Stable 1-Norm Error Minimization Based Linear Predictors for Speech Modeling

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

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9 Citations (Scopus)
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Abstract

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 second method 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
JournalI E E E Transactions on Audio, Speech and Language Processing
Volume22
Issue number5
Pages (from-to)912-922
Number of pages11
ISSN1558-7916
DOIs
Publication statusPublished - May 2014

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norms
optimization
predictions
linear prediction
Mathematical operators
Poles
coding
poles
saturation
filters
operators
evaluation
shift

Cite this

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title = "Stable 1-Norm Error Minimization Based Linear Predictors for Speech Modeling",
abstract = "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 second method 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.",
author = "Daniele Giacobello and Christensen, {Mads Gr{\ae}sb{\o}ll} and Jensen, {Tobias Lindstr{\o}m} and Murthi, {Manohar N.} and Jensen, {S{\o}ren Holdt} and Marc Moonen",
year = "2014",
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language = "English",
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Stable 1-Norm Error Minimization Based Linear Predictors for Speech Modeling. / Giacobello, Daniele; Christensen, Mads Græsbøll; Jensen, Tobias Lindstrøm; Murthi, Manohar N.; Jensen, Søren Holdt; Moonen, Marc.

In: I E E E Transactions on Audio, Speech and Language Processing, Vol. 22, No. 5, 05.2014, p. 912-922.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Stable 1-Norm Error Minimization Based Linear Predictors for Speech Modeling

AU - Giacobello, Daniele

AU - Christensen, Mads Græsbøll

AU - Jensen, Tobias Lindstrøm

AU - Murthi, Manohar N.

AU - Jensen, Søren Holdt

AU - Moonen, Marc

PY - 2014/5

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N2 - 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 second method 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.

AB - 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 second method 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.

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