Informatica

This paper introduces a novel approach that bridges the floating-point (FP) format, widely utilized in diverse fields for data representation, with the μ-law companding quantizer, proposing a method for designing and linearizing the μ-law companding quantizer to yield a piecewise uniform quantizer tailored to the FP format. A key outcome of the paper is a closed-form approximate expression for closely and efficiently evaluating the FP format’s performance for data with the Laplacian distribution. This expression offers generality across various bit rates and data variances, markedly reducing the computational complexity of FP performance evaluation compared to prior methods reliant on summation of a large number of terms. By facilitating the evaluation of FP format performance, this research substantially aids in the selection of the optimal bit rates, crucial for digital representation quality, dynamic range, computational overhead, and energy efficiency. The numerical calculations spanning a wide range of data variances provided for some commonly used FP versions with an 8-bit exponent have demonstrated that the proposed closed-form expression closely approximates FP format performance.

This paper introduces two novel algorithms for the 2-bit adaptive delta modulation, namely 2-bit hybrid adaptive delta modulation and 2-bit optimal adaptive delta modulation. In 2-bit hybrid adaptive delta modulation, the adaptation is performed both at the frame level and the sample level, where the estimated variance is used to determine the initial quantization step size. In the latter algorithm, the estimated variance is used to scale the quantizer codebook optimally designed assuming Laplace distribution of the input signal. The algorithms are tested using speech signal and compared to constant factor delta modulation, continuously variable slope delta modulation and instantaneously adaptive 2-bit delta modulation, showing that the proposed algorithms offer higher performance and significantly wider dynamic range.