A Fourier coefficients relation to Power Spectral Density

Skaiserollz89
Messages
9
Reaction score
0
TL;DR Summary
Help deriving a result found in "Numerical Simulation of Optical Wave Propagation" by Jason Schmidt. I'm trying to work out by hand an equation stating that the ensemble average of the squared fourier coefficients of a 2D phase function equals the Power Spectral Density( Phi(fx,fy) multiplied by 1/A, where A is the domain area ( either delta_fx*delta_fy in frequency space, or 1/(L_x*L_y) in real space). I am having trouble seeing how to get this result. Please assist in the derivation.
1685548399868.png

1685548469321.png

1685548546562.png
 
Physics news on Phys.org
Thread 'Is there a white hole inside every black hole?'

Thread 'Is there a white hole inside every black hole?'

This is what I am thinking. How much feasible is it? There is a white hole inside every black hole The white hole spits mass/energy out continuously The mass/energy that is spit out of a white hole drops back into it eventually. This is because of extreme space time curvature around the white hole Ironically this extreme space time curvature of the space around a white hole is caused by the huge mass/energy packed in the white hole Because of continuously spitting mass/energy which keeps...
View full post »

Thread 'Is Gravity an entropic property like Surface Tension'

Why do two separately floating objects in a liquid "attract" each other ?? What if gravity is an emergent property like surface tension ? What if they both are essentially trying to *minimize disorder at the interfaces — where non-aligned polarized particles are forced to mix with each other* What if gravity is an emergent property that is trying to optimize the entropy emerging out of spin aligned quantum bits
View full post »

Similar threads

Relationship between Fourier coefficients and power spectral density
Replies
1
Views
2K
I Is this the Fourier Number, or some other formula?
Replies
2
Views
3K
Characterize Fourier coefficients
Replies
2
Views
2K
Fourier transform of PSD
Replies
4
Views
1K
Integral of sinc function using Fourier series
Replies
6
Views
1K
Trigonometric Polynomial vs Fourier Polynomial
Replies
25
Views
1K
MATLAB Turning Fourier coefficients into an interpolated freq domain function
Replies
8
Views
2K
I On differentiability and Fourier coefficients (Vretblad's text)
Replies
4
Views
2K
Understanding Fourier Coefficients in the Fourier Transform of a Function
Replies
9
Views
2K
A few questions to make sure I understand Fourier series
Replies
3
Views
2K

Hot Threads

Recent Insights

Back
Top