Filtering practice - Digital linear filtering

This work was born out of the need to make available to engineers and technicians a wide range of current filtering methods. It also aims to demystify aspects considered abstruse by providing keys to good practice in filtering operations.

In 1988, the late Jacques Max, scientific assistant at the Commissariat à l'énergie Atomique in Grenoble, wrote a very interesting contribution to "Techniques de l'Ingénieur" on the practice of digital filtering: our article is part of an effort to complement and extend the practice of filtering to recent developments in one- and two-dimensional digital linear filtering.

But what is filtering?

Filtering is an operation that consists in transforming the information (contained in a signal) at the input of a hardware or software system into output information that is different from the original information, but more useful to the experimenter.

In the case of a one- or two-dimensional signal, this transformation can take the form, for example, of either the selection or elimination of certain frequencies, or the reduction or even suppression of unwanted information. Examples include white light being transformed into blue light, or an e-mail or website being blocked or "filtered" by an electronic device or computer code acting according to certain criteria. The extraction or estimation of relevant information and useful characteristics can also be considered as filtering.

After a review of the fundamental concepts of signal digitization, and the use of analysis tools specific to digital systems, methods for synthesizing FIR (finite impulse response) and IIR (infinite impulse response) digital linear filters will be presented in a simplified form and implemented in MATLAB. The advantages and limitations of these two types of filter will also be analyzed. Two applications illustrating the use of these filters in the real world are proposed: one on global warming and the other in the audio field.

We'll then focus on optimal filtering, especially recursive filtering, which is of vital practical importance, for example in the field of Radar and target tracking in the presence of strong disturbances, or in the biomedical field.

The extension of linear filtering to digital images is illustrated in smoothing, sharpening, denoising and edge detection.

Throughout this article, the reader is provided with numerous examples and application exercises to illustrate the results obtained: the examples always have a pedagogical purpose or an approach to the concrete with a view to creating a "tailor-made" filter. MATLAB codes are provided to enable the experimenter to put filtering into practice....