NMLM Spectral Estimation

NMLM: A non-parametric procedure Spectral Estimation

Measuring the power at a given frequency P(w) of a given data record can be performed by using a FIR filter steered to this frequency such that it minimizes the power at its output. The method is know in the literature as MLM and it was derived by Capon, The mentioned filter is know as the minimum variance filter. The corresponding estimate is given as P(w)=h'inv(R)h being h the impulse response of the FIR and R the sample auto-covariance matrix of the original data signal. The use of the power estimate is inadequate for power density since it requires to divide P(w) by the bandwidth of the filter. Selecting the so-called white noise bandwidth of the filter (B=h'h) an spectral density estimate results.
The final spectral estimate is S(w)=(h'Rh)/(h'h). Using the minimum variance filter S(w)=('h'(R^-1)h)/(h'R^-2)h).
Since the basic framework of NMLM is based on filter bank spectral estimation, the extension to cross-spectral estimation and 2D special estimation mimic the periodogram method just replacing the frequency vector s by the minimum variance impulse response h.
Reference:
M.A. Lagunas et al. "Maximum Likelihood Filters in Spectral Estimation"
Signal Processing, EURASIP, "Special Issue on Major Trends in Spectral Analysis".
Volume 10, No. 1, January 1986, ISSN-0165-1584, pp. 19-35, (16 pages).