Multidimensional harmonic analysis of fourier for measurements of marine environment

V.A. Gaisky, P.V. Gaisky

Institute of Natural and Technical Systems, RF, Sevastopol, Lenin St., 28


DOI: 10.33075/2220-5861-2019-4-33-42

UDC 544.623


     A method of monitoring the fields of the marine environment, which involves measuring the field parameters of a certain region by known means, in order to increase the accuracy of field representation and interpolation, additionally use a navigation system to measure and fix coordinates in time and space of the points of information selection from the environment, take bases of orthogonal Fourier functions for representing coordinate profiles of variability of field parameters, form a system of four-dimensional orthonormal functions of Fourier series, determine the coefficients of expansion of the field in four-dimensional orthogonal functions from the set of samples of field parameters in known coordinates and use this representation to interpolate the field to any point in the region covered by joint measurements of the time and coordinate parameters is presented.

     When using the basis of trigonometric functions for representing the field in two-dimensional measurements, systems of four groups of functions of two two-dimensional base frequencies are used; for three-dimensional measurements, a system of eight groups of functions of four three-dimensional base frequencies; for four-dimensional measurements, a system of sixteen groups of functions of eight four-dimensional basic frequencies are used.Multidimensional harmonic analysis covers almost all types of oceanographic surveys. So standard soundings from the ship to the specified depths and vice versa can be considered two-dimensional, cuts towed by scanning media are three-dimensional,  sounding ranges, buoy station networks, shooting with unmanned autonomous carriers are four-dimensional, remote measurements and video images from a satellite from two to four-dimensional. In all cases, the point of selection of information from the environment should be linked by place and time.

Ключевые слова: field of marine environment, harmonic Fourier analysis.

To quote, follow the DOI link and use the Actions-Cite option or copy:
[IEEE] V.A. Gaisky and P.V. Gaisky, “MULTIDIMENSIONAL HARMONIC ANALYSIS OF FOURIER FOR MEASUREMENTS OF MARINE ENVIRONMENT”, Monitoring systems of environment, vol. 4, pp. 33–42, Dec. 2019.

Full text in PDF(RUS)


  1. Guide to hydrological work in the oceans and seas. Hydrometeoizdat. M., 2016. 540 p.
  2. Dotsenko S.V. Theoretical foundations for measuring the physical fields of the ocean. Hydrometeoizdat. L., 1974. 180 p.
  3. Smirnov V.I. A course of higher mathematics. V. 2. Publishing house of Technical and theoretical literature. M., 1954. 628 p.
  4. Bronshtein I.N., Semendiaev K.A. Handbook of mathematics for engineers, technical colleges. Publishing house “Nauka”. M., 1964. 608 p.

If you have found a spelling error, please, notify us by selecting that text and pressing Ctrl+Enter.

Translate »

Spelling error report

The following text will be sent to our editors: