Iterative algorithm for nonuniform inverse fast Fourier transform (NU-IFFT)

1998 ◽  
Vol 34 (20) ◽  
pp. 1913 ◽  
Author(s):  
Qing Huo Liu ◽  
Xue Yuan Tang
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Iterative Algorithm ◽  
Inverse Fast Fourier Transform

An Efficient Iterative Algorithm for Accurately Calculating Impulse Response Functions in Modal Testing

2011 ◽  
Vol 133 (6) ◽  
Author(s):  
J. M. Liu ◽  
W. D. Zhu ◽  
Q. H. Lu ◽  
G. X. Ren
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Iterative Algorithm ◽  
Impulse Response ◽  
Mimo Systems ◽  
Spectral Lines ◽  
Modal Testing ◽  
Impulse Response Functions ◽  
Response Functions ◽  
Modal Parameter

Impulse response functions (IRFs) and frequency response functions (FRFs) are bases for modal parameter identification of single-input, single-output (SISO) and multiple-input, multiple-out (MIMO) systems, and the two functions can be transformed from each other using the fast Fourier transform and the inverse fast Fourier transform. An efficient iterative algorithm is developed in this work to directly and accurately calculate the IRFs of SISO and MIMO systems in the time domain using relatively short input and output data series. The iterative algorithm can avoid the time-consuming inversion of a large matrix in the conventional least-square method for calculating an IRF, greatly reducing the computation time. In addition, a fitting index and an error energy decreasing coefficient are introduced to evaluate the accuracy in calculating an IRF and to provide the termination criterion for the iterative algorithm. A new coherence function is also introduced to evaluate the accuracy of calculated IRFs and FRFs at different spectral lines. Two examples are given to illustrate the effectiveness and efficiency of the methodology.

scholarly journals Two- and Three-Dimensional Fast Intrawall Imaging with Microwave Tomographic Algorithm

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Wenji Zhang ◽  
Ahmad Hoorfar ◽  
Christopher Thajudeen
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Real Time ◽  
Three Dimensional ◽  
Inverse Fast Fourier Transform ◽  
Real Time Processing ◽  
Time Processing ◽  
Imaging Algorithm ◽  
Reflection Model ◽  
Effectiveness And Efficiency

A fast and efficient microwave tomographic algorithm is proposed for 2-D and 3-D real-time intrawall imaging. The exploding reflection model is utilized to simplify the imaging formulation, and the half-space Green’s function is expanded in the spectral domain to facilitate the easy implementation of the imaging algorithm with the fast Fourier transform (FFT) and inverse fast Fourier transform (IFFT). The linearization of the inversion scheme and employment of FFT/IFFT in the imaging formula make the algorithm suitable for various applications pertaining to the inspection of a large probed region and allow real-time processing. Representative numerical and experimental results are presented to show the effectiveness and efficiency of the proposed algorithm for real-time intrawall characterization.

scholarly journals Design of Acoustic Bifocal Lenses Using a Fourier-Based Algorithm

Sensors ◽  
2021 ◽  
Vol 21 (24) ◽  
pp. 8285
Author(s):  
José Miguel Fuster ◽  
Sergio Pérez-López ◽  
Pilar Candelas
Keyword(s):  
Fourier Transform ◽  
Reverse Engineering ◽  
Fast Fourier Transform ◽  
Design Method ◽  
Binary Sequence ◽  
Inverse Fast Fourier Transform ◽  
Design Algorithm ◽  
Bifocal Lenses ◽  
Absolute Control ◽  
Novel Design

In this work, we develop a new design method based on fast Fourier transform (FFT) for implementing zone plates (ZPs) with bifocal focusing profiles. We show that the FFT of the governing binary sequence provides a discrete sequence of the same length, which indicates the location of the main foci at the ZP focusing profile. Then, using reverse engineering and establishing a target focusing profile, we are capable of generating a binary sequence that provides a ZP with the desired focusing profile. We show that this design method, based on the inverse fast Fourier transform (IFFT), is very flexible and powerful and allows to tailor the design of bifocal ZPs to achieve focusing profiles with the desired foci locations and resolutions. The key advantage of our design algorithm, compared to other alternatives presented in previous works, is that our method provides bifocal focusing profiles with an absolute control of the foci locations. Moreover, although we analyze the performance of this novel design algorithm for underwater ultrasonics, it can also be successfully extended to different fields of physics, such as optics or microwaves, where ZPs are widely employed.

scholarly journals Solving singular convolution equations using the inverse Fast Fourier Transform

2012 ◽  
Vol 57 (5) ◽  
pp. 543-550 ◽  
Author(s):  
Eduard Krajník ◽  
Vincente Montesinos ◽  
Peter Zizler ◽  
Václav Zizler
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Inverse Fast Fourier Transform ◽  
Convolution Equations
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