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Causality in system theory necessitates specific mathematical operations, such as the Riesz projection and spectral factorization mapping. The text illustrates this through the Wiener filter, which optimally estimates stationary stochastic sequences. While a non-causal filter's transfer function is straightforward, a causal filter requires additional operations to determine its optimal transfer function. This highlights the complexity involved in creating a causal estimation filter compared to its non-causal counterpart, emphasizing the importance of these mathematical tools in system analysis.
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Advanced Topics in System and Signal Theory, Volker Pohl, Holger Boche
- Language
- Released
- 2009
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- (Hardcover)
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- Title
- Advanced Topics in System and Signal Theory
- Subtitle
- A Mathematical Approach
- Language
- English
- Authors
- Volker Pohl, Holger Boche
- Publisher
- Springer, Berlin
- Released
- 2009
- Format
- Hardcover
- Pages
- 241
- ISBN13
- 9783642036385
- Category
- Mathematics, Computers, IT, Programming
- Description
- Causality in system theory necessitates specific mathematical operations, such as the Riesz projection and spectral factorization mapping. The text illustrates this through the Wiener filter, which optimally estimates stationary stochastic sequences. While a non-causal filter's transfer function is straightforward, a causal filter requires additional operations to determine its optimal transfer function. This highlights the complexity involved in creating a causal estimation filter compared to its non-causal counterpart, emphasizing the importance of these mathematical tools in system analysis.