The ordinary Fourier Transform is for a continuous function. The continuous Fourier Transform is difficult to use in real time because in real time, one is dealing with discrete data sampled using some kind of sensors. For instance, the time series from weather, traffic, stocks etc., one is getting the discrete values at each time point (e.g. 1-s, 2-s, 3-s etc.) and one does not know what is in between those samples. One just needs to infer. That is why it is better to have a high sampling frequency of say 100 samples per second instead of 1 sample per second so as to have a more accurate approximation of the real data.