Statistically optimum pre- and postfiltering in quantization
Statistically optimum pre- and postfiltering in quantization
复制标题
量化中统计上最佳的预过滤和后过滤
DOI：
10.1109/82.644563
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发表时间：
1997
期刊：
影响因子：
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通讯作者：
P. Vaidyanathan
中科院分区：
文献类型：
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作者：
J. Tuqan;P. Vaidyanathan
我们考虑优化的前，后滤波器周围的量化系统。目标是优化滤波器，使得均方误差在量化噪声方差与量化系统输入的方差成正比的关键约束下最小化。与以前的一些工作不同，后置滤波器不限于前置滤波器的逆。没有顺序约束的过滤器，我们提出了封闭形式的解决方案时，量化系统是一个统一的量化器的最佳前，后滤波器。使用这些最佳的解决方案，我们得到的编码增益表达式的系统下研究。编码增益表达式清楚地表明，在高比特率下，将后置滤波器限制为前置滤波器的逆滤波器并没有损失一般性。然后，我们用1+/spl alpha/z/sup-1/和1/（1+/spl gamma/z/sup-1/）形式的一阶前置和后置滤波器重复相同的分析。具体来说，我们研究了两种情况：1）FIR前置滤波器，IIR后置滤波器和2）IIR前置滤波器，FIR后置滤波器。对于每种情况，我们获得均方误差表达式，优化系数/spl alpha/和/spl gamma/，并提供一些示例，其中我们将编码增益性能与/spl alpha/=/spl gamma/的情况进行比较。在最后一节中，我们假设量化系统是一个正交完美重构滤波器组。为了应用前面导出的最佳前置和后置滤波器，滤波器组的输出必须是广义平稳WSS，而这通常是不正确的。我们提供了两个定理，每个下一组不同的假设，保证了广义平稳的滤波器组输出。然后，我们提出了一个次优的程序，以增加正交滤波器组的编码增益。
We consider the optimization of pre- and postfilters surrounding a quantization system. The goal is to optimize the filters such that the mean square error is minimized under the key constraint that the quantization noise variance is directly proportional to the variance of the quantization system input. Unlike some previous work, the postfilter is not restricted to be the inverse of the prefilter. With no order constraint on the filters, we present closed-form solutions for the optimum pre- and postfilters when the quantization system is a uniform quantizer. Using these optimum solutions, we obtain a coding gain expression for the system under study. The coding gain expression clearly indicates that, at high bit rates, there is no loss in generality in restricting the postfilter to be the inverse of the prefilter. We then repeat the same analysis with first-order pre- and postfilters in the form 1+/spl alpha/z/sup -1/ and 1/(1+/spl gamma/z/sup -1/). In specific, we study two cases: 1) FIR prefilter, IIR postfilter and 2) IIR prefilter, FIR postfilter. For each case, we obtain a mean square error expression, optimize the coefficients /spl alpha/ and /spl gamma/ and provide some examples where we compare the coding gain performance with the case of /spl alpha/=/spl gamma/. In the last section, we assume that the quantization system is an orthonormal perfect reconstruction filter bank. To apply the optimum preand postfilters derived earlier, the output of the filter bank must be wide-sense stationary WSS which, in general, is not true. We provide two theorems, each under a different set of assumptions, that guarantee the wide sense stationarity of the filter bank output. We then propose a suboptimum procedure to increase the coding gain of the orthonormal filter bank.