scholarly journals Regularity of the Transform of Laplace and the Transfom of Fourier

2021 ◽  
pp. 13-18
Author(s):  
Andrey Pavlov
Keyword(s):  
Cosine Transform ◽  
Sine Transform

Regularity of the transform of Laplace in the opened area of 0 is proved with help of some methods of the transform of Fourier. The class of the transform of Laplace from the transform of Fourier is considered from some functions without a regularity in null. The functions are regular in the opened area of 0. It is proved, that the sine transform of Fourier from the cosine transform of Fourier is equal to the cosine transform from the sine transform of Fourier on the module.

scholarly journals Improved Algorithm for ODCT Computation of a Running Data Sequence

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
S. Akhter ◽  
V. Karwal ◽  
R. C. Jain
Keyword(s):  
Real Time ◽  
Discrete Cosine Transform ◽  
Input Data ◽  
Time Sequence ◽  
Data Sequence ◽  
Cosine Transform ◽  
Rectangular Window ◽  
Sine Transform ◽  
Data Points ◽  
Transform Coefficients

Fast windowed update algorithms capable of independently updating the odd discrete cosine transform (ODCT) and odd discrete sine transform (ODST) of a running data sequence are analytically developed. In this algorithm, to compute the ODCT coefficients of a real-time sequence, we do not require the ODST coefficients. Similarly, the ODST coefficients of the shifted sequence can be calculated without using ODCT coefficients. The running input data sequence is sampled using a rectangular window. However, this idea can be easily extended for other windows. The update algorithm derived herein can be used to compute the transform coefficients of the shifted sequence as new data points are available. The complexity of developed algorithm isO(N). The validity of algorithm is tested by MATLAB simulations.

FOURIER SINE AND COSINE TRANSFORMS ON BOEHMIAN SPACES

2013 ◽  
Vol 06 (01) ◽  
pp. 1350005 ◽  
Author(s):  
R. Roopkumar ◽  
E. R. Negrin ◽  
C. Ganesan
Keyword(s):  
Fourier Transform ◽  
Cosine Transform ◽  
Fourier Cosine ◽  
Sine Transform ◽  
Fourier Sine ◽  
Fourier Sine Transform ◽  
Fourier Cosine Transform ◽  
One To One ◽  
The Fourier Transform

We construct suitable Boehmian spaces which are properly larger than [Formula: see text] and we extend the Fourier sine transform and the Fourier cosine transform more than one way. We prove that the extended Fourier sine and cosine transforms have expected properties like linear, continuous, one-to-one and onto from one Boehmian space onto another Boehmian space. We also establish that the well known connection among the Fourier transform, Fourier sine transform and Fourier cosine transform in the context of Boehmians. Finally, we compare the relations among the different Boehmian spaces discussed in this paper.

Unified array architecture for discrete cosine transform, sine transform and their inverses

1995 ◽  
Vol 31 (21) ◽  
pp. 1811-1812 ◽  
Author(s):  
Jiun-In Guo ◽  
Chein-Wei Jen ◽  
Chingson Chen
Keyword(s):  
Discrete Cosine Transform ◽  
Cosine Transform ◽  
Sine Transform ◽  
Array Architecture

scholarly journals A Computational Method for n-Dimensional Laplace Transforms Involved with Fourier Cosine Transform

2013 ◽  
Vol 2013 ◽  
pp. 1-4
Author(s):  
Jafar Saberi-Nadjafi
Keyword(s):  
Laplace Transform ◽  
Laplace Transforms ◽  
Computational Method ◽  
Cosine Transform ◽  
Fourier Cosine ◽  
Sine Transform ◽  
Fourier Sine ◽  
Fourier Sine Transform ◽  
Fourier Cosine Transform

In 2007, the author published some results on n-dimensional Laplace transform involved with the Fourier sine transform. In this paper, we propose some new result in n-dimensional Laplace transforms involved with Fourier cosine transform; these results provide few algorithms for evaluating some n-dimensional Laplace transform pairs. In addition, some examples are also presented, which explain the useful applications of the obtained results. Therefore, one can produce some two- and three- as well as n-dimensional Laplace transforms pairs.

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