Browsing by Subject "harmonic analysis"

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Access status: Restricted ,
Analiza składowych harmonicznych periodyczności rocznej w wieloletnich zapisach opadów
(Data obrony: 2011-10-17) Paszek, Michał
Wydział Geologii, Geofizyki i Ochrony Środowiska
The main goal of the project was to examine and analyze the time-series for along-term precipitations. The time series analysis was the first step of project. FFT algorithm was used in order to get periodograms. The expected result was to find any cycles and periodicals of precipitations in formed figures received from FFT.
Access status: Open Access ,
Frames and factorization of graph Laplacians
(2015) Jørgensen, Palle E.T.; Tian, Feng
Using functions from electrical networks (graphs with resistors assigned to edges), we prove existence (with explicit formulas) of a canonical Parseval frame in the energy Hilbert space $\mathscr{H}_{E}$ of a prescribed infinite (or finite) network. Outside degenerate cases, our Parseval frame is not an orthonormal basis. We apply our frame to prove a number of explicit results: With our Parseval frame and related closable operators in $\mathscr{H}_{E}$ we characterize the Friedrichs extension of the $\mathscr{H}_{E}$-graph Laplacian. We consider infinite connected network-graphs $G=(V,E)$, $V$ for vertices, and $E$ for edges. To every conductance function $c$ on the edges $E$ of $G$, there is an associated pair ($\mathscr{H}_{E}$, $\Delta$) where $\mathscr{H}_{E}$ in an energy Hilbert space, and $\Delta\left(=\Delta_{c}\right)$ is the $c$-graph Laplacian; both depending on the choice of conductance function $c$. When a conductance function is given, there is a current-induced orientation on the set of edges and an associated natural Parseval frame in $\mathscr{H}_{E}$ consisting of dipoles. Now $\Delta$ is a well-defined semibounded Hermitian operator in both of the Hilbert $l^{2}\left(V\right)$ and $\mathscr{H}_{E}$. It is known to automatically be essentially selfadjoint as an $l^{2}\left(V\right)$-operator, but generally not as an $\mathscr{H}_{E}$ operator. Hence as an $\mathscr{H}_{E}$ operator it has a Friedrichs extension. In this paper we offer two results for the Friedrichs extension: a characterization and a factorization. The latter is via $l^{2}\left(V\right)$.
Access status: Open Access ,
Harmonic analysis in the power supply system of a selected single-phase industrial robot
(AGH University Press, 2025) Ziółkowski, Eugeniusz
The selection of industrial robots in technological lines is primarily based on their technical characteristics, such as the type of construction, the number of axes, reach, maximum load, and power supply parameters (power consumption in single-phase or three-phase systems). In the overall energy balance, the transient states and the harmonics of voltages and currents in the power supply system of the selected industrial robot are also operationally significant. The article presents the results of the harmonic analysis of voltage and current in the power supply system of a chosen industrial single-phase robot.
Access status: Open Access ,
Presentation of a wavelet‑based harmonic model for tidal level forecasting at Sabah and Sarawak
(Wydawnictwa AGH, 2020) Abubakar, Auwal Garba; Mahmud, Mohd Razali; Tang, Kelvin Kang Wee; Hussaini, Alhaji
The world's tides are a result of the combined forces of celestial forces and centrifugal force exerted by the Earth‑Moon and the Sun acting on the water body, earth tides and the atmospheric tides. Harmonic analysis is the most popular and widely accepted method used for the processing and expression of tidal behavior as well as its characteristics. Despite its strengths, harmonic analysis has a few drawbacks when short data are involved for long term‑prediction. However, to enhance the accuracy of the popular methodology of harmonic analysis (HA), this study presents a wavelet‑based harmonic model for tidal analysis and prediction. Six months of water level heights at four tide gauge stations in Sabah and Sarawak of Malaysia were employed. The results obtained agrees with the original data when a comparison was made. The root mean square error (RMSE) and Pearson correlation coefficient (r) are the statistical index tools applied to test the functioning of the model. The residual error is the deviation between the original data and the predicted data which was also computed in this study. The new wavelet‑based harmonic model improves the accuracy of prediction. Moreover, the model is efficient and feasible for tidal analysis and prediction.