You need really one dimensional Fourier transform. In fact you need to transform function V which depends on time t and some parameters (x,y,z).

I think that it is possible to do this in Mathlab, but I'm working in Mathematica. In Mathematica you need just to specify the order of coordinates to carry on the transformation correctly. 

For example, i, j,k,l - integers which define the data in the array, assuming that tha i corresponds to x, j to y, k to z and l corresponds to time t. You have a function V. The needed transform is Vt = Fourier[ V[[i,j,k]] ].

If you need to make transformation just through the z - coordinate, then you need previously to do tranposing: Vtr=Transpose[V,{1,2,4,3}]  and after this Vz = Fourier[Vtr[[i,j,k]] ]. But in my example the number of points for each dimension is equal.

 Even if I did not completely understand what kind of information you want to retrieve, I might be able to help:

Computing to 2D FFT of a matrix X can be done by

Y = fft(fft(X).').'

Consequently a 3D FFT of a 3D matrix X should be done by computing

Y = fft(fft(fft(X).').').'

A fast way to get this done is the function fftn(). You can find examples for 3D FFT in the reference:

https://de.mathworks.com/help/matlab/ref/fftn.html

Yes, the DFT is separable so it can be done sequentially in each dimension. But interpreting your spectrum might be tricky. What kind of info were you hoping to obtain? You may want to apply some kind of taper before you apply the transform, to reduce spurious artifacts (i.e. sidelobes).