1 Sektion Aalborg, The Technical Faculty of IT and Design, Aalborg University, VBN2 Media Technology, The Technical Faculty of IT and Design, Aalborg University, VBN3 Audio Analysis Lab, The Technical Faculty of IT and Design, Aalborg University, VBN4 Department of Architecture, Design and Media Technology, The Technical Faculty of IT and Design, Aalborg University, VBN5 The Faculty of Engineering and Science (TECH), Aalborg University, VBN6 Department of Electronic Systems, The Technical Faculty of IT and Design, Aalborg University, VBN7 Signal and Information Processing, The Technical Faculty of IT and Design, Aalborg University, VBN8 University of Miami9 K.U. Leuven10 University of Miami
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.
I E E E Transactions on Audio, Speech and Language Processing, 2014, Vol 22, Issue 5, p. 912-922