Signal Processing Models

This chapter conveys the ideas from digital signal processing (DSP) to be clearly kept in mind when working on kernel‐based signal processing algorithms. It presents the basic concepts of signal Hilbert spaces, noise, and optimization. The chapter provides a brief overview of vector spaces and basis. It discusses the general signal model and introduces specific signal models for the most common problems in DSP; namely, nonparametric spectral estimation, system identification, interpolation, deconvolution, and array processing. The chapter then introduces two signal models for system identification that will be used in the following chapters when dealing with kernel functions; namely, the autoregressive exogenous (ARX) signal model and a particular instantiation of an autoregressive moving average model (ARMA) filter called the γ‐filter. It further presents the state‐space models and signal models which are used for recursion in many DSP applications. Finally, the chapter discusses the main aspects of the signal models encountered in DSP.