Fourier Series

Residual analysis using Fourier series transform in Fuzzy time series model

In this paper, we propose a new residual analysis method using Fourier series transform into fuzzy time series model for improving the forecasting performance. This hybrid model takes advantage of the high predictable power of fuzzy time series model and Fourier series transform to fit the estimated residuals into frequency spectra, select the low-frequency terms, filter out high-frequency term...

Determination of a jump by Fourier and Fourier-Chebyshev series

‎By observing the equivalence of assertions on determining the jump of a‎ ‎function by its differentiated or integrated Fourier series‎, ‎we generalize a‎ ‎previous result of Kvernadze‎, ‎Hagstrom and Shapiro to the whole class of‎ ‎functions of harmonic bounded variation‎. ‎This is achieved without the finiteness assumption on‎ ‎the number of discontinuities‎. ‎Two results on determination of ...

Linear and Nonlinear Analysis of Cable Stayed Bridges By Fourier Series

Dynamic Harmonic Analysis of Long Term over Voltages Based on Time Varying Fourier series in Extended Harmonic Domain

Harmonics have become an important issue in modern power systems. The widespread penetration of non-linear loads to emerging power systems has turned power quality analysis into an important operation issue under both steady state and transient conditions. This paper employs an Extended Harmonic Domain (EHD) based framework for dynamic analysis of long term analysis over voltages during the tra...

Thermal anomalies detection before earthquake using three filters (Fourier, Wavelet and Logarithmic Differential Filter), A Case Study of two Earthquakes in Iran

Earthquake is one of the most destructive natural phenomena which has human and financial losses. The existence of an efficient prediction system and early warning system will be useful for reducing effects of destroying earthquake. In this research, the soil temperature time-series data, obtained from three meteorological station, using three filters (Fourier, Wavelet and Logarithmic Different...

Fractional Fourier series expansion for finite signals and dual extension to discrete-time fractional Fourier transform

Conventional Fourier analysis has many schemes for different types of signals. They are Fourier transform (FT), Fourier series (FS), discrete-time Fourier transform (DTFT), and discrete Fourier transform (DFT). The goal of this correspondence is to develop two absent schemes of fractional Fourier analysis methods. The proposed methods are fractional Fourier series (FRFS) and discrete-time fract...