Modern spectral analysis in HF radar remote sensing.

High-Frequency (HF) radar systems are currently used to collect wave data. By applying spectral analysis methods, such as the Fast Fourier Transform (FFT) method, to the radar backscatter from the ocean surface, the so-called Doppler spectrum is calculated, and from this the directional wave spectrum and wave measurements are obtained. Because of the random nature of the ocean surface, spectral measurements are subject to random variability. In order to reduce variability, and hence to obtain relatively precise estimates, each spectrum is usually calculated by averaging a number of FFT estimates. Naturally, this method requires long data series, and problems may arise. In rapidly varying sea conditions, for example, successive FFT estimates may be quite inconsistent with each other (in non-stationary conditions), and then the spectrum estimate obtained by averaging is not only difficult to interpret but it may also be distorted. It is known that the more recent spectral analysis methods such as methods based on autoregressive (AR) and autoregressive-moving average (ARMA) stochastic models can provide stable estimates from short data sets. Thus these methods are potentially good alternatives to the FFT, as they avoid problems inherent to the use of large data sets. The aim of this thesis is to investigate how some of the modem spectral analysis methods may be used to obtain reliable spectral estimates from small data sets. Unlike the FFT method, the AR- and ARMA-based methods presuppose specific parametric forms for the spectral function, and therefore consist in estimating certain parameters from the data (as opposed to estimating the function itself). The modified covariance method and Burg's method are among several methods of estimating the parameters of the spectral function.