Fourier transformation on discrete function

KFC
Messages
477
Reaction score
4
Hi there,
I am reading a material on the application of Fourier transformation in physics. One application is to transform the position-dependent function to k-dependent function, i.e.## F(k) = FFT[f(x)]##

We know that the in physics, the wavenumber could be written in momentum as ##k=p/\hbar##. My question is if I have a discrete function

##f(x) = {f_0, f_1, ... f_{N-1}, f_N}##

which doesn't have close form but just given by a simulation. If I do the discrete Fourier transformation, I can have the discrete ##F(k)## but is that any way to obtain ##F(p)## from ##F(k)##?
 
Mathematics news on Phys.org
Thanks for the post! Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
 
It is possible to take a continuous FT of a function of a discrete variable. Look up the DTFT, "discrete time Fourier transform."
 
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
Thread 'Imaginary Pythagorus'
I posted this in the Lame Math thread, but it's got me thinking. Is there any validity to this? Or is it really just a mathematical trick? Naively, I see that i2 + plus 12 does equal zero2. But does this have a meaning? I know one can treat the imaginary number line as just another axis like the reals, but does that mean this does represent a triangle in the complex plane with a hypotenuse of length zero? Ibix offered a rendering of the diagram using what I assume is matrix* notation...

Similar threads

Back
Top