Frequency analysis of time series using Fourier transform

This bachelor’s thesis focuses on the decomposition of a temperature time series in the Czech Republic using the Fourier transform. The thesis provides a detailed description of the application of frequency-domain analysis and compares this approach with the more traditional time-domain methods. Specifically, it contrasts the method based on decomposing a time series into elementary sine and cosine functions with the method of moving averages. Understanding this approach serves as a foundation for more advanced and robust techniques, such as wavelet transforms. The thesis pursues several objectives. The main goal is to analyze long-term average air temperature data recorded at a meteorological station in the Czech Republic using the Fourier transform. The results of this approach are subsequently compared with those obtained from time-domain analysis. The findings demonstrate that the use of the Fourier transform allows for more accurate results compared to the classical moving average method, primarily due to the ability to specify a targeted filtering frequency. The thesis first presents the Fourier transform method from a theoretical perspective, followed by its practical implementation on sample data using the Fast Fourier Transform (FFT) in the R environment. These examples are intended to facilitate the understanding of the relatively complex theoretical principles.