
5611517
5611517
You seem to believe that the Fourier transform of $a/(1+a)$ is $A/(1+A)$. This is wrong.
– Julián Aguirre
Jul 24 at 16:39
Well there is a difference between $A/(1 + A)$ and $int A e^iomega d omega/ left [ 2pi + int A e^iomega t d omega right ]$ right? I'm trying to substitute in the inverse Fourier transform. Though I agree that the forward direction is probably better.
– Mike Flynn
Jul 24 at 18:31
add a comment |Â
You seem to believe that the Fourier transform of $a/(1+a)$ is $A/(1+A)$. This is wrong.
– Julián Aguirre
Jul 24 at 16:39
Well there is a difference between $A/(1 + A)$ and $int A e^iomega d omega/ left [ 2pi + int A e^iomega t d omega right ]$ right? I'm trying to substitute in the inverse Fourier transform. Though I agree that the forward direction is probably better.
– Mike Flynn
Jul 24 at 18:31
You seem to believe that the Fourier transform of $a/(1+a)$ is $A/(1+A)$. This is wrong.
– Julián Aguirre
Jul 24 at 16:39
You seem to believe that the Fourier transform of $a/(1+a)$ is $A/(1+A)$. This is wrong.
– Julián Aguirre
Jul 24 at 16:39
Well there is a difference between $A/(1 + A)$ and $int A e^iomega d omega/ left [ 2pi + int A e^iomega t d omega right ]$ right? I'm trying to substitute in the inverse Fourier transform. Though I agree that the forward direction is probably better.
– Mike Flynn
Jul 24 at 18:31
Well there is a difference between $A/(1 + A)$ and $int A e^iomega d omega/ left [ 2pi + int A e^iomega t d omega right ]$ right? I'm trying to substitute in the inverse Fourier transform. Though I agree that the forward direction is probably better.
– Mike Flynn
Jul 24 at 18:31
add a comment |Â
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You seem to believe that the Fourier transform of $a/(1+a)$ is $A/(1+A)$. This is wrong.
– Julián Aguirre
Jul 24 at 16:39
Well there is a difference between $A/(1 + A)$ and $int A e^iomega d omega/ left [ 2pi + int A e^iomega t d omega right ]$ right? I'm trying to substitute in the inverse Fourier transform. Though I agree that the forward direction is probably better.
– Mike Flynn
Jul 24 at 18:31