Paper Info
Title
A new class of invertible FIR filters for spectral shaping
Abstract
Spectral shaping filters find a rich set of applications in the statistical signal processing problems such as signal modeling, spectral estimation, system identification, and channel equalization. In this paper, we present a new class of LTI causal FIR filters for converting a set of autocorrelation samples representing the input to a prescribed set of output autocorrelation samples. The input autocorrelation samples may represent a MA, AR, or ARMA process, with or without additive white noise, whose stable model is minimum or non-minimum phase. In contrast to the existing methods, derivation of a FIR filter of this class is direct requiring no intermediate step and no direct application of orthogonality principle or minimization of a cost function. The FIR filter is minimum-phase and its output autocorrelation lags, except the lag zero, match the set of prescribed values precisely. We characterize the filters solution space and present a novel time-domain algorithm for finding a unique invertible FIR filter of minimum-order in the solution space. We refer to the solution filter as an ''optimal invertible FIR (OIFIR)'' filter, in general, and as a ''semi-whitening filter (SWF)'', in particular, when the prescribed output autocorrelation lags, except the lag zero, are all equal to zero. It is shown that the whitening filter obtained by Yule-Walker equations (or by the orthogonality principle) belongs to the solution space of SWF only if the set of input autocorrelation samples accurately represents an AR process of finite order. Examples show performance of the proposed class of filters in spectral shaping applications including the AR modeling of a stationary process.
Year
DOI
Venue
2009
10.1016/j.sigpro.2008.12.008
Signal Processing
Keywords
Field
DocType
lag zero,invertible fir filter,whitening filter,new class,solution filter,autocorrelation sample,input autocorrelation sample,fir filter,solution space,orthogonality principle,semi-whitening filter,lti causal fir filter,system identification,channel equalization,white noise,statistical signal processing,stationary process,ar model,time domain,cost function,spectral estimation
Spectral density estimation,Digital filter,Autocorrelation technique,Half-band filter,Control theory,White noise,Finite impulse response,Mathematics,Orthogonality principle,Autocorrelation
Journal
Volume
Issue
ISSN
89
7
Signal Processing
Citations 
PageRank 
References 
4
0.47
16
Authors
2
Name
Order
Citations
PageRank
Issa M. S. Panahi14914.53
Kripasagar Venkat2131.12