TABLE OF CONTENTS Chapter written by Dominique MILLER.
When carrying out numerical analysis in real time, it is not enough to sample the signal to be analyzed at a rhythm that complies with Shannon's criterion. It is also necessary to calculate at a speed compatible with the flow of the incoming samples. If, for a sampling frequency fe, we make M basic operations [1] between each sampling, the necessary calculation power is M f e, expressed in MOPS (millions of operations per second). This calculation power is a datum of the processor being used and is a compromise between the sampling frequency and the sophistication of the chosen analysis. But the lower the sampling frequency, the higher the order of the anti-folding filter; [2] thus it will be difficult to integrate into the numerical system. The popular technique currently used to solve this issue (over-sampling and decimation) is discussed at length in this chapter. Part of this discussion will deal with ? - ? analog-to-digital converters using this technique. This will lead us into a presentation of implanting digital filters in cabled or programmed models (these can be comb or half-band filters).
In this chapter, we will only discuss "real" signals, that is, those with a physical existence. It is also quite often a question of limited spectrum signals. These are signals with a spectrum assumed to be zero outside a band [ f min f max]. From a mathematical...
