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 space...

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Veröffentlicht in:Digital Signal Processing with Kernel Methods S. 97 - 164
Hauptverfasser: Rojo-Álvarez, José Luis, Martínez-Ramón, Manel, Muñoz-Mar&iacute, Jordi, Camps-Valls, Gustau
Format: Buchkapitel
Sprache:Englisch
Veröffentlicht: Chichester, UK Wiley 2018
John Wiley & Sons, Ltd
Ausgabe:1
Schriftenreihe:Wiley - IEEE
Schlagworte:
autoregressive exogenous signal model
autoregressive moving average model
digital signal processing
Hilbert spaces
kernel functions
kernel‐based signal processing algorithms
vector spaces
Correlation
Signal processing algorithms
Estimation
Signal processing
Hilbert space
Data models
Kernel
ISBN:9781118611791, 1118611799
Online-Zugang:Volltext
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Beschreibung
Zusammenfassung: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.
ISBN:9781118611791
1118611799
DOI:10.1002/9781118705810.ch3