Stable 1-norm error minimization based linear predictors for speech modeling

Daniele Giacobello, Mads Græsbøll Christensen, Tobias Lindstrøm T.L. Jensen, Manohar N. Murthi, Søren Holdt Jensen, Marc Moonen

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


In linear prediction of speech, the 1-norm error minimization criterion has been shown to provide a valid alternative to the 2-norm minimization criterion. However, unlike 2-norm minimization, 1-norm minimization does not guarantee the stability of the corresponding all-pole filter and can generate saturations when this is used to synthesize speech. In this paper, we introduce two new methods to obtain intrinsically stable predictors with the 1-norm minimization. The first method is based on constraining the roots of the predictor to lie within the unit circle by reducing the numerical range of the shift operator associated with the particular prediction problem considered. The secondmethod uses the alternative Cauchy bound to impose a convex constraint on the predictor in the 1-norm error minimization. These methods are compared with two existing methods: the Burg method, based on the 1-norm minimization of the forward and backward prediction error, and the iteratively reweighted 2-norm minimization known to converge to the 1-norm minimization with an appropriate selection of weights. The evaluation gives proof of the effectiveness of the new methods, performing as well as unconstrained 1-norm based linear prediction for modeling and coding of speech.

Original languageEnglish (US)
Article number2311324
Pages (from-to)910-920
Number of pages11
JournalIEEE Transactions on Audio, Speech and Language Processing
Issue number5
StatePublished - May 1 2014


  • All-pole modeling
  • Autoregressive modeling
  • Convex optimization
  • Linear prediction
  • Sparse linear prediction

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Acoustics and Ultrasonics


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