Informatica

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.

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.