谱分解、白化和估计滤波器--稳定性、光滑性和FIR逼近行为
Spectral Factorization, Whitening- and Estimation Filter -- Stability, Smoothness Properties and FIR Approximation Behavior
摘要：
维纳滤波器可以被解释为白化滤波器和估计滤波器的级联。本文详细研究了这两种滤波器的性质。然后，确定整个维纳滤波器的实际后果。它示出，如果给定的谱密度是光滑（Hoelder连续）的功能，所得到的维纳滤波器将始终是稳定的，可以近似任意好的有限脉冲响应（FIR）滤波器。此外，频谱密度的平滑度表征FIR滤波器接近期望滤波器特性的速度。另一方面，如果谱密度是连续的但不够平滑，则所得到的维纳滤波器可能不稳定。
英文摘要：
A Wiener filter can be interpreted as a cascade of a whitening- and an estimation filter. This paper gives a detailed investigates of the properties of these two filters. Then the practical consequences for the overall Wiener filter are ascertained. It is shown that if the given spectral densities are smooth (Hoelder continuous) functions, the resulting Wiener filter will always be stable and can be approximated arbitrarily well by a finite impulse response (FIR) filter. Moreover, the smoothness of the spectral densities characterizes how fast the FIR filter approximates the desired filter characteristic. If on the other hand the spectral densities are continuous but not smooth enough, the resulting Wiener filter may not be stable.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
