Design of periodic window functions in filter window filter banks for harsh environments

Yang, Chuqi; Xiao, Jun; Zeng, Yan; Deng, Baiwei; Ling, Wing‐Kuen

doi:10.1109/indin.2016.7819305

Cited by 1 publication

(5 citation statements)

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“…For the compatibility of the filter window bank, it requires the existence of at least two nonzero elements in each row of H(z) in order to have a possibility to cancel the transfer functional distortion or the aliasing distortion. Therefore, we have the following results on the compatibility of the filter window bank [14], [29].…”

Section: Notations a Block Diagram Of A Filter Window Bank Is Shown Inmentioning

confidence: 99%

“…Here, textf loor(a) denotes the small integer less than or equal to a . Then, we have the following results [14], [29]. For the compatible filter window bank, the exact perfect reconstruction condition becomes:…”

Section: Notations a Block Diagram Of A Filter Window Bank Is Shown Inmentioning

confidence: 99%

“…It is worth noting thatH(z) is an N × M −1 i=0N i matrix. Therefore, we have the following results on the compatibility of the filter window bank [14], [29]: Definẽ…”

Section: Notations a Block Diagram Of A Filter Window Bank Is Shown Inmentioning

confidence: 99%

“…Since the sampling structure in the analysis block nonuniform filter bank is symmetric to that in the synthesis block nonuniform filter bank, the aliasing distortions can only be suppressed for some block nonuniform filter banks and the exact perfect reconstruction cannot be achieved. Recently, a filter window bank is proposed [14], [29]. It consists of a bank of analysis filters, a bank of analysis periodic windows, a bank of synthesis filters and a bank of synthesis periodic windows.…”

mentioning

confidence: 99%

“…This is because the joint conventional downsampling functions and the conventional upsampling functions of the conventional nonuniform filter bank as well as the joint block downsampling functions and the block upsampling functions of the block nonuniform filter bank are the particular types of the analysis periodic window functions of the filter window bank. However, it is shown in [14], [29] that this filter window bank still does not achieve the exact perfect reconstruction and only the near perfect reconstruction can be achieved. As a result, several fundamental issues are required to be addressed.…”

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confidence: 99%

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Optimal design of window functions for filter window bank

Zhou¹,

Ling²,

Dam³

et al. 2021

Journal of Industrial &Amp; Management Optimization

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This paper considers the designs of the periodic window functions in the filter window banks. First, the filter window bank with the constant synthesis periodic window functions is considered. The total number of the nonzero coefficients in the impulse responses of the analysis periodic window functions is minimized subject to the near perfect reconstruction condition. This is an L 0 norm optimization problem. To find its solution, the L 0 norm optimization problem is approximated by the L 1 norm optimization problem. Then, the column of the constraint matrix corresponding to the element in the solution with the smallest magnitude is removed. Next, it is tested whether the feasible set corresponding to the new L 0 norm optimization problem is empty or not. By repeating the above procedures, a solution of the L 0 norm optimization problem is obtained. Second, the filter window bank with the time varying synthesis periodic window functions is considered. Likewise, the design of the periodic window functions in both the analysis periodic window functions and the synthesis periodic window functions is formulated as an L 0 optimization problem. However, this L 0 norm optimization problem is subject to a quadratic matrix inequality constraint. To find its solution, the set of the synthesis periodic window functions is initialized. Then, the set of the analysis periodic window functions is optimized based on the initialized set of the synthesis periodic window functions. Next, the set of the synthesis periodic window functions is optimized based on the found set of the analysis periodic window functions. Finally, these two procedures are iterated. It is shown that the iterative algorithm converges. A design example of a filter window bank with the constant synthesis periodic window functions and a design example of a filter window bank with the time varying synthesis periodic window functions are illustrated. It is shown that the near perfect reconstruction condition is satisfied, whereas this is not the cases for the nonuniform filter banks with the conventional samplers and the conventional block samplers.

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Section: Notations a Block Diagram Of A Filter Window Bank Is Shown Inmentioning

confidence: 99%

Section: Notations a Block Diagram Of A Filter Window Bank Is Shown Inmentioning

confidence: 99%

“…It is worth noting thatH(z) is an N × M −1 i=0N i matrix. Therefore, we have the following results on the compatibility of the filter window bank [14], [29]: Definẽ…”

Section: Notations a Block Diagram Of A Filter Window Bank Is Shown Inmentioning

confidence: 99%

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confidence: 99%

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confidence: 99%

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