Digital signal processing — Deterministic signals

The word signal refers to a series of observations indexed by an ordered sequence of real or integer values, usually time. When the index is in (R), we speak of a continuous-time or analog signal. If it is in (N) or (Z), we speak of a discrete-time or digital signal.

Digital signal processing, or DSP for short, is the processing of discrete-time signals. As in many other fields, the emergence of DSP is linked to the development of powerful computing resources, which have opened up its field of application to increasingly complex problems. Just look at "consumer" applications such as "high-definition television", "digital broadcasting", "mobile telephony", "multimedia applications" and so on. All these services make extensive use of digital signal processing, implementing algorithms that sometimes require considerable computing power. Here are just a few examples:

• background noise suppression during a telephone transmission from the passenger compartment of a car;

• cell phone signal processing ;

• image and speech coding in a videophone system ;

• speech recognition and synthesis ;

• mechanical part fault detection and preventive maintenance;

• sonar location of fish shoals;

• radar evaluation of target position and speed;

• seismic profile inversion for oil exploration ;

• vibration analysis of an oil platform;

• analysis of electroencephalographic signals to aid medical diagnosis;

• reception of information from the GPS satellite navigation system;

• electronic synthesis of musical sounds ;

• processing acoustic signals from multiple microphones, etc.

Some of these issues have not yet been satisfactorily resolved, and are still under investigation. In addition to the complexity of the problems it tackles, TNS offers great flexibility in the development phase . Tests are perfectly reproducible. There is no risk of drift in component characteristics, as is the case with analog processing. Does this mean that analog processing is irretrievably doomed? In fact, even if their share is constantly...