ABSTRACT
We have seen in Chapters 1 and 2 that Fourier analysis is used to describe the resolution associated with beamforming and apodisation. No inversion is involved in these applications, and the potential resolution enhancement (measured in terms of the main-lobe width of the point-spread function) typically occurs at the expense of increased sidelobes. Such modification of the system, point-spread function is accomplished by the use of windows, and these are the main feature of the current chapter, which is concerned with convolution equations and deterministic spectral analysis. The first of these topics involves inversion, whereas the secondmay just involve modifying the pointspread function, as in standard beamforming and apodisation, or can involve inversion. Windowing has its origins in the theory of convergence of Fourier series and Fourier integrals, and we review briefly some aspects of this theory in Section 7.3.
