Statistical Signal Processing in Engineering

Why are there so many matrixes in this book?

Any textbook or journal in advanced signal processing investigates methods to solve large scale problems where there are multiple signals, variables, and measurements to be manipulated. In these situations, matrix algebra offers tools that are heavily adopted to compactly manage a large set of variables and this is a necessary background.¹ An example application can justify this statement.

The epicenter in earthquakes is obtained by measuring the delays at multiple positions, and by finding the position that best explains the collected measurements (in jargon, data). Figure 1 illustrates an example in 2D with epicenter at coordinates . At the time the earthquake occurs, it generates a spherical elastic wave that propagates with a decaying amplitude from the epicenter, and hits a set of N geophysical sensing stations after propagation through a medium with velocity v (typical values are 2000–5000 m/s for shear waves, and above 4000 m/s for compressional, or primary, waves). The signals at the sensing stations are (approximately) a replica of the same waveform as in the Figure 1 with delays x₁, x₂, …, x_N that depend on the propagating distance from the epicenter to each sensing station. The correspondence of each delay with the distance from the epicenter depends on the physics of propagation of elastic waves in a solid, and it is called ...