Fundamentals of Electronics 3 by Pierre Muret

Author:Pierre Muret
Language: eng
Format: epub
ISBN: 9781119522461
Publisher: John Wiley & Sons, Inc.
Published: 2018-04-30T00:00:00+00:00

1.4.7. Filtering and digital processing

The operations that correspond to the mathematical operations previously analyzed in this chapter can be implemented on digital data. We can classify them into two categories, depending on the number of variables upon which the result depends: (1) in the first category, operations which result in a sampled signal only depending on time kTe, or on the index of the time numbering k, and whose result can therefore be expressed by y[k]; (2) in the second category, operations whose final result depends on a second variable, other than the variable kTe, while the latter acts as an internal variable in the computation. The first category may refer to computations continuously flowing, also referred to as being “in real time” or in a “streaming” way, especially when the processing system is part of a chain in which the samples follow each other at the rate of the sampling period. The application of such a computational method is slightly more problematic in the second case because it requires the storage of intermediate results. All can be performed by computerized systems, which can be either digital signal processors (DSPs), or functions developed based on those available in instrumentation and signal-processing software and made autonomous (run time). The benefits or requirements to operate by means of computer or micro-computing systems are justified by the possibility of working in floating point, eventually with complex numbers, and using memory storage. It then becomes possible to exploit all the possibilities of computation, of software development, of adapting to external constraints by changing computational parameters and of taking advantage of the memory size that these systems offer. This solution is well suited to the methods of the second category in which the storage in memory of input samples or samples after intermediate computations is essential. It is also well adapted if the constraint of the delay due to computational times is not an imperative priority, as is the case for the processing of signals already recorded in digital format. On the other hand, this solution may result in limitations on the execution speed and on the implementation of micro-programmed circuits of excessive complexity with regard to the task to be achieved, especially in the case where processing should be incorporated into a fixed integrated circuit and without adjustable parameters, as frequently met in embedded electronics. On the other hand, there is the possibility to perform the methods of the first category using standard logic circuits, without recourse to micro-programming or a system for storing data or intermediate results. This case is presented in the following section. The operations of the second category are then briefly discussed.

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