Adaptive Polynomial Filters

1996 ◽  
pp. 237-277 ◽  
Author(s):  
W. Kenneth Jenkins ◽  
Andrew W. Hull ◽  
Jeffrey C. Strait ◽  
Bernard A. Schnaufer ◽  
Xiaohui Li
Keyword(s):  
Polynomial Filters

Non-linear polynomial filters for edge enhancement of mammogram lesions

2016 ◽  
Vol 129 ◽  
pp. 125-134 ◽  
Author(s):  
Vikrant Bhateja ◽  
Mukul Misra ◽  
Shabana Urooj
Keyword(s):  
Edge Enhancement ◽  
Linear Polynomial ◽  
Non Linear ◽  
Polynomial Filters

New Nonlinear Adaptive Filters with Applications to Chaos

1997 ◽  
Vol 07 (08) ◽  
pp. 1791-1809 ◽  
Author(s):  
Fawad Rauf ◽  
Hassan M. Ahmed
Keyword(s):  
Adaptive Filters ◽  
Broad Class ◽  
Chaotic Map ◽  
New Class ◽  
Chaotic Signals ◽  
Data Points ◽  
Modeling Prediction ◽  
Polynomial Filters ◽  
And Performance ◽  
Nonlinear Adaptive Filtering

We present a new approach to nonlinear adaptive filtering based on Successive Linearization. Our approach provides a simple, modular and unified implementation for a broad class of polynomial filters. We refer to this implementation as the layered structure and note that it offers substantial computational efficiency over previous methods. A new class of Polynomial Autoregressive filters is introduced which can model limit cycle and chaotic dynamics. Existing geometric methods for modeling and characterizing chaotic processes suffer from several drawbacks. They require a huge number of data points to reconstruct the attractor geometry and performance is severely limited by noisy experimental measurements. We present a new method for processing chaotic signals using nonlinear adaptive filters. We demonstrate the modeling, prediction and filtering of these signals. We also show how the prediction error growth rate can be used to estimate the effective Lyapunov exponent of the chaotic map. Our approach requires orders of magnitude fewer data points and is robust to noise in the experimental data. Although reconstruction of the attractor geometry is unnecessary, the adaptive filter contains most of the geometric information.

Critically sampled graph filter banks with polynomial filters from regular domain filter banks

2017 ◽  
Vol 131 ◽  
pp. 66-72 ◽  
Author(s):  
David B.H. Tay ◽  
Yuichi Tanaka ◽  
Akie Sakiyama
Keyword(s):  
Filter Banks ◽  
Regular Domain ◽  
Polynomial Filters

Stability condition for certain recursive second-order polynomial filters

1996 ◽  
Vol 32 (16) ◽  
pp. 1522 ◽  
Author(s):  
E. Roy ◽  
R.W. Stewart ◽  
T.S. Durrani
Keyword(s):  
Stability Condition ◽  
Second Order ◽  
Order Polynomial ◽  
Polynomial Filters

Wavelet denoising of powder diffraction patterns

1999 ◽  
Vol 14 (4) ◽  
pp. 300-304 ◽  
Author(s):  
Ľubomír Smrčok ◽  
Marián Ďurík ◽  
Vladimír Jorík
Keyword(s):  
Fourier Transform ◽  
Powder Diffraction ◽  
Wavelet Denoising ◽  
Wavelet Function ◽  
Discrete Wavelet ◽  
Experimental Conditions ◽  
Polynomial Filters ◽  
Diffraction Patterns ◽  
Polynomial Smoothing ◽  
Integrated Intensities

Four powder diffraction patterns taken under different experimental conditions were denoised by a new method, i.e., thresholding of wavelet coefficients. The patterns were transformed by discrete wavelet transform applying Coiflet4 wavelet function. WLS refinements of peaks’ positions, FWHM, and intensity showed that wavelet denoising, in contrast to previously used polynomial smoothing, did not shift the maxima and preserved peak and integrated intensities. This method may therefore represent an useful alternative to polynomial filters or filters based on Fourier transform.

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