Fundamentals of Instrumentation and Measurement

Chapter 6¹

Real-time Data Acquisition and Processing Systems

6.1 Introduction

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 operations¹ between each sampling, the necessary calculation power is M · fe, 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 Σ - Δ 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 point of view, limited spectrum “real” signals ...