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Frequency-Domain Models
Published in Clarence W. de Silva, Modeling of Dynamic Systems with Engineering Applications, 2023
The Fourier transform involves the mathematical transformation from the time domain into the frequency domain) according to Y(jω)=∫−∞∞y(t)exp(−jωt)dtorY(jω)=Fy(t)
Butterflies and Bits
Published in Ted G. Lewis, The Signal, 2019
I may have lost the reader, here. What Fourier did was important in two respects. Fourier said:1.Every well-behaved function of time is composed of the sum of oscillating functions of time, each with a distinct frequency.2.The Fourier Transform can decompose a function in the time domain into a number of functions in the frequency domain, each with a different oscillation frequency.3.An inverse Fourier Transform can compose a function in the time domain by transforming frequency domain signals back into a time domain signal.
Modelling of Nonlinear Propagation in Waveguides
Published in Andrei V. Lavrinenko, Jesper Lægsgaard, Niels Gregersen, Frank Schmidt, Thomas Søndergaard, Numerical Methods in Photonics, 2018
Andrei V. Lavrinenko, Jesper Lægsgaard, Niels Gregersen, Frank Schmidt, Thomas Søndergaard
or, in other words, the convolution of two functions in the frequency domain is given by the Fourier transform of their direct product in the time domain. Inspection of Equation 5.73 reveals that it can be regarded as two successive convolutions: the ω2 integral convolves Ã* (z, ω2) with à (z, ω – ω1 + ω2) to produce a function of ω – ω1. This is then multiplied by R(ω – ω1), and the ω1 integral represents a convolution of the resulting function with Ã(z,ω1). This implies that Equation (5.73) can be evaluated by means of FFTs with a time complexity of Nlog(N) – a vast improvement over the N3 complexity of the direct-summation approach. This huge gain in computational efficiency means that practically all numerical schemes for solving nonlinear propagation equations in waveguides are based on the Fourier transform methods.
Classification of Nonlinear Features of Uterine Electromyogram Signal Towards the Prediction of Preterm Birth
Published in IETE Journal of Research, 2022
P. Shaniba Asmi, Kamalraj Subramaniam, Nisheena V. Iqbal
Herein, seven non-linear features were compared with four features that have been analyzed in different literatures. Among these four features, the RMS showed the highest classification accuracy. When 11 features were considered, the entropy, Teager energy, detrended fluctuation analysis, and bi-spectrum analysis showed better performance. The Fourier transform converts a signal from the time domain to the frequency domain, in which the amplitude or power is a function of frequency. The power spectrum also limits the information to power and frequency. These two information ignore the phase information present in the signal. The bi-spectral analysis revealed the phase coupling characteristics of the signal. This phase-coupling information along with the context layer of the ENN architecture, which stores the prior information, renders the system useful for clinical purposes to predict preterm labor. This earlier prediction will facilitate the proper treatment for patients. The classification accuracy of the bi-spectrum feature with the ENN classifier is 99.8875% with sensitivity 100% and specificity 99.77%.
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.
Construction of intelligent multi-construction management platform for bridges based on BIM technology
Published in Intelligent Buildings International, 2023
When calculating -point DFT, calculations are needed, and with the increase of , the amount of DFT calculations increases sharply. Fast Fourier Transform (FFT) is a fast algorithm of DFT, and it is also a commonly used method for frequency domain analysis of signals in digital systems. By properly combining these DFTs, the frequency domain information of the original signal can be obtained, thereby greatly reducing the number of multiplication operations and improving operation efficiency.