Abstract
A novel method on designing bispectral windows is proposed in this letter. Compound functions based on a function with binary quadric form, starting from the symmetry characteristic of three-order moments are used as the 2-D window functions. Two approaches on how to find the expressions of the compound functions are discussed in detail. One is to approximate the compound function after being Taylor expanded under the Minimum Mean Square Error (MMSE) criteria. Another is to compound the hyperbolic secant function and the binary quadric function directly. According to theoretical analysis, the first type new windows have been proved as slightly better than the conventional ones, the second type new windows are much better than the conventional ones, and the bispectral estimation mean square error approximates to 0.
Key words
Bispectral estimation Bispectral windows 2-D window functionsPreview
Unable to display preview. Download preview PDF.
References
- [1]X. D. Zhang, Time Series Analysis—Higher-Order Statistics Method, Beijing, Academic Publishers of Qsinghua University, 1999, Chapter 3, (in Chinese).Google Scholar
- [2]K. Sasaki, T. Sata, Y. Yamashita, Minimum bias windows for bispectral estimation, J. Sound Vibration, 40(1975)1, 139–148.CrossRefGoogle Scholar
- [3]K. Ira, A new class of two-dimensional windows for bispectrum estimation, Signal Processing, 37(1994), 147–156.MATHCrossRefGoogle Scholar
- [4]T. R. Yao, H. Sun, Advanced Digital Signal Processing, Wuhan, Academic Publishers of Huazhong University of Sci. & Tech., 1999, Chapter 5, (in Chinese).Google Scholar