因果带限均方逼近
On causal band-limited mean square approximation
摘要：
我们研究因果动态逼近的非带限过程的带限过程，使一部分的历史路径的基础过程是近似的$L_2$ -范数的带限过程的痕迹。这允许覆盖不规则非平滑过程的情况。我们证明了这个问题有唯一的最优解。在时域中以sinc级数的形式得到了近似的带限过程。为了适应当前的观测流，该系列的系数和相关的带限过程必须动态地改变。这可以被解释为不是时不变的因果和线性滤波。
英文摘要：
We study causal dynamic approximation of non-bandlimited processes by band-limited processes such that a part of the historical path of the underlying process is approximated in $L_2$-norm by the trace of a band-limited process. This allows to cover the case of irregular non-smooth processes. We show that this problem has an unique optimal solution. The approximating band-limited process is obtained in time domain in a form of sinc series. To accommodate the current flow of observations, the coefficients of this series and the related band-limited process have to be changed dynamically. This can be interpreted as a causal and linear filter that is not time invariant.
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