Digital Signal Processing with Kernel Methods

7Dual Signal Models for Signal Processing

7.1 Introduction

In this chapter, a third set of signal processing algorithms with kernels is introduced: the so‐called DSMs. The shared property among them is that the primal model consists of a nonlinear mapping from sampled or discrete time instants of a unidimensional time series to an RKHS in a conventional nonlinear regression signal model, and then one uses the kernel trick, and a time series expansion is stated in terms of a kernel comparing each two different time instants of the series. The use of autocorrelation kernels at this point, with well‐known properties in time and spectral domains, supports the generation of algorithms with underlying convolutional signal models, such as for classical sinc interpolation and nonblind deconvolution. Advanced topics on autocorrelation kernels are also given in terms of the fundamentals for spectrally adapted Mercer kernels for signal interpolation. In the second part of the chapter we give empirical evidence of the performance of these dual‐form signal processing models via dedicated tutorials and real‐life examples: HRV estimation, Doppler ultrasound processing for fault detection, Doppler cardiac images in M‐mode for heart‐filling monitoring, indoor location based on power measurements from mobile devices, and interpolation of cardiac meshes representations from cardiac navigation systems.

7.2 Dual Signal Model Elements

As explained in Chapter 4, and following the framework introduced ...