Spectrum Features Analysis of Ocean Wind and Wave Based on Fast Fourier Transform Algorithm

This paper presents a full and well-developed view of the Fast Fourier Transform (FFT). It is intended for the reader who wishes to learn and develop his own fast Fourier algorithm. The approach presented here utilizes the matrix description of fast Fourier transforms. This approach leads to a systematic method for greatly reducing the complexity and the space required by variety of signal flow graph descriptions. This reduced form is called SNOCRAFT. From this representation, it is then shown how one can derive all possible fast Fourier transform algorithms, including the Weinograd Fourier transform algorithm. It is also shown from the SNOCRAFT representation that one can easily compute the number of multiplications and additions required to perform a specified fast Fourier transform algorithm. After an elementary introduction to matrix representation of fast Fourier transform algorithm, the method of generating all possible fast Fourier transform algorithms is presented in detail and is given in three sections. The first section discusses the Generation of SNOCRAFT and the second section illustrates how Operations on SNOCRAFT are made. These operations include inversion and rotation. The last section deals with the FFT Analysis. In this section, examples are provided to illustrate how one counts the number of multiplications and additions involved in performing the transform that one has developed.

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Application of two-dimensional fast Fourier transform algorithm, analog of the Cooley-Tukey algorithm, for 4k fixed format digital image of satellite data in frequency domain processing

E3S Web of Conferences ◽

10.1051/e3sconf/202014902010 ◽

2020 ◽

Vol 149 ◽

pp. 02010 ◽

Cited By ~ 1

Author(s):

Mikhail Noskov ◽

Valeriy Tutatchikov

Keyword(s):

Fourier Transform ◽

Numerical Experiment ◽

Fast Fourier Transform ◽

Frequency Domain ◽

Discrete Fourier Transform ◽

Satellite Data ◽

Digital Image ◽

Digital Images ◽

Two Dimensional ◽

Fast Fourier Transform Algorithm

Currently, digital images in the format Full HD (1920 * 1080 pixels) and 4K (4096 * 3072) are widespread. This article will consider the option of processing a similar image in the frequency domain. As an example, take a snapshot of the earth's surface. The discrete Fourier transform will be computed using a two-dimensional analogue of the Cooley-Tukey algorithm and in a standard way by rows and columns. Let us compare the required number of operations and the results of a numerical experiment. Consider the examples of image filtering.

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Design of a 16-point Winograd fast Fourier transform algorithm integrated circuit system

Proceedings of VHDL International Users Forum ◽

10.1109/viuf.1994.323958 ◽

2002 ◽

Author(s):

T.S. Wailes ◽

W.D. O'Connor ◽

M.A. Mehalic

Keyword(s):

Fourier Transform ◽

Fast Fourier Transform ◽

Integrated Circuit ◽

Fast Fourier Transform Algorithm

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Note on the FFT Based Computational Code and Its Application

STLE/ASME 2008 International Joint Tribology Conference ◽

10.1115/ijtc2008-71216 ◽

2008 ◽

Cited By ~ 5

Author(s):

Xiaoqing Jin ◽

Leon M. Keer ◽

Qian Wang

Keyword(s):

Numerical Simulation ◽

Fourier Transform ◽

Fast Fourier Transform ◽

Toeplitz Matrix ◽

Contact Problems ◽

Point Of View ◽

Fast Fourier Transform Algorithm ◽

Discrete Convolution ◽

Mathematical Point ◽

Computational Code

The discrete convolution based Fast Fourier Transform algorithm (DC-FFT) has been successfully applied in numerical simulation of contact problems. The algorithm is revisited from a mathematical point of view, equivalent to a Toeplitz matrix multiplied by a vector. The nature of the convolution property permits one to implement the algorithm with fewer constraints in choosing the computational domains. This advantageous feature is explored in the present work, and is expected to be beneficial to many tribological studies.

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