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In realtime systems and any system where data is processed as it arrives the values of the future samples are not known. This is as in an analogue system where we send for example a signal into an amplifier and it needs to process it as it arrives. The amplifier won't know if the next music track is Mozart or Jimmy Hendrix. It just needs to react to what it's fed into it.
However, the Fourier Transform is not real time. We need the whole signal from the first to the last sample. For that reason we need to develop a new mathematical framework which we call “Causal Signal Processing”. These systems should ideally react to an incoming signal as an analogue system does, namely as fast as possible with little latency as possible.
In the next section we are now developing a mathematical framework for causal digital signal processing. We draw here heavily from analoge circuit design as this is by its own nature performs realtime causal processing.
