Quantization Of Line Spectral Frequencies Research Articles

Dirichlet mixture modeling to estimate an empirical lower bound for LSF quantization

The line spectral frequencies (LSFs) are commonly used for the linear predictive/autoregressive model in speech and audio coding. Recently, probability density function (PDF)-optimized vector quantization (VQ) has been studied intensively for quantization of LSF parameters. In this paper, we study the VQ performance bound of the LSF parameters. The LSF parameters are transformed to the Δ LSF domain and the underlying distribution of the ΔLSF parameters is modeled by a Dirichlet mixture model (DMM) with a finite number of mixture components. The quantization distortion, in terms of the mean squared error (MSE), is calculated with high rate theory. For LSF quantization, the mapping relation between the perceptually motivated log spectral distortion (LSD) and the MSE is empirically approximated by a polynomial. With this mapping function, the minimum required bit rate (an empirical lower bound) for transparent coding of the LSF under DMM modeling is derived.

Gaussian Mixture Model-based Quantization of Line Spectral Frequencies for Adaptive Multirate Speech Codec

In this paper, we investigate the use of a Gaussian MixtureModel (GMM)-based quantizer for quantization of the Line Spectral Frequencies (LSFs) in the Adaptive Multi-Rate (AMR) speech codec. We estimate the parametric GMM model of the probability density function (pdf) for the prediction error (residual) of mean-removed LSF parameters that are used in the AMR codec for speech spectral envelope representation. The studied GMM-based quantizer is based on transform coding using Karhunen-Loeve transform (KLT) and transform domain scalar quantizers (SQ) individually designed for each Gaussian mixture. We have investigated the applicability of such a quantization scheme in the existing AMR codec by solely replacing the AMR LSF quantization algorithm segment. The main novelty in this paper lies in applying and adapting the entropy constrained (EC) coding for fixed-rate scalar quantization of transformed residuals thereby allowing for better adaptation to the local statistics of the source. We study and evaluate the compression efficiency, computational complexity and memory requirements of the proposed algorithm. Experimental results show that the GMM-based EC quantizer provides better rate/distortion performance than the quantization schemes used in the referent AMR codec by saving up to 7.32 bits/frame at much lower rate-independent computational complexity and memory requirements.

A New Segment Quantization Using Lempel–Ziv Algorithm and Its Application to Quantization of Line Spectral Frequencies

A new segment quantization method using the Lempel-Ziv algorithm is proposed, and it is applied to quantize line spectral frequency parameters in speech codec. The proposed segment quantizer can save four bits per frame, compared with the ITU-T G.729 speech codec (18 bits/frame), without degradation of subjective or objective speech quality

On entropy-constrained vector quantization using gaussian mixture models

A flexible and low-complexity entropy-constrained vector quantizer (ECVQ) scheme based on Gaussian mixture models (GMMs), lattice quantization, and arithmetic coding is presented. The source is assumed to have a probability density function of a GMM. An input vector is first classified to one of the mixture components, and the Karhunen-Loeve transform of the selected mixture component is applied to the vector, followed by quantization using a lattice structured codebook. Finally, the scalar elements of the quantized vector are entropy coded sequentially using a specially designed arithmetic coder. The computational complexity of the proposed scheme is low, and independent of the coding rate in both the encoder and the decoder. Therefore, the proposed scheme serves as a lower complexity alternative to the GMM based ECVQ proposed by Gardner, Subramaniam and Rao. The performance of the proposed scheme is analyzed under a high-rate assumption, and quantified for a given GMM. The practical performance of the scheme was evaluated through simulations on both synthetic and speech line spectral frequency (LSF) vectors. For LSF quantization, the proposed scheme has a comparable performance to at rates relevant for speech coding (20-28 bits per vector) with lower computational complexity.

Embedded quantization of line spectral frequencies using a multistage tree-structured vector quantizer

This paper presents a multistage tree-structured vector quantization (MTVQ) scheme for line spectral frequencies (LSF), where two advantages exist: It supports embedded quantization which is required for scalable coder designs, and the tree-structure at each stage can be relied on to accelerate the encoding process. The different codebook design strategies suitable for MTVQ are analyzed. Two speech coding standards are modified by replacing their original LSF quantizers with an MTVQ; it is shown that graceful quality degradation can be obtained for the synthetic speech when the number of bits available for LSF decoding is decremented one-by-one. Moreover, the search complexity is substantially reduced with slight performance degradation

A new distortion measure for spectral quantization based on the LSF intermodel interlacing property

The line spectral frequencies (LSFs) extracted from successive analysis orders are interlaced with each other. This intermodel interlacing property gives a new relationship between the closeness of LSFs and their spectral sensitivities, which motivates a new weighting function for LSF distortion measurement. By applying this new weighting function to LSF quantization, we have achieved a significantly better performance than the conventional heuristic weighting functions in both clean and noise environments. In addition, the proposed weighting function gives better performance than the weighting function based on a high-rate approximation (Gardner weighting (GW)) [W.R. Gardner, B.D. Rao, IEEE Trans. Speech Audio Processing 3 (5) (1995) 367] in noise environments while their performances are comparable in clean environments. Moreover, the complexity of the proposed weighting function is much lower than that of the GW function.

Fast methods for split codebooks

This paper presents a fast method for building and searching split codebooks for vector quantization. The proposed method is evaluated in near transparent quality vector quantization of Line Spectral Frequencies (LSF) at 24-bit per frame. The method is based on a family of fractals called Space-Filling Curves (SFC). The SF curves achieve a significant saving in the complexity of vector quantization by reducing the problem to quantization in one-dimensional space. The paper presents algorithms for the generation of the SFC mapping utilizing the self-replication feature of the curves, and a number of simulation experiments to demonstrate the effectiveness of the method. It is shown that the SFC can reduce the search complexity of split codebooks by a factor of 8–32 times with a slight degradation in the vector quantization performance.

Split matrix quantization of LPC parameters

This paper examines in detail the design issues and performance characteristics of linear predictive coding (LPC) split matrix quantization (SMQ). This efficient LPC quantization method which was proposed by Xydeas and Papanastasiou (1995) can be viewed as an extension of the conventional split vector quantization (SVQ) process. SMQ removes existing interframe/intraframe line spectral frequency (LSF) redundancy by applying VQ principles on trajectories of smoothly evolving, with time, LSF coefficients. Using a 20 ms LPC analysis frame size, transparent quantization is achieved at 900 b/s, whereas high quality LSF quantization is easily obtained at 650 b/s, Furthermore, the SMQ methodology offers valuable flexibility in the way quantization of LPC coefficients is performed and leads into several schemes of varying computational complexity/storage characteristics.

A two codebook format for robust quantization of line spectral frequencies

An important problem in speech coding is the quantization of linear predictive coefficients (LPCs) with the smallest possible number of bits while maintaining robustness to a large variety of speech material and transmission media. Since direct quantization of LPCs is known to be unsatisfactory, the authors consider this problem for an equivalent representation, namely, the line spectral frequencies (LSFs). To achieve an acceptable level of distortion a scalar quantizer for LSFs requires a 36 bit codebook. The authors derive a 30 bit two-quantizer scheme which achieves a performance equivalent to this scalar quantizer. The two-quantizer format consists of both a vector and a scalar quantizer such that for each input, the better quantizer is used. The vector quantizer is designed from a training set that reflects the joint density (for coding efficiency) and which ensures coverage (for robustness). The scalar quantizer plays a pivotal role in dealing better with regions of the space that are sparsely covered by its vector quantizer counterpart. A further reduction of 1 bit is obtained by formulating a new adaptation algorithm for the vector quantizer and doing a dynamic programming search for both quantizers. The method of adaptation takes advantage of the ordering of the LSFs and imposes no overhead in memory requirements. The dynamic programming search is feasible due to the ordering property. Subjective tests in a speech coder reveal that the 29 bit scheme produces equivalent perceptual quality to that when the parameters are unquantized. >