用二次样条函数确定量化器分段阈值的最佳值
Numerical determination of the optimal value of quantizer's segment threshold using quadratic spline functions
摘要：
本文提出了一种用二次样条函数逼近最优压气机函数的方法。二次样条函数的系数通过最小化均方误差（MSE）来确定。基于所得到的近似二次样条函数，对高斯信源进行了压扩量化器的设计。建议的压扩量化器的支持区域被划分在大小不等的段上，其中段阈值的最佳值在数值上取决于信号量化噪声比（SQNR）的最大值来确定。结果表明，本文提出的压缩扩展量化器的SQNR与非线性最优压缩扩展量化器的SQNR非常接近。
英文摘要：
In this paper, an approximation of the optimal compressor function using the quadratic spline functions has been presented. The coefficients of the quadratic spline functions are determined by minimizing the mean-square error (MSE). Based on the obtained approximative quadratic spline functions, the design for companding quantizer for Gaussian source is done. The support region of proposed companding quantizer is divided on segments of unequal size, where the optimal value of segment threshold is numerically determined depending on maximal value of the signal to quantization noise ratio (SQNR). It is shown that by the companding quantizer proposed in this paper, the SQNR that is very close to SQNR of nonlinear optimal companding quantizer is achieved.
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