Real time with DFT is a bit sketchy. Just view it as a matrix vector multiplication. The vector is the sampled signal at discrete time steps of equal spacing, t

Real time with DFT is a bit sketchy. Just view it as a matrix vector multiplication. The vector is the sampled signal at discrete time steps of equal spacing, the matrix is the DFT of fixed size. You need to fill your vector before the multiplication. This time needs to pass. You might shift it by just one value in time to create a sliding DFT, but nonetheless you will need to sample your time vector first. The length of each chunk is fixed by the size of the DFT. Let's say it is 1 millisecond long, each sample is 1 microsecond spaced, so it has a length of 1000. You may then create a spectrogram that captures 1 millisecond and then advances by 1 microsecond every step and this will be as close as real time as you can get. The initial delay of your analysis vector, then advancing by one sample, plus all the time you need for the calculations included cause a delay. Although this is sometimes called real time DFT. Since you may observe the change in the signal basically in real time, but after some delay. It is always done in chunks. Hope this helps.