Fourier-detrended fluctuation analysis

Many features of natural phenomena can be observed using time records or series of observations. The time records of phenomena such as physiological and economic data or the temperature of a river can display short- and long-term time scales. These signals can also present trends which are an important aspect of their complexity. These trends can lead to difficulties in the analysis of the signals. In this short note we suggest a modified approach for the analysis of low frequency trends added to a noise in time series. We will name this method Fourier-detrended fluctuation analysis, but it is a simple high-pass filter. Using this approach, we will attempt to quantify correlations with trends in a time series. By cutting the first few coefficients of a Fourier expansion, we show that we are able to efficiently remove the globally varying trends.