Precompute parts of an FFT on streamed data inputs I've implemented Radix-2 &amp; Radix-4, DIT &amp; DIF variants of the cooley-tukey FFT algorithm and they perform well on test data.

Now for a project, my algorithms will be applied to a real-time data stream of complex values. My current approach is window-based, meaning that I'm creating a buffer that stores values in a 2d array for a certain amount of time and after that, the FFT is applied to the matrix stored in the buffer.

As far as my understanding of the algorithm goes (having implemented it and read some papers on DFT/FFT in general but no prior experience in DSP), there is no way of speeding this up by doing some computation live as the data points arrive in the stream connector?

I was wondering if this is correct since I did not find any literature/paper that does this. Any hint is appreciated.

Edit: Example for clarification

Say my input is a Matrix of size N x N of complex numbers and I'm getting the values one point at a time from the data stream, can I do anything more than just buffering them in a 2d array and doing the FFT after a certain time.
A sliding DFT can be used to compute the equivalent of a new FFT as each input element arrives.  However, the cost of a sliding DFT is O(N^2), not O(NLogN).