Statistical spectral analysis : a nonprobabilistic theory

  title={Statistical spectral analysis : a nonprobabilistic theory},
  author={William A. Gardner},
This book presents a general theory and methodology for empirical spectral analysis. The treatment is original because it does not make use of the difficult concept of ergodicity to provide a link between the empirical methods and the abstract probabilistic theory of stochastic processes. Instead, it shows that all the concepts and methods of empirical spectral analysis can be explained in a more straightforward fashion in terms of a deterministic theory: a theory based on time-averages of a… 
Central Limit Theorem in the Functional Approach
The central limit theorem is proved within the framework of the functional approach for signal analysis, showing that if a sequence of independent signals fulfills some mild regularity assumptions, then the asymptotic distribution of the appropriately scaled average of such signals has a limiting normal distribution.
Stochastic time-frequency analysis using the analytic signal: why the complementary distribution matters
The fact that the analytic signal constructed from a nonstationary real signal is, in general, improper, which means that its complementary correlation function is nonzero is stressed.
On the spectral correlation measurement of nonstationary stochastic processes
  • A. Napolitano
  • Mathematics
    Conference Record of Thirty-Fifth Asilomar Conference on Signals, Systems and Computers (Cat.No.01CH37256)
  • 2001
In this paper, the problem of the single sample-path based spectral correlation measurement for a new class of nonstationary stochastic processes is addressed. Processes belonging to this class,
Foundations of the functional approach for signal analysis
Spectral Theory for Periodically and Almost Periodically Correlated Random Processes: A Survey
This paper contains a survey of the spectral theory of periodically correlated and almost periodically correlated stochastic processes. These processes are also called cyclostationary and almost
Asymptotic theory of mixed time averages and k th-order cyclic-moment and cumulant statistics
It is shown that time averages of such mixtures converge in the mean-square sense to their ensemble averages and that sample averages of arbitrary orders are jointly complex normal and provide their covariance expressions.
Sampling and Ergodic Theorems for Weakly Almost Periodic Signals
  • G. Casinovi
  • Mathematics
    IEEE Transactions on Information Theory
  • 2009
The theory of abstract harmonic analysis on commutative groups is used to prove sampling and ergodic theorems concerning a particular class of finite-power signals, which are known as weakly almost periodic, and it is shown that the value of the time shift between consecutive windows may contribute to the asymptotic bias of the estimates.