Multiresolution Analysis of EEG Signals

Borowska, Marta; Białobłocka, Natalia

doi:10.1515/slgr-2016-0044

“…The wavelets transform is first introduced for transient continuous signal time -frequency domain analysis, and subsequently expanded to the concept for multi-resolution wavelet transform utilizing filtering approximations [20]. A signal is represented by a wavelet transform in the form of specific short time intervals [21][22][23]:…”

Section: Wavelet Transformmentioning

confidence: 99%

Extend Nearly Pseudo Quasi-2-Absorbing submodules(II)

Ahmed

¹

,

Mohammed

²

2023

IHJPAS

0

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Time series analysis is the statistical approach used to analyze a series of data. Time series is the most popular statistical method for forecasting, which is widely used in several statistical and economic applications. The wavelet transform is a powerful mathematical technique that converts an analyzed signal into a time-frequency representation. The wavelet transform method provides signal information in both the time domain and frequency domain. The aims of this study are to propose a wavelet function by derivation of a quotient from two different Fibonacci coefficient polynomials, as well as a comparison between ARIMA and wavelet-ARIMA. The time series data for daily wind speed is used for this study. From the obtained results, the proposed wavelet-ARIMA is the most appropriate wavelet for wind speed. As compared to wavelets the proposed wavelet is the most appropriate wavelet for wind speed forecasting, it gives us less value of MAE and RMSE.

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“…Multi-resolution frequency spectrum analysis is widely used in many areas to process signals from different sources, such as signals from mechanical structures, acoustic sensors, human body signal sensors, and digital RF/microwave receivers. A few examples are given in [ 1 , 2 , 3 , 4 ]. Multi-resolution analysis (MRA) is a powerful tool used in image and signal processing.…”

Section: Introductionmentioning

confidence: 99%

FFT-Based Simultaneous Calculations of Very Long Signal Multi-Resolution Spectra for Ultra-Wideband Digital Radio Frequency Receiver and Other Digital Sensor Applications

Wu,

Low

2024

Sensors

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The discrete Fourier transform (DFT) is the most commonly used signal processing method in modern digital sensor design for signal study and analysis. It is often implemented in hardware, such as a field programmable gate array (FPGA), using the fast Fourier transform (FFT) algorithm. The frequency resolution (i.e., frequency bin size) is determined by the number of time samples used in the DFT, when the digital sensor’s bandwidth is fixed. One can vary the sensitivity of a radio frequency receiver by changing the number of time samples used in the DFT. As the number of samples increases, the frequency bin width decreases, and the digital receiver sensitivity increases. In some applications, it is useful to compute an ensemble of FFT lengths; e.g., 2P−j for j=0, 1, 2, …, J, where j is defined as the spectrum level with frequency resolution 2j·Δf. Here Δf is the frequency resolution at j=0. However, calculating all of these spectra one by one using the conventional FFT method would be prohibitively time-consuming, even on a modern FPGA. This is especially true for large values of P; e.g., P≥20. The goal of this communication is to introduce a new method that can produce multi-resolution spectrum lines corresponding to sample lengths 2P−j for all J+1 levels, concurrently, while one long 2P-length FFT is being calculated. That is, the lower resolution spectra are generated naturally as by-products during the computation of the 2P-length FFT, so there is no need to perform additional calculations in order to obtain them.

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Forecasting Wind Speed Using the Proposed Wavelet Neural Network

Mohammed

¹

,

Ahmed

²

2023

Discrete Dynamics in Nature and Society

2

0

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Wind energy is one of the speedy processing technologies in the energy generation industry and the most economical methods of electrical power generation. For the reliability of system, it is wanted to improve highly appropriate wind speed forecasting methods. The wavelet transform is a powerful mathematical technique that converts an analyzed signal into a time-frequency representation. This technique has proven useful in a nonstationary time series forecasting. The aims of this study are to propose a wavelet function by derivation of a quotient from two different Lucas polynomials, as well as a comparison between an artificial neural network (ANN) and wavelet-artificial neural network (WNN). We used the proposed wavelet, Mexican hat, Morlet, Gaussian, Haar, Daubechies, and Coiflet to transform the wind speed data using the continuous wavelet transform (CWT). MATLAB software was used to implement the CWT and ANN. The proposed models were applied in the meteorological field to forecast the daily wind speed data that were collected from the meteorological directorate of Sulaymaniyah which is a city located in the Kurdistan region of Iraq for the period (Jan. 2011–Dec. 2020). Five different performance criteria during calibration and validation, the root mean square error ( R M S E ), mean square error ( M S E ), mean absolute percentage error M A P E , mean absolute error M A E , and coefficient of determination ( R 2 ), were evaluated. When studying, analyzing, and comparing these models, the results of the study concluded that the proposed wavelet-ANN is the best result ( M S E = 0.00072 , R M S E = 0.02683 , M A P E = 2.32400 , and R 2 = 0.99983 .

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Multiresolution Analysis of EEG Signals

Cited by 3 publications

References 23 publications

Extend Nearly Pseudo Quasi-2-Absorbing submodules(II)

Extend Nearly Pseudo Quasi-2-Absorbing submodules(II)

FFT-Based Simultaneous Calculations of Very Long Signal Multi-Resolution Spectra for Ultra-Wideband Digital Radio Frequency Receiver and Other Digital Sensor Applications

Forecasting Wind Speed Using the Proposed Wavelet Neural Network

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