Optimal Joint Design of Discrete Fractional Fourier Transform Matrices and Mask Coefficients for Multichannel Filtering in Fractional Fourier Domains

The concept of mask operation in fractional Fourier domains is a generalization of the conventional Fourier-based filtering in the frequency domain. It is known that simultaneously employing multiple mask operations in multiple different fractional Fourier domains can lead to significant performance...

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Main Authors: Zhang, X., Ling, B., Dam, Hai Huyen Heidi, Teo, Kok Lay, Wu, Changzhi
Format: Journal Article
Published: IEEE 2018
Online Access:http://hdl.handle.net/20.500.11937/71082
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author Zhang, X.
Ling, B.
Dam, Hai Huyen Heidi
Teo, Kok Lay
Wu, Changzhi
author_facet Zhang, X.
Ling, B.
Dam, Hai Huyen Heidi
Teo, Kok Lay
Wu, Changzhi
author_sort Zhang, X.
building Curtin Institutional Repository
collection Online Access
description The concept of mask operation in fractional Fourier domains is a generalization of the conventional Fourier-based filtering in the frequency domain. It is known that simultaneously employing multiple mask operations in multiple different fractional Fourier domains can lead to significant performance advantages when compared with just employing a single mask operation in a single fractional Fourier domain. However, there is no systematic scheme for optimal joint design of the discrete fractional Fourier transform (DFrFT) matrices and the corresponding sets of mask coefficients. In this paper, we consider this design problem and construct a formulation that does not depend on the knowledge of noise statistics. We then develop an iterative algorithm, which is a hybrid descent (HD) approach, to solve the formulated optimization problem. For this HD approach, a gradient descent method is supplemented by a modified simulated annealing algorithm. It is employed to find the global optimal rotation angles of the DFrFT matrices. During the iterative process, the corresponding sets of mask coefficients can be constructed analytically. Simulation results demonstrate that the proposed scheme is highly effective.
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institution Curtin University Malaysia
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publishDate 2018
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spelling curtin-20.500.11937-710822019-03-27T02:11:15Z Optimal Joint Design of Discrete Fractional Fourier Transform Matrices and Mask Coefficients for Multichannel Filtering in Fractional Fourier Domains Zhang, X. Ling, B. Dam, Hai Huyen Heidi Teo, Kok Lay Wu, Changzhi The concept of mask operation in fractional Fourier domains is a generalization of the conventional Fourier-based filtering in the frequency domain. It is known that simultaneously employing multiple mask operations in multiple different fractional Fourier domains can lead to significant performance advantages when compared with just employing a single mask operation in a single fractional Fourier domain. However, there is no systematic scheme for optimal joint design of the discrete fractional Fourier transform (DFrFT) matrices and the corresponding sets of mask coefficients. In this paper, we consider this design problem and construct a formulation that does not depend on the knowledge of noise statistics. We then develop an iterative algorithm, which is a hybrid descent (HD) approach, to solve the formulated optimization problem. For this HD approach, a gradient descent method is supplemented by a modified simulated annealing algorithm. It is employed to find the global optimal rotation angles of the DFrFT matrices. During the iterative process, the corresponding sets of mask coefficients can be constructed analytically. Simulation results demonstrate that the proposed scheme is highly effective. 2018 Journal Article http://hdl.handle.net/20.500.11937/71082 10.1109/TSP.2018.2870365 IEEE restricted
spellingShingle Zhang, X.
Ling, B.
Dam, Hai Huyen Heidi
Teo, Kok Lay
Wu, Changzhi
Optimal Joint Design of Discrete Fractional Fourier Transform Matrices and Mask Coefficients for Multichannel Filtering in Fractional Fourier Domains
title Optimal Joint Design of Discrete Fractional Fourier Transform Matrices and Mask Coefficients for Multichannel Filtering in Fractional Fourier Domains
title_full Optimal Joint Design of Discrete Fractional Fourier Transform Matrices and Mask Coefficients for Multichannel Filtering in Fractional Fourier Domains
title_fullStr Optimal Joint Design of Discrete Fractional Fourier Transform Matrices and Mask Coefficients for Multichannel Filtering in Fractional Fourier Domains
title_full_unstemmed Optimal Joint Design of Discrete Fractional Fourier Transform Matrices and Mask Coefficients for Multichannel Filtering in Fractional Fourier Domains
title_short Optimal Joint Design of Discrete Fractional Fourier Transform Matrices and Mask Coefficients for Multichannel Filtering in Fractional Fourier Domains
title_sort optimal joint design of discrete fractional fourier transform matrices and mask coefficients for multichannel filtering in fractional fourier domains
url http://hdl.handle.net/20.500.11937/71082