Обработка сигналов в системах телекоммуникаций

Обработка сигналов в системах телекоммуникаций

FAST VECTOR QUANTIZATION SEARCH ALGORITHM BASED ON STRUCTURALIZED CODEBOOK OF LSF COEFFICIENTS^*

Sawicki A., Petrovsky A.

Department of Real–Time Systems, Bialystok Technical University, Poland

ul. Wiejska 45 A, 15-351 Bialystok, [email protected], [email protected]

Abstract. Computational complexity and memory requirements are serious problems in real-time digital signal processing of speech signal. In this article we proposed new structure of Split Vector Quantizer (SVQ) codebook for Line Spectral Frequency (LSF) to speech processing applications. Intraframe correlations between LSF coefficients allow reducing searching regions in codebook through elimination codevectors with minimal probability of belonging to solution. Structuralization allows reduce the entire quantity of comparisons over searching the codebook. New fast codebook search algorithm based on proposed codebook configuration with supplementary search tree is presented.

1. Introduction

Great problem is assurance of suitable efficiency digital signal processing algorithms working at real-time allowing good quality of processed signal. One of the most complicated tasks is coding and quantization of speech coefficients in coder and decoder. Various forms of suboptimal vector quantizers, more computationally efficient than full codebook search, have been proposed. Structurally constrained vector quantization techniques reduce the complexity of codebook realization with minimal degradation in the reconstruction quality compared to the optimal VQ. It may be realized by splitting the vector into smaller vectors - Split VQ or by VQ implementation in multiple stages (Multistage VQ). Also many other methods were introduced [1] [8], but most of them still require large complexity for real-time implementations.

We propose in this article a new structure of codebook for Split VQ and fast codebook search technique based on presented scheme.

The paper is organized as follows. Section 2 of document provides description of LSF properties. Section 3 describes construction of split codebook and analysis of distances between codebook and test vectors. In section 4 new codebook structure and fast codebook searching algorithm is introduced. In section 5 performance of Structuralized Split Vector Quantizer is presented. Section 6 comprises conclusions of the paper.

2. Line Spectral Frequencies properties

Most of modern speech coding algorithms use LPC (Linear Prediction Coding) parameters to represent spectral envelope of harmonic and noise components of speech [8]. A 10-th order LPC parameters can be transformed without loss of information into LSF (Line Spectral Frequency) coefficients.

LSF parameters have important property, successive coefficients {ω_i} are in order in range (0,π): 0 < ω₁ < ω₂ < … < ω_p <π. This enable to get stability of equivalent LPC synthesis filter, even for LSF parameters changed in process of quantization/dequantization.

Quantization errors in the LSFs result only in localized distortion in the power spectrum, i.e. modification in a specified LSF generates a change in LPC power spectrum merely in its local area.

It is known that LSF parameters are correlated inside a frame. In order to find dependencies in LSF vector, the intraframe correlation between LSF coefficients was calculated over the whole training set as was shown in [2]. We can see a strongest correlation between successive LSFs.

These observations allow us to propose new structure of LSFs codebook.

3. Standard Split VQ Codebook

For the vector quantization simulations a database of about 24 minutes of male and female speech utterances from Polish language Corpora base [3] was used. Speech signal was down-sampled to 8 kHz. Using 20 ms analysis window and no overlapping, there were about 70000 LSF vectors for training. Evaluation set, used for tests, consist next 16000 LSF vectors.

To build quantizer that minimizes average spectral distortion, LBG algorithm [4] was used, with some modifications, as proposed Giuseppe Patanè and Marco Russo in ELBG algorithm [5]. For complexity reduction of the codebook creation process, Split Vector Quantization algorithm with two 5-dimensions vector partitioning was utilized.

We apply Euclidean distance measure between LSF vectors according to formula:

For i-th frame of analysis, spectral distortion SD_i is defined as:

, where and are the LPC power spectrum of original and quantized i-th frame of speech.

K.K Paliwal and B.S. Atal show in [6] that average SD about 1 dB is “transparent”. It means that speech coded with unquantized LPC coefficients and with quantized LPC coefficients are indistinguishable through listening. Vector quantization witch 24 bit/frame ensure average SD on level about 1 dB. In [2] were shown, that best bit splitting design for 24 bit quantization is 12-12 bits for 5-5 dimensions.