Source Localization: Frequency Wavenumber Spectrum
A wavefi eld produced by sources in the far-fi eld region may be expressed as a sum of plane waves with random phase (see plane wave decomposition in Chapter 1, Section 2). The quantity of interest is power (or energy when transient waves are involved) as a function of azimuth and elevation. This is the frequency wavenumber (ω, k) spectrum introduced in Chapter 2. As the
array is of limited size, the task of estimating the frequency wavenumber spectrum becomes too ambitious. What can be estimated with reasonable certainty is the spectral matrix by treating the array output as a multichannel time series. The spectral matrix is indeed related to the frequency wavenumber spectrum. Fortunately, for the purpose of source localization it is enough if we can accurately estimate the spectral matrix.