China
Africa
Explore chapters and articles related to this topic
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.
Typical Sources and Characteristics of Radiated and Conducted Emissions
Published in David A. Weston, Electromagnetic Compatibility, 2017
A number of programs exist for use on both mainframe and personal computers that perform fast Fourier transforms (FFTs). A typical program enables the fast Fourier transform of a vector of real data representing measurements at regular intervals in the time domain. The result is a vector of complex coefficients in the frequency domain. The phase information is retained, and thus the inverse Fourier transform can be used to convert from the frequency domain back into the time domain. The real data contains magnitude and phase or time information. The program can also accept complex data containing real and imaginary magnitudes, and the phase information is then implicit in the complex data. An inverse Fourier transform of the resultant vector of data representing values in the frequency domain returns a vector representing values in the time domain.
Computational Characteristics of High Performance Embedded Algorithms and Applications
Published in David R. Martinez, Robert A. Bond, Vai M. Michael, High Performance Embedded Computing Handbook, 2018
Arakawa Masahiro, A. Bond Robert
The Fourier transform, one of the most important and fundamental operations in signal processing, is a more complicated example. The Fourier transform takes a signal defined in the time domain and converts it into a frequency domain signal. (The dual operation, which takes a frequency domain signal and transforms it to the time domain, is referred to as the inverse Fourier transform; it has the same computational structure as the Fourier transform and differs only in the conjugation of the coefficients and a scaling constant.) To compute the Fourier transform of an arbitrary signal using a digital computer, the signal must be sampled at discrete intervals to create a sequence of digitized samples. The discrete Fourier transform (DFT) is then applied to the sequence. The DFT is found at the heart of many HPEC applications, where it is used to analyze the frequency content of signals or images and to perform filtering operations such as circular convolution. Excellent discussions of the DFT appear in several textbooks, for example, Van Loan (1992). The direct expression for the computation of the DFT is X[k]=∑n=0N−1x[n]WNkn,k=0,1,…,N−1,
A new recursive Simpson integral algorithm in vibration testing
Published in Australian Journal of Mechanical Engineering, 2021
Jingbo Xu, Xiaohong Xu, Xiaomeng Cui
So far, the commonly applied integral methods are frequency domain integral and time domain integral. Frequency domain integration converts the original signal into frequency domain signal by Fourier transform firstly, then integrates the frequency domain signal, and finally obtains the time domain signal by inverse Fourier transform. Because signal processing has undergone positive transformation and inverse transformation, truncation error is easy to cause. The time domain integration directly integrates the measured acceleration signal, which will produce trend term interference. It is necessary to remove the trend term causing signal offset by fitting method. Usually in low-frequency vibration testing, considering the resource and efficiency requirements of real-time analysis, time domain integration method is more accurate and effective as referred toYang, Li, and Lin (2006) and Hu Yumei et al. (2015).
Numerical formulation based on ocean wave mechanics for offshore structure analysis – a review
Published in Ships and Offshore Structures, 2022
N. A. Mukhlas, N. I. Mohd Zaki, M. K. Abu Husain, S.Z.A. Syed Ahmad, G. Najafian
A Fourier transform method is one of the most potent procedures in mathematical analysis. As underlined by Walker (2017), this method is also a numerical tool that is utilised to transform domains. The Fourier transform has the ability to convert waveform data in the time domain into the frequency domain (Suen et al. 2016). Also, the inverse Fourier transform performs the conversion frequency domain by discrete time-based waveform into a series of sinusoidal terms, each with different amplitude, frequency and phase (Hallowell et al. 2019).
GNSS-aided accelerometer frequency domain integration approach to monitor structural dynamic displacements
Published in International Journal of Image and Data Fusion, 2021
Xu Liu, Jian Wang, Jie Zhen, Houzeng Han, Craig Hancock
As for, is the frequency resolution while and are the upper and lower cut-off frequencies respectively. After all Fourier components of different frequencies are calculated according to the frequency domain relationship, time domain signals can be obtained by inverse Fourier transform.