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2 votes
0 answers
45 views

How to extract the "matter fluctuation amplitude" from the CMB power spectrum?

How do you convert the value listed in Planck 2018 results. VI. Cosmological parameters, $A_s = 2.101\times10^{-9}$ to the value of the matter fluctuation amplitude $\sigma_8=0.8111$? I tried ...
Finerichmen's user avatar
1 vote
1 answer
85 views

Evaluate action of $f(\frac{d}{dx})$ using the Fourier/Laplace transform

Initially I asked this question on mathoverflow. I however thought physicists may face this sort of problem more than mathematicians (I am an engineer). Due to that, I decided to ask here as well. ...
Mirar's user avatar
  • 213
0 votes
0 answers
43 views

FFT on a signal with a length that is not a multiple of the period of its harmonics

I was very surprised to find an apparent limitation to a FFT on a simple signal. Let's consider a timeseries made of L=100 points, and simply composed of the sum of two sinus waves: one with a ...
François Ritter's user avatar
1 vote
1 answer
183 views

Power Spectrum Density of real valued time series data

There are real valued time-series data X(t) and corresponding auto-correlation function ACF(t)=$\left<X(0)X(t)\right>$. As written in wikipedia, Power Spectrum Density (PSD) can be calculated ...
Ji woong Yu's user avatar
0 votes
0 answers
282 views

Measuring typical distance between patches using 2D Fourier Transform

I need to extract information about the typical distance between the black patches in an image like the one I attached here. I tried to perform 2D FFT on it (using OpenCF fdt function in Python), but ...
Ohm's user avatar
  • 133