Spectral Factorization, Whitening- and Estimation Filter -- Stability, Smoothness Properties and FIR Approximation Behavior
Holger Boche, Volker Pohl
Abstract
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.
Create a lesson
Related papers
Distributed Consensus, Optimization, and Learning under Communication Constraints
Zheng Chen, Nicolò Michelusi, Themistoklis Charalambous et al.
Energy-Accumulate-Then-Act Backscatter Communications With Retransmission Under Imperfect Feedback Detection
Rui Xu, Yinghui Ye, Guangyue Lu et al.
The Exact Memory-Rate Tradeoff for Three-User Secure Coded Caching
Han Fang, Nan Liu, Wei Kang
Cross-Modal Semantic Successive Refinement for Generative Image Communication over Underwater Acoustic Channels
Xu Pei, Bin Wang, Guangxu Zhu et al.
Fano's Inequality and Channel Capacity in the Individual-Sequence Regime
Neri Merhav
Exact Transport-Information Correspondence for Distribution-Adaptive Discretization
Koretaka Yuge