@TechReport{	  it:2017-018,
  author	= {Antonio Cicone and Carlo Garoni and Stefano
		  Serra-Capizzano},
  title		= {Spectral and Convergence Analysis of the Discrete {ALIF}
		  Method},
  institution	= {Department of Information Technology, Uppsala University},
  department	= {Division of Scientific Computing},
  year		= {2017},
  number	= {2017-018},
  month		= sep,
  abstract	= {The Adaptive Local Iterative Filtering (ALIF) method is a
		  recently proposed iterative procedure to decompose a signal
		  into a finite number of ``simple components'' called
		  intrinsic mode functions. % It is an alternative to the
		  well-known and widely used empirical mode decomposition, a
		  method proposed in 1998 by Huang and his research team at
		  NASA. % In this paper we consider the discrete version of
		  the ALIF method and we perform a spectral analysis of the
		  related iteration matrices, with particular focus on the
		  eigenvalue clustering and the eigenvalue distribution. %
		  Based on the eigenvalue distribution, we formulate a
		  necessary condition for the convergence of the Discrete
		  ALIF method. We also provide a simple criterion to
		  construct appropriate filters satisfying this condition. %
		  Our analysis, which represents a first step toward a
		  complete mathematical understanding of the ALIF method,
		  relies on recent matrix-theoretic results about sampling
		  matrices and, above all, on the theory of generalized
		  locally Toeplitz sequences, which we extend in this paper.
		  % Several numerical examples in support of the theoretical
		  analysis are presented.}
}