Filtering and estimation

This course is a continuation of the continuous signal and digital signal processing courses taught in previous semesters.
The aim of this course is to propose a methodology for carrying out an estimation approach in signal processing that can be developed at BAC+4, based on basic concepts such as Fourier transform, windowing and linear filtering. This approach can be useful for carrying out signal classification approaches based on the extraction of "signatures" and machine learning-type approaches.
To this end, aspects of temporal, frequency (from the Fourier transform of a continuous-time signal to the periodogram) and time-frequency (spectrogram) characterization are initially covered. Additional information on the catacterization of linear filters is also given.
Then, based on a speech processing example, we propose to model the signal, justifying the choice of model, and then to estimate the model parameters. The interest of this approach is highlighted for the compression and classification of speech signals.
Finally, while the digital signal processing course of semester 7 is based on the characterization of linear filters (RIF/RII, causality, etc.), we address the synthesis of digital filters through different methods. Finally, we introduce the concept of matched filtering.

notions of signal processing and possibly continuous filter synthesis (reminders of the latter are provided in the course material)

1. Reminders
2. RIF filters: frequency characterization, synthesis methods with reminders about windows.
3. RII filters: characterization, stability study, synthesis methods (bilinear transformation, impulse response invariance).
4. Choice of structures (direct, parallel, cascade) and problems related to finite precision.
5. Applications.

Course handout.