Introduction

Measurements of the sea-surface elevation are almost always obtained with an electrical current in some instrument. This analogue signal can be transformed into an estimate of the variance density spectrum of the waves, using analogue systems, such as electronic circuits or optical equipment. However, with today's small and fast computers the analogue signal can also be transformed into a digital signal for a subsequent numerical analysis. The latter option has been accepted widely and it will be treated here.

The numerical analysis depends on the type of measurement. The most common and simplest measurement in this respect is a record of the sea-surface elevation at one location as a function of time (i.e., a one-dimensional record). Records like these are produced by instruments such as a heave buoy, a wave pole or a low-altitude altimeter. These can be analysed with a one-dimensional Fourier transform. Other types of measurements generate multivariate signals (i.e., several, simultaneously obtained, time records), e.g., the two slope signals of a pitch-and-roll buoy. Such signals require a cross-spectral analysis (e.g., Tucker and Pitt, 2001), or some other, advanced method (e.g., Hashimoto, 1997; Young, 1994; Pawka, 1983; Lygre and Krogstad, 1986 and many others). Two-dimensional images, e.g., from a surface-contouring radar, require a two-dimensional Fourier transform (e.g., Singleton, 1969) and moving images (e.g., those produced by a ship's radar) require a three-dimensional Fourier transform. Here, we consider only the simplest possible measurement: the sea-surface elevation at one location as a function of time.