Optimal design of filters and filter banks using a symbolic approach
The theories and applications of the discrete wavelet transform (DWT) have developed greatly over the last twenty years and the discrete wavelet transform (DWT) itself has also been recognized as a useful signal analyzing tool in areas like mul-tiresolution signal and image processing....
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| Format: | Final Year Project |
| Language: | English |
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Nanyang Technological University
2020
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| Online Access: | https://hdl.handle.net/10356/140431 |
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| Institution: | Nanyang Technological University |
| Language: | English |
| Summary: | The theories and applications of the discrete wavelet transform (DWT) have developed greatly over the last twenty years and the discrete wavelet transform (DWT) itself has also been recognized as a useful signal analyzing tool in areas like mul-tiresolution signal and image processing. Among all kinds of wavelet filter banks, theorthogonal filter bank stands out due to its advantage of energy preservation. In this project, the optimization is in the sense of time and frequency localization. A finite energy function cannot be compactly supported both in the time and frequency domains. So the Heisenberg balanced-uncertainty metric is used to represent the rela-tionship between time and frequency localization. In the literature, most of the researches focus on frequency localization. In thisproject, the optimization of time localization is taken into account first. Both the sym-bolic method and the numerical method are applied to time localization optimization.Theoretically, the symbolic method is more comprehensive and can find the global minimum precisely, but it requires too much computation power in higher order. So forhigher-order optimization, the numerical method which is less precise but less complex to the computer is adopted. Furthermore, if the time localization is optimized withoutany constraints, it tends to end at the origin, so the first vanishing moment is introducedas the constraint. After that, the frequency localization and the joint time-frequency localization are optimized using the same numerical method. The final optimization is completed by finding a minimum of an unconstrained multi-variable function using the derivative-free method. |
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