Construction of Wavelets Through Walsh Functions

Farkov, Yu. A.; Manchanda, Pammy; Siddiqi, Abul Hasan

doi:10.1007/978-981-13-6370-2

Cited by 16 publications

(2 citation statements)

References 10 publications

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“…It has such advantages as concerning with addition and subtraction only, needing less memories and having faster rate of operation as used in computation. We refer readers to other works [38][39][40][41] for a complete description of Walsh functions and their properties. We define vector-valued Walsh Fourier transform…”

Section: Introductionmentioning

confidence: 99%

A characterization of nonhomogeneous dual and weak dual wavelet superframes for Walsh‐reducing subspace of L2(ℝ+,ℂL)$$ {L}&amp;amp;amp;#x0005E;2\left({\mathbb{R}}_{&amp;amp;amp;#x0002B;},{\mathbb{C}}&amp;amp;amp;#x0005E;L\right) $$

Zhang

2022

Math Methods in App Sciences

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The concept of superframe was first introduced by Balan in the context of signal multiplexing and by Han and Larson from the perspective of pure mathematics. Since then, the theory of super wavelet (Gabor) frames has been well developed. In recent years, due to enjoying the same fast algorithm as affine wavelet frames and having more freedom to design wavelet masks, nonhomogeneous wavelet frames have attracted much attention of many mathematicians. This paper addresses (weak) nonhomogeneous dual wavelet superframes in the setting of Walsh‐reducing subspaces of L2false(ℝ+,0.1emℂLfalse)$$ {L}&amp;amp;#x0005E;2\left({\mathbb{R}}_{&amp;amp;#x0002B;},{\mathbb{C}}&amp;amp;#x0005E;L\right) $$. We present a characterization of nonhomogeneous (weak) dual wavelet superframe pairs in a Walsh‐reducing subspace of L2false(ℝ+,0.1emℂLfalse)$$ {L}&amp;amp;#x0005E;2\left({\mathbb{R}}_{&amp;amp;#x0002B;},{\mathbb{C}}&amp;amp;#x0005E;L\right) $$. Some examples are also provided.

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Section: Introductionmentioning

confidence: 99%

A characterization of nonhomogeneous dual and weak dual wavelet superframes for Walsh‐reducing subspace of L2(ℝ+,ℂL)$$ {L}&amp;amp;amp;#x0005E;2\left({\mathbb{R}}_{&amp;amp;amp;#x0002B;},{\mathbb{C}}&amp;amp;amp;#x0005E;L\right) $$

Zhang

2022

Math Methods in App Sciences

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“…Dalgacık dönüşümü, ses ve işitsel işaret işleme, görüntü ve video işleme, haberleşme, jeofizik, ekonomi ve tıp gibi özellikle bir boyutlu ve iki boyutlu işaret işleme uygulamalarında yoğun olarak kullanılmaktadır. Dalgacık dönüşüm konusunda teorinin ayrıntılarını içeren pek çok çalışma mevcuttur [5][6][7][8][9]. Dalgacık dönüşümü 1990'lardan beri farklı veri türleri üzerinde denenmiş olmasına karşın metin üzerine dalgacık dönüşümü nispeten yeni ve daha az çalışılmış bir konudur.…”

Section: Gi̇ri̇ş (Introduction)unclassified

Metin Duygu sınıflandırılmasında hibrit wavelet yönteminin kullanımı

Dönmez

Aslan

2021

Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi

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Haar transformation in text analysis  Using wavelet in sentiment analysis  Text visualization using waveletSentiment and semantic analysis of a text are very important issues of today because of increasing text data.Our study proposes a new method to reveal the hypernym relations (generic term) of the words in the text and to enhance the accuracy of sentiment classification result of the texts. We used wavelet transform method that has been rarely used in text analysis. Figure A. General Flow Diagram of Wavelet Sentiment ClassificationPurpose: The aim of the study is finding new approaches that uses wavelet transformation technique for text semantic representation and text sentiment analysis. We investigate the contribution of wavelet on the sentiment analysis classification problem. We used classical algorithms and hybrid wavelet algorithm for sentiment analysis problem. Theory and Methods:The wavelet transformation, which is generally utilized for signal processing, is used for text semantic representation and text sentiment analysis. The frequency vectors that include term frequency of special words in the reviews are transformed to D matrix using a discrete wavelet transformation. The flow of the wavelet sentiment classification is seen on Figure A. We used 5 polarity classes, which are "high positive", "low positive", "neutral", "high negative", and "low negative" in our classification problem. Results:Even wavelet is generally used for signal processing, it is seen that it is also useful for text semantic representation and sentiment analysis. In our study, to use wavelet transformation with classical classification algorithm provided % 3-5 increases in accuracy. Conclusion:As a result, wavelet transform can be used in the semantic representation of the text. When the wavelet method is added to the classical sentiment classification problem, it helps to improve accuracy. It is expected that our method will contribute to text analysis problems and applications such as decision making and text applications containing hierarchical data.

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Certain Areas of Industrial and Applied Mathematics

Siddiqi

2020

Mathematical Modelling, Optimization, Analytic and Numerical Solutions

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Construction of Wavelets Through Walsh Functions

Cited by 16 publications

References 10 publications

A characterization of nonhomogeneous dual and weak dual wavelet superframes for Walsh‐reducing subspace of L2(ℝ+,ℂL)$$ {L}&amp;amp;amp;#x0005E;2\left({\mathbb{R}}_{&amp;amp;amp;#x0002B;},{\mathbb{C}}&amp;amp;amp;#x0005E;L\right) $$

A characterization of nonhomogeneous dual and weak dual wavelet superframes for Walsh‐reducing subspace of L2(ℝ+,ℂL)$$ {L}&amp;amp;amp;#x0005E;2\left({\mathbb{R}}_{&amp;amp;amp;#x0002B;},{\mathbb{C}}&amp;amp;amp;#x0005E;L\right) $$

Metin Duygu sınıflandırılmasında hibrit wavelet yönteminin kullanımı

Certain Areas of Industrial and Applied Mathematics

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Construction of Wavelets Through Walsh Functions

Cited by 16 publications

References 10 publications

A characterization of nonhomogeneous dual and weak dual wavelet superframes for Walsh‐reducing subspace of L2(ℝ+,ℂL)$$ {L}&amp;amp;amp;amp;#x0005E;2\left({\mathbb{R}}_{&amp;amp;amp;amp;#x0002B;},{\mathbb{C}}&amp;amp;amp;amp;#x0005E;L\right) $$

A characterization of nonhomogeneous dual and weak dual wavelet superframes for Walsh‐reducing subspace of L2(ℝ+,ℂL)$$ {L}&amp;amp;amp;amp;#x0005E;2\left({\mathbb{R}}_{&amp;amp;amp;amp;#x0002B;},{\mathbb{C}}&amp;amp;amp;amp;#x0005E;L\right) $$

Metin Duygu sınıflandırılmasında hibrit wavelet yönteminin kullanımı

Certain Areas of Industrial and Applied Mathematics

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Product

Resources

About

A characterization of nonhomogeneous dual and weak dual wavelet superframes for Walsh‐reducing subspace of L2(ℝ+,ℂL)$$ {L}&amp;amp;#x0005E;2\left({\mathbb{R}}_{&amp;amp;#x0002B;},{\mathbb{C}}&amp;amp;#x0005E;L\right) $$

A characterization of nonhomogeneous dual and weak dual wavelet superframes for Walsh‐reducing subspace of L2(ℝ+,ℂL)$$ {L}&amp;amp;#x0005E;2\left({\mathbb{R}}_{&amp;amp;#x0002B;},{\mathbb{C}}&amp;amp;#x0005E;L\right) $$