Estymacja parametrów szeregu Fouriera i ich praktyczne zastosowania
How to estimate fourier series parameters and to use them in practice

Summary/Abstract: Proposed is identification of a periodical phenomenon – that of seasonal character in particular - by means of the first terms of its periodical function expanded into Fourier series. We will operate over those phenomena where values yt employed to identify them can be factorised into three components: a development trend f(t) a periodical component (that of seasonal character in particular) z(t) and a random komponent Et . Such an event can be identified in the following way: y f (t) z(t) Et dla t  1,2,...,n. The parameters of the trend f(t) of any analytical form can be determined by using the mean value theorem. The determined new analytical points (t, zt) we identify by means of a periodical variation model in its harmonic sum form: Estimation of the model parameters made with the use of the method of least squares has the following form: Application examples are presented.

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