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Mobile and Home Electroencephalography in the Usual Environment of Children
Published in Ricardo A. Ramirez-Mendoza, Jorge de J. Lozoya-Santos, Ricardo Zavala-Yoé, Luz María Alonso-Valerdi, Ruben Morales-Menendez, Belinda Carrión, Pedro Ponce Cruz, Hugo G. Gonzalez-Hernandez, Biometry, 2022
Belinda Carrion, Luis Felipe Herrera Padilla
In the case of Autism Spectrum Disorder (ASD), much of the EEG related research has been through the use of different analytical methods to produce distinct biomarkers that reflect the core EEG differences between a healthy control and a patient with ASD. Several studies have shown a possible lead into quantitative electroencephalography, an analysis method in which EEG signals are differentiated into their frequency bands through the use of Fourier Analysis. Fourier Analysis is a mathematical transformation that decomposes functions depending on space or time into functions depending on spatial or temporal frequency. In simpler terms, it is a type of analysis that allows the identification of patterns and cycles in a timed series of data. Several key EEG profiles have been identified through Fourier Analysis such as the U-shaped pattern, in which the resting-state EEG from patients with ASD show excessive power from delta and theta frequency bands while alpha frequency bands are diminished [546]. This pattern reflects a distinct rhythm maturation when compared to healthy subjects, in which the standard observation is an age-related decrease in delta and theta power and an overall increase of alpha power [217, 129].
A Qualitative Look at Fourier Analysis
Published in Richard J. Jagacinski, John M. Flach, Control Theory for Humans, 2018
Richard J. Jagacinski, John M. Flach
Fourier analysis provides a mathematical technique for decomposing signals that extend over time and/or space into a sum of sinusoidal components. As illustrated in Fig. 12.1, a periodic signal such as a square wave can be approximated by a sum of sinusoidal components. The top of Fig. 12.1 shows the sum of three sinusoids (a sinusoid with the same frequency and 4/π times the amplitude of the square wave plus a sinusoid with 4/3π times the amplitude and three times the frequency of the square wave plus a sinusoid with 4/5π times the amplitude and five times the frequency of the square wave). The bottom of Fig. 12.1 shows the sum of seven sinusoids, the same three as in the top graph plus four more sine waves with higher frequencies. Note that with the addition of the higher frequency components, the sum better approximates the square wave.
Fourier Methods and Integral Transforms
Published in Abul Hasan Siddiqi, Mohamed Al-Lawati, Messaoud Boulbrachene, Modern Engineering Mathematics, 2017
Abul Hasan Siddiqi, Mohamed Al-Lawati, Messaoud Boulbrachene
Fourier analysis shows that we can represent periodic functions, even very jagged and irregular-looking ones, in form of a finite or infinite sum of sine and cosine functions, called Fourier series. Non-periodic functions can be treated with the Fourier transform. Fourier showed how these mathematical tools can be used to study natural phenomena such as heat diffusion, making it possible to solve equations that had until then remained intractable. Under the action of the Fourier transform, derivatives are transformed into multiplications, thus turning differential equations into equations containing algebraic expressions. In this way, many important differential equations are transformed into equations which are much easier to study and solve.
An Adaptive Algorithm for Battery Charge Monitoring based on Frequency Domain Analysis
Published in IETE Journal of Research, 2021
Poulomi Ganguly, Surajit Chattopadhyay, B.N Biswas
The Fourier transform is a powerful analytical tool in various fields of science. It can help solve cumbersome dynamic response equations. Fourier analysis of a periodic function denotes the extraction of the series of sines and cosines, which when combined will mimic the function. This analysis can be expressed as a Fourier series. The following equation represents the decomposed form of a period function f (t). Here a0, an, and bn are Fourier coefficients and are defined as The Fast Fourier transform (FFT) is an improvement of the Discrete Fourier transform (DFT), which removes duplicated terms in the mathematical algorithm, thereby reducing the number of mathematical operations to be performed. Thus large numbers of samples can be used without compromising the transformation speed. The FFT reduces computation by a factor of N/(log2 (N)). FFT produces the same result as the DFT but at a much faster rate.
Optimized Structural Compressed Sensing Matrices for Speech Compression
Published in IETE Journal of Research, 2020
Yuvraj V Parkale, Sanjay L Nalbalwar
Fourier analysis is a representation of a signal with an orthonormal set of sinusoidal functions. The coefficients of the functions are called frequency components and the waveforms are arranged by frequency. Walsh presented a complete orthonormal set of square-wave functions to represent these functions. The Walsh functions are real and take only two values either +1 or −1 and hence exhibits the computational simplicity. The Walsh functions are ordered by the number of zero sequency or crossings called as sequency components. The important property of Walsh functions is called frequency components and the waveforms function is such that the inner product between two adjacent rows or columns is zero. The Walsh–Hadamard transform [56] with naturally order H (2n) are N×N matrices; Whereas, N = 2n (n = 1, 2, 3).
Comparison of the cerebral activities exhibited by expert and novice visual communication designers during idea incubation
Published in International Journal of Design Creativity and Innovation, 2019
Chaoyun Liang, Chi-Cheng Chang, Yu-Cheng Liu
With the exception of one outlier cluster, the components of each cluster in each imagination indicator were transformed into spectra by using the Fast Fourier Transform (FFT) function in EEGLAB. Fourier analysis is usually used to convert a signal from its original domain into a representation in the frequency domain and vice versa. In the current study, FFT was used to transform time domain data into frequency domain data. The component spectra could not be assumed to be normally distributed, and the sample size was small; therefore, a paired-sample Wilcoxon signed-rank test, a method of nonparametric statistical analysis, was applied to test the differences in brain activities in spectra between expert and novice designers.