System identification: theory for the user
System identification: theory for the user
Statistical Digital Signal Processing and Modeling
Statistical Digital Signal Processing and Modeling
SIAM Journal on Optimization
Blind wideband source separation
ICASSP '94 Proceedings of the Acoustics, Speech, and Signal Processing,1994. on IEEE International Conference - Volume 04
ARMA model parameter estimation based on the equivalent MA approach
Digital Signal Processing
MA estimation in polynomial time
IEEE Transactions on Signal Processing
An improved inverse filtering method for parametric spectralestimation
IEEE Transactions on Signal Processing
Cepstral coefficients, covariance lags, and pole-zero models forfinite data strings
IEEE Transactions on Signal Processing
On the parameterization of positive real sequences and MA parameterestimation
IEEE Transactions on Signal Processing
A direct optimization method for low group delay FIR filter design
Signal Processing
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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.