"Spectral Estimation is at the heart of almost all modern-day signal
processing systems.  Current systems typically employ the FFT (Fast
Fourier Transform), which is inherently limited in resolution by the
data record length.  With the advent of high speed digital computing it
is now possible to implement in practice more modern approaches to
spectral estimation."*

At Lockheed Missiles & Space Co. we were able to find signals down some
50+ dB by using Kay's AutoCorr method.  This was great for our work.
Electronic 'Black-Box' manufactures assumed the standard 30 dB and
below was noise.  Wrong.  And these manufactures became our number one
problem.  Manufactures need to move their definition of noise to below
100 dB or so.

"Important techniques of spectral estimation including linear
prediction, AutoRegressive (AR), Maximum Entropy, AutoRegressive Moving
Average (ARMA), Maximum Likelihood Method (MLM), and eigen-analysis
methods."*

Areas of spectral interest include:

"1. The Spectral Estimation Problem.  Review of random process theory.
Spectral estimation and filtering. Applications to sonar, speech, data
processing, etc. Parametric vs. nonparametric approaches.  Concept of
resolution. Comparison of estimators.
2. Classical (Fourier Methods).  Periodogram. Averaged periodogram.
Bias-variance tradeoffs. Computation of periodogram. Blackman-Tukey.
Correlation estimation. Resolution comparisons.
3. Time Series Modeling.  Time series model definitions.  AR/MA/ARMA.
Yule-Walker equations. Levinson algorithm. Model fitting of empirical
data. Effect of observation noise.
4. Statistical Estimation Review.  Maximum likelihood estimation (MLE).
 Cramer-Rao lower bound (CRLB).
5. Autoregressive Spectral Estimation.  Autocorrelation, covariance,
modified covariance (forward/backward),  Burg, and recursive maximum
likelihood methods. Properties of estimators. Linear prediction/maximum
entropy/autoregressive modeling relationships. Reflection coefficients
and lattice filters. Autocorrelation matching. Model order selection -
Akaike and MDL. Observation noise effects. Performance for sinusoids in
noise.
6. Autoregressive Moving Average Spectral Estimation.  Akaike MLE and
iterative implementations. Modified Yule-Walker. Least squares modified
Yule-Walker. Input/output identification approaches (two stage least
squares).  Choosing the best method for your application.
7. Moving Average Spectral Estimation.  Durbin's method and
performance.
8. Capon's Method (MLM).  Filtering interpretation. Comparison to
periodogram.  Resolution vs. conventional and autoregressive
estimators.
9. Sinusoidal Frequency Estimation.  Signal and noise subspaces.
Eigenanalysis of covariance matrix. MLE. Periodogram. Principal
components/SVD approaches. MUSIC. Pisarenko methods. Iterative
filtering method. Statistical performance vs. CRLB for all methods.
10. Empirical Spectral Estimation.  Examples using the Modern
Interactive Spectral Analysis software package. Hands-on experience by
student analysis of mystery data sets. Evaluation of student-supplied
data."*

I highly recommend Kay's textbook "Modern Spectral Estimation: Theory
and Application" by Steven Kay (Prentice-Hall, 1988), which includes
Fortran subroutines for all the basic methods, as well as MATLAB
subroutines, suggested problems and solutions.
------
* From newsgroup messages titled "spectral analysis course" by Steve
Kay before April 1998.