# fast Fourier transform

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## fast Fourier transform

An MRI term for a very fast and efficient computational method of performing a Fourier transform—the mathematical process by which raw data is processed into a usable image.
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Theoretically, there are many ways to compute the DFT rule in (1) and (2), however, in this work a FFT algorithm is employed to compute the DFT of an input ECG sequence, x[n].
Due to their inherent parallelism and reconfigurability, FPGAs are attractive for accelerating FFT computations, since they fully exploit the parallel nature of the FFT algorithm. FPGAs are particularly an attractive target for medical and biomedical imaging apparatus and instruments such as electron microscopes and tomographic scanners.
It is found that considering the constraints of the FFT algorithm when choosing [gamma] can yield calculation speed-ups.
In order to conclude the system it is enabled to reduce the harmonic defects using the Total Harmonic Distortion (THD) in the source side of the 110kV substation which has been detected by FFT Algorithm and compensated by using the Shunt Active Filter.
The proposed architecture implements the FFT algorithm, for sizes in correspondence with N = 2"s ranging from 16 through 1024 with various combinations.
The algorithm introduced in Section 3.3 is based on the FFT algorithm and does not require solving an optimization problem.
Take the 2D FFT case as example, user only needs to select template, write FFT algorithm or call other existing APIs, and type this piece of codes in SAC, in such function the input plane and output plane are already defined by SAC.
These data symbols are converted from serial to parallel format and then FFT algorithm is applied, described in eq.
In the FFT algorithm, the complex floating point add, subtract, and multiply operations shown in figure 1 can be realized with a discrete implementation that uses three reversible single precision floating point adders to perform the complex add and four reversible single precision floating point multipliers and three reversible single precision floating point subtractors to perform the complex subtract.
For the past decades, there were several attempts to parallelize the FFT algorithm which was mostly based on parallelizing each stage (iteration) of the FFT process [26-28].
For the latter, we suppose to use the FFT algorithm due to the discrete nature of the simulation.
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