A Rational Approximation of the Fourier Transform by Integration with Exponential Decay Multiplier

Abrarov, S. M.; Siddiqui, Rehan; Jagpal, Rajinder K.; Quine, Brendan M.

doi:10.4236/am.2021.1211063

Cited by 2 publications

(3 citation statements)

References 20 publications

(21 reference statements)

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“…Transform itself is a lossless and reversible technology, but in order to obtain better coding effect, some unimportant coefficients are ignored; so, it becomes a lossy technology. Commonly used transform coding schemes include discrete cosine transform (DCT) and Fourier transform coding [6,7].…”

Section: Literature Reviewmentioning

confidence: 99%

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Multimedia Image Data Compression Based on Wavelet Analysis

Wang

Zhu

2022

Wireless Communications and Mobile Computing

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In order to improve the compression technology of multimedia image data, a compression method of multimedia image data based on wavelet analysis was proposed. By combining Fourier transform and wavelet packet multithreshold denoising method, the image data was denoised and compressed through the transform of wavelet analysis and multithreshold processing, so as to realize the compression of image data with high quality. The experimental results showed that it was effective to analyze signal singularity, singularity position, and singularity degree by using wavelet analysis. And the signal mutation position near t = 0 could be seen clearly from the wavelet coefficient diagram, while the Fourier transform diagram did not provide any information about when the frequency mutation occurred. It was concluded that the method of multimedia image data compression based on wavelet analysis could promote the development of multimedia image data compression technology effectively.

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Section: Literature Reviewmentioning

confidence: 99%

“…The decomposition algorithm of wavelet packet is that fd j,2k t g and fd j,2k+1 t g are solved through fd j+1,k t g, as shown in Formula (7).…”

Section: Key Technologies Of Wavelet Packet Multithresholdmentioning

confidence: 99%

Multimedia Image Data Compression Based on Wavelet Analysis

Wang

Zhu

2022

Wireless Communications and Mobile Computing

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“…Nyengeri et al [5] produced economized series truncated at relatively lower orders by the use of power series together with Chebyshev polynomials and then applied this approach to the solution of ordinary differential equations via Frobenius and Taylor methods. Abrarov et al [6] introduced a method to approximate the Fourier transform of a function as rational polynomials.…”

Section: Introductionmentioning

confidence: 99%

Estimating Sums of Convergent Series via Rational Polynomials

Beji¹

2023

APM

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Sums of convergent series for any desired number of terms, which may be infinite, are estimated very accurately by establishing definite rational polynomials. For infinite number of terms the sum infinite is obtained by taking the asymptotic limit of the rational polynomial. A rational function with seconddegree polynomials both in the numerator and denominator is found to produce excellent results. Sums of series with different characteristics such as alternating signs are considered for testing the performance of the proposed approach.

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A Rational Approximation of the Fourier Transform by Integration with Exponential Decay Multiplier

Cited by 2 publications

References 20 publications

Multimedia Image Data Compression Based on Wavelet Analysis

Multimedia Image Data Compression Based on Wavelet Analysis

Estimating Sums of Convergent Series via Rational Polynomials

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