Author(s)

G Rodríguez

Abstract

The Hartley transform, a real valued alternative to the complex Fourier transform, is presented as an efficient tool for data analysis in physical oceanography. Basic theoretical properties of this real-valued transform are briefly reviewed. Similarities and differences between Fourier and Hartley integral transforms and their discrete versions, as well as computational benefits or disadvantages between numerical algorithms used to evaluate their discrete versions are presented. The Hartley transform is used to estimate the spectral density function of ocean surface waves and coastal current time series. 1 Introduction In physical oceanography, as in many other areas of science and engineering, the spectral analysis of time series is an standard procedure to investigate the physics underlying the observed dynamical processes. The basic idea of spectral analysis rests on the method of Fourier series, which states that any periodic function satisfying certain conditions, chiefly those of convergence, may be represented by a series of complex exponencial functions. The generalization of this idea to non- periodic functions implies the substitution of Fourier series by the Fourier integral, leading to the concepts of Fourier transform and spectral analysis. The Fourier transform utility lies in its ability to transform a time signal into the frequency domain to analize its frequency content in terms of amplitude and phase. This capability is due to the fact that the Fourier coefficients of the transformed function represent the contribution of each sine and cosine function at a given frequency.

Keywords