Unlimited Sampling Theorem Based on Fractional Fourier Transform
The recovery of bandlimited signals with high dynamic range is a hot issue in sampling research. The unlimited sampling theory expands the recordable range of traditional analog-to-digital converters (ADCs) arbitrarily, and the signal is folded back into a low dynamic range measurement, avoiding the...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-04-01
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| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/7/4/338 |
| _version_ | 1827744998693535744 |
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| author | Hui Zhao Bing-Zhao Li |
| author_facet | Hui Zhao Bing-Zhao Li |
| author_sort | Hui Zhao |
| collection | DOAJ |
| description | The recovery of bandlimited signals with high dynamic range is a hot issue in sampling research. The unlimited sampling theory expands the recordable range of traditional analog-to-digital converters (ADCs) arbitrarily, and the signal is folded back into a low dynamic range measurement, avoiding the saturation problem. Since the non-bandlimited signal in the Fourier domain cannot be directly applied to its existing theory, the non-bandlimited signal in the Fourier domain may be bandlimited in the fractional Fourier domain. Therefore, this brief report studies the unlimited sampling problem of high dynamic non-bandlimited signals in the Fourier domain based on the fractional Fourier transform. Firstly, a mathematical signal model for unlimited sampling is proposed. Secondly, based on this mathematical model, the annihilation filtering method is used to estimate the arbitrary folding time. Finally, a novel fractional Fourier domain unlimited sampling theorem is obtained. The theory proves that, based on the folding characteristics of the self-reset ADC, the number of samples is not affected by the modulo threshold, and any folding time can be handled. |
| first_indexed | 2024-03-11T04:59:55Z |
| format | Article |
| id | doaj.art-4137d5c307d54080895a91cb0154ca60 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-11T04:59:55Z |
| publishDate | 2023-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-4137d5c307d54080895a91cb0154ca602023-11-17T19:19:47ZengMDPI AGFractal and Fractional2504-31102023-04-017433810.3390/fractalfract7040338Unlimited Sampling Theorem Based on Fractional Fourier TransformHui Zhao0Bing-Zhao Li1School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, ChinaSchool of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, ChinaThe recovery of bandlimited signals with high dynamic range is a hot issue in sampling research. The unlimited sampling theory expands the recordable range of traditional analog-to-digital converters (ADCs) arbitrarily, and the signal is folded back into a low dynamic range measurement, avoiding the saturation problem. Since the non-bandlimited signal in the Fourier domain cannot be directly applied to its existing theory, the non-bandlimited signal in the Fourier domain may be bandlimited in the fractional Fourier domain. Therefore, this brief report studies the unlimited sampling problem of high dynamic non-bandlimited signals in the Fourier domain based on the fractional Fourier transform. Firstly, a mathematical signal model for unlimited sampling is proposed. Secondly, based on this mathematical model, the annihilation filtering method is used to estimate the arbitrary folding time. Finally, a novel fractional Fourier domain unlimited sampling theorem is obtained. The theory proves that, based on the folding characteristics of the self-reset ADC, the number of samples is not affected by the modulo threshold, and any folding time can be handled.https://www.mdpi.com/2504-3110/7/4/338Fourier transformfractional Fourier transformunlimited sampling theoremnonlinear modulus mapping |
| spellingShingle | Hui Zhao Bing-Zhao Li Unlimited Sampling Theorem Based on Fractional Fourier Transform Fractal and Fractional Fourier transform fractional Fourier transform unlimited sampling theorem nonlinear modulus mapping |
| title | Unlimited Sampling Theorem Based on Fractional Fourier Transform |
| title_full | Unlimited Sampling Theorem Based on Fractional Fourier Transform |
| title_fullStr | Unlimited Sampling Theorem Based on Fractional Fourier Transform |
| title_full_unstemmed | Unlimited Sampling Theorem Based on Fractional Fourier Transform |
| title_short | Unlimited Sampling Theorem Based on Fractional Fourier Transform |
| title_sort | unlimited sampling theorem based on fractional fourier transform |
| topic | Fourier transform fractional Fourier transform unlimited sampling theorem nonlinear modulus mapping |
| url | https://www.mdpi.com/2504-3110/7/4/338 |
| work_keys_str_mv | AT huizhao unlimitedsamplingtheorembasedonfractionalfouriertransform AT bingzhaoli unlimitedsamplingtheorembasedonfractionalfouriertransform |