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This paper presents a simple differential speech signal coding algorithm, based on backward adaptation. The considered algorithm is executed in frame by frame manner, by implementing predictive and adaptive quantization techniques. Both prediction and adaptation are performed backward, based on the previously quantized input signal frame. This enables us to obtain high quality output signal, without increasing the bit rate. This research puts emphasis on the quantizer design, with the optimal support limit determination, and theoretical performance evaluation. Objective quality of the output signal is evaluated through signal to quantization noise ratio (SQNR). We perform theoretical and experimental analysis of the algorithm performance and provide comparative results of implementing speech signal coding techniques with similar complexity. Experimental results show that our simple differential speech coding algorithm satisfies the G.712 Recommendation for high-quality speech coding at the bit rate of 6 bits per sample. This indicates that the algorithm can be successfully implemented in high quality speech signal coding.

Scalar quantizer selection for processing a signal with a unit variance is a difficult problem, while both selection and quantizer design for the range of variances is even tougher and to the authors’ best knowledge, it is not theoretically solved. Furthermore, performance estimation of various image processing algorithms is unjustifiably neglected and there are only a few analytical models that follow experimental analysis. In this paper, we analyse application of piecewise uniform quantizer with Golomb-Rice coding in modified block truncation coding algorithm for grayscale image compression, propose design improvements and provide a novel analytical model for performance analysis. Besides the nature of input signal, required compression rate and processing delay of the observed system have a strong influence on quantizer design. Consequently, the impact of quantizer range choice is analysed using a discrete designing variance and it was exploited to improve overall quantizer performance, whereas variable-length coding is applied in order to reduce quantizer’s fixed bit-rate. The analytical model for performance analysis is proposed by introducing Inverse Gaussian distribution and it is obtained by discussing a number of images, providing general closed-form solutions for peak-signal-to-noise ratio and the total average bit-rate estimation. The proposed quantizer design ensures better performance in comparison to the other similar methods for grayscale image compression, including linear prediction of pixel intensity and edge-based adaptation, whereas analytical model for performance analysis provides matching with the experimental results within the range of 1 dB for PSQNR and 0.2 bpp for the total average bit-rate.

This paper presents a model for signal compression, which consists of a piecewise uniform quantizer and a new lossless coder. The model is designed in a general manner, i.e. for any symmetrical signal distribution; this general theory is applied to design models for Gaussian and Laplacian distributions. Rigorous mathematical derivation of the expression for the bit-rate is presented. Forward adaptation of the model is done for non-stationary signals. Theory is proved by simulations in MATLAB and by an experiment with a real speech signal. The most important advantages of the model are low complexity and good performances – it satisfies G.712 standard for the speech transmission quality with 6.18 bps (bits per sample), which is significantly smaller than 8 bps required for quantizers used in PSTN (public switched telephone network) defined with G.711 standard.

The problem we address in this paper is the design of a quantizer that in comparison to the classical fixed-rate scalar quantizers provides more sophisticated bit rate reduction while restricting the class of quantizers to be scalar. We propose a switched variable-length code (VLC) optimal companding quantizer composed of two optimal companding scalar quantizers, the inner and the outer one, both designed for the memoryless Gaussian source of unit variance. Quantizers composing the proposed quantizer have a different codebook sizes and a different compressor functions. Particularly, we assume a smaller size of the inner quantizer's codebook in order to provide assignment of the shorter codewords to the high probability low amplitude speech samples belonging to the support region of the inner quantizer. We study the influence of codebook size of the inner and the outer quantizer on the Signal to Quantization Noise Ratio (SQNR). In such a manner the conclusion of the proposed quantizer significance in speech compression is distinctly shown in the paper. For the proposed quantizer model and its forward adaptive version the SQNR robustness analysis in a wide variance range is also presented in the paper. It is shown that our multi-resolution quantizer can satisfy G.712 Recommendation for high-quality quantization at the bit rate of 6.3 bit/sample achieving the compression of 1.7 bit/sample over the G.711 quantizer.

In this paper, a piecewise uniform quantizer for input samples with discrete amplitudes for Laplacian source is designed and analyzed, and its forward adaptation is done. This type of quantizers is very often used in practice for the purpose of compression and coding of already quantized signals. It is shown that the design and the adaptation of quantizers for discrete input samples are different from the design and the adaptation of quantizers for continual input samples. A weighting function for PSQNR (peak signal-to-quantization noise ratio), which is obtained based on probability density function of variance of standard test images is introduced. Experiments are done, applying these quantizers for compression of grayscale images. Experimental results are very well matched to the theoretical results, proving the theory. Adaptive piecewise uniform quantizer designed for discrete input samples gives for 9 to 20 dB higher PSQNR compared to the fixed piecewise uniform quantizer designed for discrete input samples. Also it is shown that the adaptive piecewise uniform quantizer designed for discrete input samples gives higher PSQNR for 1.46 to 3.45 dB compared the adaptive piecewise uniform quantizer designed for continual input samples, which proves that the discrete model is more appropriate for image quantization than continual model.

In this paper new semilogarithmic quantizer for Laplacian distribution is presented. It is simpler than classic A-law semilogarithmic quantizer since it has unit gain around zero. Also, it gives for 2.97 dB higher signal-to-quantization noise-ratio (SQNR) for referent variance in relation to A-law, and therefore it is more suitable for adaptation. Forward adaptation of this quantizer is done on frame-by-frame basis. In this way G.712 standard is satisfied with 7 bits/sample, which is not possible with classic A-law. Inside each frame subframes are formed and lossless encoder is applied on subframes. In that way, double adaptation is done: adaptation on variance within frames and adaptation on amplitude within subframes. Joined design of quantizer and lossless encoder is done, which gives better performances. As a result, standard G.712 is satisfied with only 6.43 bits/sample. Experimental results, obtained by applying this model on speech signal, are presented. It is shown that experimental and theoretical results are matched very well (difference is less than 1.5%). Models presented in this paper can be applied for speech signal and any other signal with Laplacian distribution.

This paper has two achievements. The first aim of this paper is optimization of the lossy compression coder realized as companding quantizer with optimal compression law. This optimization is achieved by optimizing maximal amplitude for that optimal companding quantizer for Laplacian source. Approximate expression in closed form for optimal maximal amplitude is found. Although this expression is very simple and suitable for practical implementation, it satisfy optimality criterion for Lloyd–Max quantizer (for R >= 6 bits/sample). In the second part of this paper novel simple lossless compression method is presented. This method is much simpler than Huffman method, but it gives better results. Finally, at the end of the paper, we join optimal companding quantizer and lossless coding method together in one generalized compression method. This method is applied on the concrete still image and good results are obtained. Besides still images, this method also could be used for compression speech and bio-medical signals.