Periodogram and correlogram. Blackman – Tukey, Bartlett, Welch and Daniel methods. Window design considerations.
Parametric methods for rational spectra. Covariance structure of ARMA processes. AR, MA and ARMA signals. Multivariate ARMA signals.
Parametric methods for line spectra. Models of sinusoidal signals in noise. Nonlinear least squares, high order Yule-Walker, min-norm, Pisarenko, MUSIC and ESPRIT methods.
Filter bank methods. Filter-bank interpretation of the periodogram. Refined filter-bank and Capon methods. Spatial methods. Array model. Nonparametric methods; beam forming and Capon method. Parametric methods; nonlinear least squares, Yule-Walker, min-norm, Pisarenko, MUSIC and ESPRIT methods.
1. P.Stoica & R.Moses, “Spectral Analysis of signals”, Pearson,2005.
2. Marple, “Introduction to Spectral Analysis”, Prentice Hall.
1. S.M.Key, “Fundamentals of Statistical Signal Processing”, Prentice Hall PTR, 1998.
Students are able to
CO1: derive and analyse the statistical properties of the conventional spectral estimators, namely the periodogram, averaged & modified periodogram and Blackman-Tukey methods.
CO2: formulate modern, parametric, spectral estimators based upon autoregressive (AR), moving average (MA), and autoregresive moving average (ARMA) models, and detail their statistical properties. Describe the consequence of the term resolution as applied to a spectral estimator.
CO3: define techniques for calculating moments in spectral and temporal domains; Analyze filter bank method, capon methods for spectrum estimation.
CO4: demonstrate knowledge and understanding of the principles of parametric and non-parametric array processing algorithms.
CO5: select an appropriate array processing algorithms for frequency estimation and sonar, radar applications.
