Four-Term Recurrence for Fast Krawtchouk Moments Using Clenshaw Algorithm
Krawtchouk polynomials (KPs) are discrete orthogonal polynomials associated with the Gauss hypergeometric functions. These polynomials and their generated moments in 1D or 2D formats play an important role in information and coding theories, signal and image processing tools, image watermarking, and...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-04-01
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| Series: | Electronics |
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| Online Access: | https://www.mdpi.com/2079-9292/12/8/1834 |
| _version_ | 1797605644042240000 |
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| author | Barmak Honarvar Shakibaei Asli Maryam Horri Rezaei |
| author_facet | Barmak Honarvar Shakibaei Asli Maryam Horri Rezaei |
| author_sort | Barmak Honarvar Shakibaei Asli |
| collection | DOAJ |
| description | Krawtchouk polynomials (KPs) are discrete orthogonal polynomials associated with the Gauss hypergeometric functions. These polynomials and their generated moments in 1D or 2D formats play an important role in information and coding theories, signal and image processing tools, image watermarking, and pattern recognition. In this paper, we introduce a new four-term recurrence relation to compute KPs compared to their ordinary recursions (three-term) and analyse the proposed algorithm speed. Moreover, we use Clenshaw’s technique to accelerate the computation procedure of the Krawtchouk moments (KMs) using a fast digital filter structure to generate a lattice network for KPs calculation. The proposed method confirms the stability of KPs computation for higher orders and their signal reconstruction capabilities as well. The results show that the KMs calculation using the proposed combined method based on a four-term recursion and Clenshaw’s technique is reliable and fast compared to the existing recursions and fast KMs algorithms. |
| first_indexed | 2024-03-11T05:03:59Z |
| format | Article |
| id | doaj.art-5dd68040fada42589d6dbbe57fc84ef8 |
| institution | Directory Open Access Journal |
| issn | 2079-9292 |
| language | English |
| last_indexed | 2024-03-11T05:03:59Z |
| publishDate | 2023-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Electronics |
| spelling | doaj.art-5dd68040fada42589d6dbbe57fc84ef82023-11-17T19:01:33ZengMDPI AGElectronics2079-92922023-04-01128183410.3390/electronics12081834Four-Term Recurrence for Fast Krawtchouk Moments Using Clenshaw AlgorithmBarmak Honarvar Shakibaei Asli0Maryam Horri Rezaei1Centre for Life-Cycle Engineering and Management, School of Aerospace, Transport and Manufacturing, Cranfield University, Bedfordshire MK43 0AL, UKIndependent Researcher, Milton Keynes MK10 9AA, UKKrawtchouk polynomials (KPs) are discrete orthogonal polynomials associated with the Gauss hypergeometric functions. These polynomials and their generated moments in 1D or 2D formats play an important role in information and coding theories, signal and image processing tools, image watermarking, and pattern recognition. In this paper, we introduce a new four-term recurrence relation to compute KPs compared to their ordinary recursions (three-term) and analyse the proposed algorithm speed. Moreover, we use Clenshaw’s technique to accelerate the computation procedure of the Krawtchouk moments (KMs) using a fast digital filter structure to generate a lattice network for KPs calculation. The proposed method confirms the stability of KPs computation for higher orders and their signal reconstruction capabilities as well. The results show that the KMs calculation using the proposed combined method based on a four-term recursion and Clenshaw’s technique is reliable and fast compared to the existing recursions and fast KMs algorithms.https://www.mdpi.com/2079-9292/12/8/1834Krawtchouk momentsfour-term recurrencedigital filterZ-transformClenshaw formula |
| spellingShingle | Barmak Honarvar Shakibaei Asli Maryam Horri Rezaei Four-Term Recurrence for Fast Krawtchouk Moments Using Clenshaw Algorithm Electronics Krawtchouk moments four-term recurrence digital filter Z-transform Clenshaw formula |
| title | Four-Term Recurrence for Fast Krawtchouk Moments Using Clenshaw Algorithm |
| title_full | Four-Term Recurrence for Fast Krawtchouk Moments Using Clenshaw Algorithm |
| title_fullStr | Four-Term Recurrence for Fast Krawtchouk Moments Using Clenshaw Algorithm |
| title_full_unstemmed | Four-Term Recurrence for Fast Krawtchouk Moments Using Clenshaw Algorithm |
| title_short | Four-Term Recurrence for Fast Krawtchouk Moments Using Clenshaw Algorithm |
| title_sort | four term recurrence for fast krawtchouk moments using clenshaw algorithm |
| topic | Krawtchouk moments four-term recurrence digital filter Z-transform Clenshaw formula |
| url | https://www.mdpi.com/2079-9292/12/8/1834 |
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