Integrated representation for discrete Fourier and wavelet transforms using vector notation
Many mathematical operations are implemented easily through transform domain operations. Multiple transform domain operations are used independently in large and complex applications. There is a need to develop integrated representations for multiple transform domain operations. This paper presents...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Mehran University of Engineering and Technology
2022-07-01
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| Series: | Mehran University Research Journal of Engineering and Technology |
| Online Access: | https://publications.muet.edu.pk/index.php/muetrj/article/view/2533 |
| _version_ | 1811339137336213504 |
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| author | Tariq Javid Muhammad Faris Arshad Aziz Pervez Akhtar |
| author_facet | Tariq Javid Muhammad Faris Arshad Aziz Pervez Akhtar |
| author_sort | Tariq Javid |
| collection | DOAJ |
| description | Many mathematical operations are implemented easily through transform domain operations. Multiple transform domain operations are used independently in large and complex applications. There is a need to develop integrated representations for multiple transform domain operations. This paper presents an integrated mathematical representation for the discrete Fourier transformation and the discrete wavelet transformation. The proposed combined representation utilizes the powerful vector notation. A mathematical operator, called the star operator, is formulated that merges coefficients from different transform domains. The star operator implements both convolution and correlation processes in a weighted fashion to compute the aggregated representation. The application of the proposed mathematical formulation is demonstrated successfully through merging transform domain representations of time-domain and image-domain representations. Heart sound signals and magnetic resonance images are used to describe transform-domain data merging applications. The significance of the proposed technique is demonstrated through merging time-domain and image-domain representations in a single- stage that may be implemented as the primary processing engine inside a typical digital image processing and analysis system. |
| first_indexed | 2024-04-13T18:20:54Z |
| format | Article |
| id | doaj.art-85791fd587c94075acfabb0d207bb7c6 |
| institution | Directory Open Access Journal |
| issn | 0254-7821 2413-7219 |
| language | English |
| last_indexed | 2024-04-13T18:20:54Z |
| publishDate | 2022-07-01 |
| publisher | Mehran University of Engineering and Technology |
| record_format | Article |
| series | Mehran University Research Journal of Engineering and Technology |
| spelling | doaj.art-85791fd587c94075acfabb0d207bb7c62022-12-22T02:35:27ZengMehran University of Engineering and TechnologyMehran University Research Journal of Engineering and Technology0254-78212413-72192022-07-0141317518410.22581/muet1982.2203.182533Integrated representation for discrete Fourier and wavelet transforms using vector notationTariq Javid0Muhammad Faris1Arshad Aziz2Pervez Akhtar3Department of Biomedical Engineering, Faculty of Engineering Sciences and Technology, Hamdard University, Karachi PakistanDepartment of Biomedical Engineering, Faculty of Engineering Sciences and Technology, Hamdard University, Karachi PakistanDepartment of Electronic and Power Engineering, National University of Sciences and Technology, Karachi Campus, PakistanDepartment of Electrical Engineering, Sir Syed University of Engineering and Technology, Karachi PakistanMany mathematical operations are implemented easily through transform domain operations. Multiple transform domain operations are used independently in large and complex applications. There is a need to develop integrated representations for multiple transform domain operations. This paper presents an integrated mathematical representation for the discrete Fourier transformation and the discrete wavelet transformation. The proposed combined representation utilizes the powerful vector notation. A mathematical operator, called the star operator, is formulated that merges coefficients from different transform domains. The star operator implements both convolution and correlation processes in a weighted fashion to compute the aggregated representation. The application of the proposed mathematical formulation is demonstrated successfully through merging transform domain representations of time-domain and image-domain representations. Heart sound signals and magnetic resonance images are used to describe transform-domain data merging applications. The significance of the proposed technique is demonstrated through merging time-domain and image-domain representations in a single- stage that may be implemented as the primary processing engine inside a typical digital image processing and analysis system.https://publications.muet.edu.pk/index.php/muetrj/article/view/2533 |
| spellingShingle | Tariq Javid Muhammad Faris Arshad Aziz Pervez Akhtar Integrated representation for discrete Fourier and wavelet transforms using vector notation Mehran University Research Journal of Engineering and Technology |
| title | Integrated representation for discrete Fourier and wavelet transforms using vector notation |
| title_full | Integrated representation for discrete Fourier and wavelet transforms using vector notation |
| title_fullStr | Integrated representation for discrete Fourier and wavelet transforms using vector notation |
| title_full_unstemmed | Integrated representation for discrete Fourier and wavelet transforms using vector notation |
| title_short | Integrated representation for discrete Fourier and wavelet transforms using vector notation |
| title_sort | integrated representation for discrete fourier and wavelet transforms using vector notation |
| url | https://publications.muet.edu.pk/index.php/muetrj/article/view/2533 |
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