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About 10,000 papers for “Fast Fourier transform”

Fast Fourier Transform

Frits Agterberg · Encyclopedia of earth sciences series/Encyclopedia of earth sciences · 2023

Cited by 8

Fast Fourier transform.

Martina Klejchová · Digital Repository (National Repository of Grey Literature) · 2008

Cited by 0

Fast Fourier Transform

Andrew Seagar · 2023

Standard fast Fourier transform (FFT) algorithms support at best complex signals (functions of time) or waveforms (functions of space). It is of interest to use the FFT to calculate derivatives of an electromagnetic field in order to simulate wave propagation using the finite difference time domain method. Inspection of analytical results for the Fourier series of signals with square and triangular shapes indicates that the non-zero harmonics are proportional to the reciprocal of the frequency for the square shape, and proportional to the square of the reciprocal of the frequency for the triangular shape. The chapter provides comprehensive explorations of a variety of worked and computed examples at various levels of complexity, and practical discussions of the conceptual and computational tools for solving common engineering problems.

Cited by 7

Fast Fourier Transform

2002

The fast Fourier transform (FFT) is an efficient algorithm that is used for converting a time-domain signal into an equivalent frequency-domain signal, based on the discrete Fourier transform (DFT). Several real-time programming examples on FFT are included.

Cited by 16

Fast Fourier Transform GUI

Nikesh Bajaj · Figshare · 2017

MATLAB GUI for 8 -point FFT, with computation at all the stage. This is to help student to check their computation of FFT

Cited by 0Open access

Fast Fourier transform telescope

Max Tegmark, Matías Zaldarriaga · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D, Particles, fields, gravitation, and cosmology · 2009

We propose an all-digital telescope for 21 cm tomography, which combines key advantages of both single dishes and interferometers. The electric field is digitized by antennas on a rectangular grid, after which a series of fast Fourier transforms recovers simultaneous multifrequency images of up to half the sky. Thanks to Moore's law, the bandwidth up to which this is feasible has now reached about 1 GHz, and will likely continue doubling every couple of years. The main advantages over a single dish telescope are cost and orders of magnitude larger field-of-view, translating into dramatically better sensitivity for large-area surveys. The key advantages over traditional interferometers are cost (the correlator computational cost for an $N$-element array scales as $N{log}_{2}N$ rather than ${N}^{2}$) and a compact synthesized beam. We argue that 21 cm tomography could be an ideal first application of a very large fast Fourier transform telescope, which would provide both massive sensitivity improvements per dollar and mitigate the off-beam point source foreground problem with its clean beam. Another potentially interesting application is cosmic microwave background polarization.

Cited by 143Open access

Fast Fourier Transform Clustering

2008

Based on the assumption that genes having similar expression profiles (co-expressed genes) may be involved in the same biological process, many clustering algorithms have emerged to identify co-expressed genes. The application of clustering techniques to time-series microarray data is commonly used in network and pathway reconstruction. One important information, which is always missing in all clustering algorithms, is the phase information. In network/pathway reconstruction, it is critical to know the order of gene expression. A good clustering algorithm must be able to identify genes that have similar expression profiles including those that are time-shifted or inverted, and provide the information known as phase. The phase information is important to decipher the potential biological relationships between genes, such as the activation, where one expects timeshifted between related expression profiles, and inhibition, where inverted expression relationship is expected. Some well known examples of clustering algorithms include hierarchical clustering, k-mean clustering and selforganizing maps. These algorithms use various similarity or dissimilarity measurements, such as Euclidean distance, Pearson correlation coefficient and Spearman rank correlation to score the similarities between gene pairs in the time domain. All these algorithms are unable to identify genes with similar but time-shifted expression patterns. Other clustering approaches such as Bayesian networks, Graph theoretic approaches, Model-based methods and Fuzzy clustering also lack the ability to address the time-shift problem. Local clustering algorithm [1] used dynamic programming to identify time-shifted genes. However, it fails

Cited by 0

The Fast Fourier Transform

Ulrich Oberst · SIAM Journal on Control and Optimization · 2007

Fast Fourier transforms (FFTs) are fast algorithms, i.e., of low complexity, for the computation of the discrete Fourier transform (DFT) on a finite abelian group. They are among the most important algorithms in applied and engineering mathematics and in computer science, in particular for one‐ and multidimensional systems theory and signal processing. We give a relatively short survey of the FFT for arbitrary finite abelian groups, cyclic or not, with complete and partially novel proofs, the main distinction being explicit induction formulas for the FFT in all cases which generalize the original FFT‐algorithm due to Cooley and Tukey and, much earlier, to Gauß. We believe that our approach has didactic advantages over the usual ones. We also present the application of the FFT to fast convolution algorithms, and the so‐called number theoretic transforms over finite coefficient rings. We do not treat those algorithms which decrease the multiplicative complexity at the expense of many more rational linear combinations, which in this context are considered costless, nor do we discuss the DFT for nonabelian finite groups.

Cited by 74