scholarly journals Time-space tradeoffs for matrix multiplication and the discrete fourier transform on any general sequential random-access computer

1984 ◽  
Vol 29 (2) ◽  
pp. 183-197 ◽  
Author(s):  
Yaacov Yesha
Keyword(s):  
Fourier Transform ◽  
Discrete Fourier Transform ◽  
Matrix Multiplication ◽  
Random Access ◽  
Time Space

A Time-Space Multigrid Method for Efficient Solution of the Harmonic Balance Equation System

2021 ◽  
Author(s):  
Hangkong Wu ◽  
Dingxi Wang ◽  
Xiuquan Huang ◽  
Shenren Xu
Keyword(s):  
Fourier Transform ◽  
Discrete Fourier Transform ◽  
Harmonic Balance ◽  
Multigrid Method ◽  
Equation System ◽  
Solution Stability ◽  
Inverse Discrete Fourier Transform ◽  
Time Space ◽  
Solution Accuracy ◽  
Coarse Grids

Abstract In this paper, an efficient time-space multigrid (TS-MG) method for solving a harmonic balance (HB) equation system is proposed. The principle of the time-space multigrid method is to coarsen grids in both space and time dimensions simultaneously when coarse grids are formed. The inclusion of time in the time-space multigrid is to address the instability issue or diminished convergence speedup of the spatial multigrid (S-MG) due to larger grid reduced frequencies on coarse grids. With the proposed method, the unsteady governing equation will be solved on all grid levels. Comparing to the finest grid, fewer harmonics and thus fewer equations will be solved consequently on coarse grids. Discrete Fourier transform (DFT) and inverse discrete Fourier transform (IDFT) are used to achieve solution prolongation and restriction between different time grid levels. Results from the proposed method are compared with those obtained from the traditional spatial multigrid and time domain methods. It is found that the TS-MG method can increase solution stability, reduce analysis time cost required for convergence, save memory usage and has no adverse effect on solution accuracy.

APPLICATION OF UNCONVENTIONAL METHODS FOR FREQUENCY ANALYSIS IN ACOUSTICS

Akustika ◽  
2020 ◽  
Vol 36 (36) ◽  
pp. 25-32
Author(s):  
Jaroslav Smutný ◽  
Dušan Janoštík ◽  
Viktor Nohál
Keyword(s):  
Fourier Transform ◽  
Discrete Fourier Transform ◽  
Frequency Analysis ◽  
Mathematical Analysis ◽  
Measured Data ◽  
Application Area ◽  
Acoustic Response ◽  
Recommendations For Practice ◽  
Unconventional Methods ◽  
Frequency Area

The goal of this study is to familiarize a wider professional public with not fully known procedures suitable for processing measured data in the frequency area. Described is the use of the so-called Multi-taper method to analyze the acoustic response. This transformation belongs to a group of nonparametric methods outgoing from discrete Fourier transform, and this study includes its mathematical analysis and description. In addition, the use of respective method in a specific application area and recommendations for practice are described.

Wideband Time-space Radon-Fourier Transform for High-speed and Weak Target Detection

2014 ◽  
Vol 35 (1) ◽  
pp. 15-23 ◽  
Author(s):  
Li-chang Qian ◽  
Jia Xu ◽  
Wen-feng Sun ◽  
Ying-ning Peng
Keyword(s):  
Fourier Transform ◽  
Target Detection ◽  
High Speed ◽  
Time Space ◽  
Weak Target
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