SNOCRAFT: A Learning-Oriented Shorthand Notation for Creating, Representing, and Analyzing Fast Fourier Transform Algorithms

1980 ◽  
Vol 17 (3) ◽  
pp. 284-284
Author(s):  
Robert J. Meir ◽  
Sathyanarayan S. Rao
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Fourier Transforms ◽  
Reduced Form ◽  
Fast Fourier Transform Algorithm ◽  
Signal Flow Graph ◽  
Shorthand Notation ◽  
The Matrix ◽  
Fourier Algorithm ◽  
Fft Analysis

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.

Parallelisation of a 2-D Fast Fourier Transform Algorithm

1991 ◽  
Vol 02 (01) ◽  
pp. 363-366 ◽  
Author(s):  
ANDREW HAMMERSLEY
Keyword(s):  
Fourier Transform ◽  
Data Analysis ◽  
Fast Fourier Transform ◽  
Fourier Transforms ◽  
Computational Physics ◽  
Fast Fourier Transforms ◽  
Two Dimensional ◽  
Fast Fourier Transform Algorithm ◽  
Higher Dimension ◽  
Parallel Network

The calculation of two and higher-dimension Fast Fourier Transforms (FFT’s) are of great importance in many areas of data analysis and computational physics. The two-dimensional FFT is implemented for a parallel network using a master-slave approach. In-place performance is good, but the use of this technique as an “accelerator” is limited by the communications time between the host and the network. The total time is reduced by performing the host-master communications in parallel with the master-slave communications. Results for the calculation of the two-dimensional FFT of real-valued datasets are presented.

scholarly journals A 2048-point Split-Radix Fast Fourier Transform Computed using Radix-4 Butterfly Units

2019 ◽  
Vol 8 (4) ◽  
pp. 2043-2046
Keyword(s):  
Fourier Transform ◽  
Power Consumption ◽  
Low Power ◽  
Fast Fourier Transform ◽  
Fourier Transforms ◽  
Low Power Consumption ◽  
Signal Flow Graph ◽  
Flow Graph ◽  
Dynamic Power ◽  
Fft Algorithms

For the low-power consumption of fast fourier transform, Split-radix fast Fourier transforms are widely used. SRFFT uses less number of mathematical calculations amongst the different FFT algorithms. Split-radix FFT has the same signal flow graph that of conventional radix-2/4 FFT’s. Therefore, the address generation method is same for SRFFT as of radix-2. A low power SRFFT architecture with modified butterfly units is presented over here. Here, it is shown that the, a 2048-point SRFFT is computed using radix-4 butterfly unist. Dynamic power is saved, on compromising the use of extra hardware. Here, the architecture size is increased from radix-2 to 4 and the dynamic power consumption is evaluated.

The extended Fourier algorithm: Application in discrete optics and electron holography

1994 ◽  
Vol 52 ◽  
pp. 918-919
Author(s):  
E. Voelkl ◽  
L. F. Allard
Keyword(s):  
Fourier Transform ◽  
Fourier Transforms ◽  
Sampling Rate ◽  
Electron Holography ◽  
Optical Bench ◽  
Fourier Space ◽  
Ccd Cameras ◽  
Simulated Image ◽  
Initial Sampling ◽  
Fourier Algorithm

The conventional discrete Fourier transform can be extended to a discrete Extended Fourier transform (EFT). The EFT allows to work with discrete data in close analogy to the optical bench, where continuous data are processed. The EFT includes a capability to increase or decrease the resolution in Fourier space (thus the argument that CCD cameras with a higher number of pixels to increase the resolution in Fourier space is no longer valid). Fourier transforms may also be shifted with arbitrary increments, which is important in electron holography. Still, the analogy between the optical bench and discrete optics on a computer is limited by the Nyquist limit. In this abstract we discuss the capability with the EFT to change the initial sampling rate si of a recorded or simulated image to any other(final) sampling rate sf.

IMPLEMENTING FAST FOURIER TRANSFORMS ON DISTRIBUTED-MEMORY MULTIPROCESSSORS USING DATA REDISTRIBUTIONS

1994 ◽  
Vol 04 (04) ◽  
pp. 477-488 ◽  
Author(s):  
S.K.S. GUPTA ◽  
C.-H. HUANG ◽  
P. SADAYAPPAN ◽  
R.W. JOHNSON
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Distributed Memory ◽  
Fourier Transforms ◽  
Experimental Performance ◽  
Minimum Number ◽  
Data Redistribution ◽  
Using Data ◽  
Performance Results ◽  
Fft Algorithms

Implementations of various fast Fourier transform (FFT) algorithms are presented for distributed-memory multiprocessors. These algorithms use data redistribution to localize the computation. The goal is to optimize communication cost by using a minimum number of redistribution steps. Both analytical and experimental performance results on the Intel iPSC/860 system are presented.

scholarly journals Flow and Fast Fourier Transform Analyses for Tip Clearance Effect in an Operating Kaplan Turbine

Energies ◽  
2019 ◽  
Vol 12 (2) ◽  
pp. 264 ◽  
Author(s):  
Hyoung-Ho Kim ◽  
Md Rakibuzzaman ◽  
Kyungwuk Kim ◽  
Sang-Ho Suh
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Operating Conditions ◽  
Tip Clearance ◽  
Tip Clearance Flow ◽  
Kaplan Turbine ◽  
Turbine Performance ◽  
Wide Range ◽  
Clearance Flow ◽  
Fft Analysis

The Kaplan turbine is an axial propeller-type turbine that can simultaneously control guide vanes and runner blades, thus allowing its application in a wide range of operations. Here, turbine tip clearance plays a crucial role in turbine design and operation as high tip clearance flow can lead to a change in the flow pattern, resulting in a loss of efficiency and finally the breakdown of hydro turbines. This research investigates tip clearance flow characteristics and undertakes a transient fast Fourier transform (FFT) analysis of a Kaplan turbine. In this study, the computational fluid dynamics method was used to investigate the Kaplan turbine performance with tip clearance gaps at different operating conditions. Numerical performance was verified with experimental results. In particular, a parametric study was carried out including the different geometrical parameters such as tip clearance between stationary and rotating chambers. In addition, an FFT analysis was performed by monitoring dynamic pressure fluctuation on the rotor. Here, increases in tip clearance were shown to occur with decreases in efficiency owing to unsteady flow. With this study’s focus on analyzing the flow of the tip clearance and its effect on turbine performance as well as hydraulic efficiency, it aims to improve the understanding on the flow field in a Kaplan turbine.

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