Digital Spectral Analysis provides a single source that offers complete coverage of the spectral analysis domain. This self-contained work includes details on advanced topics that are usually presented in scattered sources throughout the literature.
The theoretical principles necessary for the understanding of spectral analysis are discussed in the first four chapters: fundamentals, digital signal processing, estimation in spectral analysis, and time-series models.
An entire chapter is devoted to the non-parametric methods most widely used in industry.
High resolution methods are detailed in a further four chapters: spectral analysis by stationary time series modeling, minimum variance, and subspace-based estimators.
Finally, advanced concepts are the core of the last four chapters: spectral analysis of non-stationary random signals, space time adaptive processing: irregularly sampled data processing, particle filtering and tracking of varying sinusoids.
Suitable for students, engineers working in industry, and academics at any level, this book provides a rare complete overview of the spectral analysis domain.
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Yes, you can access Digital Spectral Analysis by Francis Castanié in PDF and/or ePUB format, as well as other popular books in Mathematics & Probability & Statistics. We have over one million books available in our catalogue for you to explore.
Every signal-processing tool is designed to be adapted to one or more signal classes and presents a degraded or even deceptive performance if applied outside this group of classes. Spectral analysis too does not escape this problem, and the various tools and methods for spectral analysis will be more or less adapted, depending on the class of signals to which they are applied.
We see that the choice of classifying properties is fundamental, because the definition of classes itself will affect the design of processing tools.
Traditionally, the first classifying property is the deterministic or non-deterministic nature of the signal.
1.1.1. Deterministic signals
The definitions of determinism are varied, but the simplest is the one that consists of calling any signal that is reproducible in the mathematical sense of the term as a deterministic signal, i.e. any new experiment for the generation of a continuous time signal x(t) (or discrete time x(k)) produces a mathematically identical signal. Another subtler definition, resulting from the theory of random signals, is based on the exactly predictive nature of x(t) t ≥ t0 from the moment that it is known for t < t0 (singular term of the Wold decomposition, e.g. see Chapter 4 and [LAC 00]). Here, we discuss only the definition based on the reproducibility of x(t), as it induces a specific strategy on the processing tools: as all information of the signal is contained in the function itself, any bijective transformation of x(t) will also contain all this information. Representations may thus be imagined, which, without loss of information, will demonstrate the characteristics of the signal better than the direct representation of the function x(t) itself.
The deterministic signals are usually separated into classes, representing integral properties of x(t), strongly linked to some quantities known by physicists.
Finite energy signals verify the integral properties in equations [1.1] and [1.2] with continuous or discrete time:
[1.1]
[1.2]
We recognize the membership of x(t) to standard function spaces (noted as L2 or l2), as well as the fact that this integral, to within some dimensional constant (an impedance in general), represents the energy E of the signal.
Signals of finite average power verify:
[1.3]
[1.4]
If we accept the idea that the sums of equation [1.1] or [1.2] represent “energies”, those of equation [1.3] or [1.4] then represent powers.
It is clear that these integral properties correspond to mathematical characteristics whose morphological behavior along the time axis is very different: the ...
