transforming a power spectrum into a correlation function

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Florian Beutler
Posts: 8
Joined: January 18 2010
Affiliation: student

transforming a power spectrum into a correlation function

Post by Florian Beutler » January 18 2010

Hi everyone
I am trying since a few days to transform a power spectrum into a correlation function. First I used the software fftlog which is recommended also in this forum. However I didn't get it to work so if anybody has a working example for fftlog I would be interested to see it...
I then implemented a numerical integration by myself which worked out fine (more or less). I have a power law and I can see the BAO peak at 100Mpc. However it is very noisy at large scales. I think I can improve that by using a power spectrum with more data points. I used CAMB to get a matter power spectrum and I can't find out how to increase the data points for this software... so my questions are

1. How can I modify the number of data points in the matter power spectrum output of CAMB
2. Since I am still interested in getting fftlog to work, has anybody implemented this kind of transformation already and can send me an example code?

thank you very much
and best regards
florian

Donghui Jeong
Posts: 3
Joined: June 01 2005
Affiliation: JHU
Contact:

transforming a power spectrum into a correlation function

Post by Donghui Jeong » January 19 2010

1. How can I modify the number of data points in the matter power spectrum output of CAMB

Increase the "transfer_k_per_logint" parameter

2. Since I am still interested in getting fftlog to work, has anybody implemented this kind of transformation already and can send me an example code?

I don't know what fftlog is, but why don't you use the code in CRL? You can find the correlation function code in the following URL:
http://gyudon.as.utexas.edu/~komatsu/CR ... nfunction/

Florian Beutler
Posts: 8
Joined: January 18 2010
Affiliation: student

transforming a power spectrum into a correlation function

Post by Florian Beutler » January 21 2010

Hi Donghui Jeong
thanks for your answer...

The parameter transfer_kper_logint only affects the spline spacing of the transfer function, not the output P(k).

The program you mentioned is quite good but it has similar problems as my own program since it is limited by the spacing of the matter power spectrum. Hence I am still interested to find out how to change the spacing of the output matter power spectrum in CAMB.
thanks
florian

Donghui Jeong
Posts: 3
Joined: June 01 2005
Affiliation: JHU
Contact:

transforming a power spectrum into a correlation function

Post by Donghui Jeong » January 22 2010

Hi Florian,

1. The parameter transfer_kper_logint only affects the spline spacing of the transfer function, not the output P(k).

>> Right, but you can calculate the power spectrum from transfer function. As you may know, P(k) = A k^ns T2(k), where A can be fixed by setting σ8.

2. it has similar problems as my own program since it is limited by the spacing of the matter power spectrum.

>> I read your original posting again and realized that the spacing in kspace is not a cause of the noise in your correlation function. I think you want to increase the maximum wave number in your integration in order to get the smooth correlation function. Probably kmax~3*R is enough for W(R)=exp(-k2*R2/2).

Cheers,
Donghui

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