Signal Processing 88 (2008) 1528–1538 Optimum switched split vector quantization of LSF parameters Saikat Chatterjee à , T.V. Sreenivas Department of Electrical Communication Engineering, Indian Institute of Science, Bangalore 560 012, India Received 6 April 2007; received in revised form 25 July 2007; accepted 2 January 2008 Available online 6 January 2008 Abstract We address the issue of rate–distortion (R/D) performance optimality of the recently proposed switched split vector quantization (SSVQ) method. The distribution of the source is modeled using Gaussian mixture density and thus, the non- parametric SSVQ is analyzed in a parametric model based framework for achieving optimum R/D performance. Using high rate quantization theory, we derive the optimum bit allocation formulae for the intra-cluster split vector quantizer (SVQ) and the inter-cluster switching. For the wide-band speech line spectrum frequency (LSF) parameter quantization, it is shown that the Gaussian mixture model (GMM) based optimum parametric SSVQ method provides 1 bit/vector advantage over the non-parametric SSVQ method. r 2008 Elsevier B.V. All rights reserved. Keywords: Vector quantization; Gaussian mixture model; LPC quantization 1. Introduction Most of the speech coders use linear prediction (LP) analysis and thus, more effective scheme of quantizing the LP coefficients (LPCs), equivalently line spectrum frequencies (LSFs), is in great demand. Vector quantization (VQ) of LSFs is the best way to reach lowest bitrate, but the prohibitive complexity of a full-search VQ limits its usage. Many different product code VQ methods [1–5] have been reported for LSF coding, which reduce complexity with a moderate loss of quantization performance. One of the widely reported techniques is split vector quantization (SVQ) method which was first pro- posed by Paliwal and Atal [6] for telephone-band speech and then further explored for wide-band speech [7–9]. Recently, So and Paliwal have pro- posed switched split vector quantization (SSVQ) method [10,11] which is shown to provide a better R/D performance than the traditional SVQ method, for both telephone-band and wide-band speech cases. The SSVQ is further explored in [12,13] to show its competitive performance advantage over many other product code VQ methods. The SSVQ is a non-parametric product code VQ method, where the vector space is divided into non- overlapping Voronoi regions 1 and a separate SVQ is designed for each region. Thus, the SSVQ is composed of multiple SVQs. An input vector to be quantized is first classified to a Voronoi region and then the region specific SVQ is used for quantization. Though the SSVQ provides better rate–distortion ARTICLE IN PRESS www.elsevier.com/locate/sigpro 0165-1684/$ - see front matter r 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.sigpro.2008.01.001 à Corresponding author. Tel.: +91 80 2360 2167; fax: +91 80 2360 0683. E-mail addresses: saikat@ece.iisc.ernet.in (S. Chatterjee), tvsree@ece.iisc.ernet.in (T.V. Sreenivas). 1 These Voronoi regions are referred to as ‘‘switching regions’’ in [10–13].