engleski

THE ROLE OF FOURIER SERIES IN THE ENVIRONMENTAL ENGINEERING

Fourier series represents a powerful mathematical tool which is used in many areas of natural and technical sciences. Fourier series dissembles periodical functions into the sum of trigonometric functions sinuses and cosinuses. In this paper the theory of Fourier series will be defined. Many types of functions, like periodical, aperiodical functions, and odd and steam functions, and their differences are going to be listed. The theoretical part is followed by the application of the Fourier series in the environmetal engineering. A few types of measuring sensors are given.. With usage of measuring sensors, data and variables of various physical or chemical values of natural phenomena can be collected. Signals are divided into digital and analog type of signals. An analog signal is a time continuous signal whose amplitude or the volume changes continuously and continuously over time, while the digital signal contains discrete functions, which are obtained by sampling the state record of the analog wave in certain time steps whose length depends on the frequency or frequency signal. In other words, to obtain a digital signal from an analog signal, it is necessary is to use FFT, or fast Fourier transform. Some other types of signals are going to be list, with appropriate examples for those signals. From the series of time functions the spectra will be explained. The spectrum in mathematics is defined as a two - dimensional graph of a complex wave shown in some other measures. The spectrum is the intensity distribution of the measured quantities that are in dependence on some physical quantities, such as energy, frequency, speed, mass and other measured quantities. The use of Fourier series is important in measuring sensors and processing of measured signals in environmental engineering in which the filtering of the measured signal from noise plays an important role. Signal filtering is the separation of signal frequencies from noise and interference frequencies. Signal can be filtered by a low pass filter, a high pass filter and a bandpass filter.

Fourier series, Fourier coefficients, sensors, signal, spectrum

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