# discrete fourier transform in Matlab - theoretical confusion

I have a periodic term $V(x) = \sum_K \exp(iKx) V_K$ where $K =2\pi n/a$ where $a$ is the periodicity of the term and $n =0,1,2,3....$

Now I want to find the Fourier coefficient $V_K$ corresponding to a particular $K$. Suppose I have a vector for $V(x)$ having $10000$ points for $x = 0,0.01a,0.02a,...a,1.01a,....2a....100a$ such that the size of my lattice is $100a$.

FFT on this vector gives $10000$ Fourier coefficients. The $K$ values corresponding to these Fourier coefficients are $2\pi n/(10000*0.01a)$ with $n=0,1,2,3,...9999$. But my $K$ had the form $2\pi n/a$ due to the periodicity of the lattice.

What am I missing ?

• MATLAB doesn't do indices less than 1. anyway, i cannot decode the question. – robert bristow-johnson Feb 26 '14 at 15:56
• read this for clarity physics.stackexchange.com/questions/100923/… – cleanplay Feb 26 '14 at 16:30
• first of all, LaTeX equation markup works just as well here as it does at the physics se. second of all, your "clarity" post is no better, except it uses LaTeX markup. make sure you express your summations with integer indices and make clear what the independent variable is (is it $x$? then call it "$V(x)$".) usually once the math is cleaned up and the question is made explicit, answers become clear. – robert bristow-johnson Feb 26 '14 at 17:52
• made the changes as you mentioned, at the physics.se – cleanplay Feb 26 '14 at 19:01
• This topic was also in addition to the phyisics site already extensively discussed at the duplicate (stackoverflow.com/q/22026363/3088138) – Lutz Lehmann Feb 28 '14 at 15:23