ABSTRACT
The wavenumber k is physically the radian frequency divided by wave speed (ω/c), giving it dimensions of radians/m. Wavenumbers can be seen as a measure of wavelength relative to 2π. Actually, k also equals 2π/λ and can be decomposed into kx, ky , and kz components to describe the wave for 3D spaces. The wavenumber k is the central parameter of spatial signal processing which is widely used in radar, sonar, astronomy, and in digital medical imaging [1]. Just as the phase response in the frequency domain relates to time delay in the time domain, the phase response in the wave- number domain relates to the spatial position of the waves. The wavenumber transform is a Fourier transform, where time is replaced by space. Wavenumber processing allows spatial and even directional information to be extracted from waves sampled with an array of sensors at precisely known spatial positions. The array of sensors could be a linear array of hydrophones towed behind a submarine for long-range surveillance [2], a line of geophones used for oil exploration, or a 2D phased-array radar such as those used in missile defense systems [3]. The most common 2D signal data are video which can benefit enormously from wavenumber processing in the frequency domain. Wavenumber processing can be used to enhance imagery from telescopes, digitized photographs, and video where focus or camera steadiness is poor.
