Proietti, Tommaso and Luati, Alessandra (2009): LowPass Filter Design using Locally Weighted Polynomial Regression and Discrete Prolate Spheroidal Sequences.

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Abstract
The paper concerns the design of nonparametric lowpass filters that have the property of reproducing a polynomial of a given degree. Two approaches are considered. The first is locally weighted polynomial regression (LWPR), which leads to linear filters depending on three parameters: the bandwidth, the order of the fitting polynomial, and the kernel. We find a remarkable linear (hyperbolic) relationship between the cutoff period (frequency) and the bandwidth, conditional on the choices of the order and the kernel, upon which we build the design of a lowpass filter. The second hinges on a generalization of the maximum concentration approach, leading to filters related to discrete prolate spheroidal sequences (DPSS). In particular, we propose a new class of lowpass filters that maximize the concentration over a specified frequency range, subject to polynomial reproducing constraints. The design of generalized DPSS filters depends on three parameters: the bandwidth, the polynomial order, and the concentration frequency. We discuss the properties of the corresponding filters in relation to the LWPR filters, and illustrate their use for the design of lowpass filters by investigating how the three parameters are related to the cutoff frequency.
Item Type:  MPRA Paper 

Original Title:  LowPass Filter Design using Locally Weighted Polynomial Regression and Discrete Prolate Spheroidal Sequences 
Language:  English 
Keywords:  Trend filters; Kernels; Concentration; Filter Design. 
Subjects:  E  Macroeconomics and Monetary Economics > E3  Prices, Business Fluctuations, and Cycles > E32  Business Fluctuations ; Cycles C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C14  Semiparametric and Nonparametric Methods: General C  Mathematical and Quantitative Methods > C2  Single Equation Models ; Single Variables > C22  TimeSeries Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes 
Item ID:  15510 
Depositing User:  Tommaso Proietti 
Date Deposited:  04. Jun 2009 01:50 
Last Modified:  07. Jan 2014 20:18 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/15510 