Maximally Decimated Paraunitary Linear Phase FIR Filter Bank Design via Iterative SVD Approach

Ling, Bingo Wing‐Kuen; Tian, Nili; Ho, Charlotte Yuk-Fan; Siu, Wan-Chi; Teo, Kok Lay; Dai, Qingyun

doi:10.1109/tsp.2014.2371779

Cited by 19 publications

(5 citation statements)

References 23 publications

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“…Linear and non‐adaptive time–frequency denoising techniques are found to be useful for suppressing the noise [3]. However, the denoising performances of these conventional linear and non‐adaptive time–frequency denoising techniques such as those based on the discrete fractional Fourier transform [4] and the discrete‐time wavelet transform [5] are highly dependent on the chosen linear kernels. In general, there is no simple rule for choosing these linear kernels.…”

Section: Introductionmentioning

confidence: 99%

Grouping and selecting singular spectral analysis components for denoising based on empirical mode decomposition via integer quadratic programming

Lin

Ling

et al. 2018

IET signal process.

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This study proposes an integer quadratic programming method for grouping and selecting the singular spectral analysis components based on the empirical mode decomposition for performing the denoising. Here, the total number of the grouped singular spectral analysis components is equal to the total number of the intrinsic mode functions. The singular spectral analysis components are assigned to the group indexed by the corresponding intrinsic mode function where the two norm error between the corresponding intrinsic mode function and the sum of the grouped singular spectral analysis components is minimum. Actually, this assignment of the singular spectral analysis components to a particular group is an integer quadratic programming problem. However, the required computational power for finding the solution of the integer quadratic programming problem is high. On the other hand, by representing the integer quadratic programming problem as an integer linear programming problem and employing an existing numerical optimisation computer aided design tool for finding the solution of the integer linear programming problem, the solution can be found efficiently. Computer numerical simulation results are presented.

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Section: Introductionmentioning

confidence: 99%

Grouping and selecting singular spectral analysis components for denoising based on empirical mode decomposition via integer quadratic programming

Lin

Ling

et al. 2018

IET signal process.

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“…Filter banks have been designed for a wide range of applications, such as sub-band coding [1], multi-resolution analysis [1,2], feature extraction and classification [3], and high-speed data-rate communication [4]. In most designs, linear-phase finite impulse response (FIR) filters have been employed, since they avoid phase distortion in the sub-band components and ensure the filter bank stability.…”

Section: Introductionmentioning

confidence: 99%

Performance of analogue, digital and hybrid finite impulse response filter banks affected by realisation errors and noise

Pinheiro

Petraglia²,

Petraglia³

2018

IET signal process.

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In this study, the performance of analogue, digital and hybrid finite impulse response filter banks affected by coefficient errors, mismatches among sub-processors, and noise is investigated. A simple yet important class, the so-called time-interleaved filter bank, is also considered. Analytic models are derived to properly describe the impact of these imperfections on the filter bank performance. An estimator for the signal-to-noise ratio of these filter banks is advanced, from which comparisons are made among a large variety of structures. Computer simulations are carried out to verify the theory.

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“…In particular, an effective and an efficient design of this type of filter banks is challenging. To address this issue, the factorization approach [7,8,9,11,12,13,14,15,16,17,18,19,20,21] is proposed for designing this type of filter banks. However, as the filter bank is realized as the cascade of a set of lattices and these lattices are characterized by their rotational angles, the frequency responses of the filters are expressed as a set of very high order polynomials of the trigonometric functions of the filter coefficients.…”

mentioning

confidence: 99%

“…It is shown that the above paraunitary condition can be represented as a set of equations relating to the sum of the products of the frequency responses of the analysis filters. As these equality constraints are the quadratic equations of the filter coefficients, the problem formulation [22,23] is simpler compared to the existing problem formulations defined in the frequency domain [7,8,9,11,12,13,14,15,16,17,18,19,20,21]. Besides, this paper proposes to employ the norm relaxed sequential quadratic programming approach to find the solution of the optimization problem.…”

mentioning

confidence: 99%

Optimal maximally decimated <i>M</i>-channel mirrored paraunitary linear phase FIR filter bank design via norm relaxed sequential quadratic programming

Liu¹,

Ling²,

Dai³

et al. 2021

JIMO

Self Cite

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It is worth noting that the conventional maximally decimated Mchannel mirrored paraunitary linear phase finite impulse response condition is defined in the frequency domain. As the frequency domain is a continuous set, it is expressed as a matrix functional (a continuous function of the frequency) equation. On the other hand, this paper expresses the condition as a finite number of discrete (a set of functions of the sampled frequencies) equations. Besides, this paper proposes to sample the magnitude responses of the filters with the total number of the sampled frequencies being more than the filter lengths. Hence, the frequency selectivities of the filters can be controlled more effectively. This filter bank design problem is formulated as an optimization problem in such a way that the total mirrored paraunitary linear phase error is minimized subject to the specifications on the magnitude responses of the filters at these sampling frequencies. However, this optimization problem is highly nonconvex. To address this difficulty, a norm relaxed sequential quadratic programming approach is applied for finding its local optimal solution. By iterating the above procedures using different initial conditions, a near global optimal solution is obtained. Computer numerical simulation results show that our proposed design outperforms the existing designs.

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Maximally Decimated Paraunitary Linear Phase FIR Filter Bank Design via Iterative SVD Approach

Cited by 19 publications

References 23 publications

Grouping and selecting singular spectral analysis components for denoising based on empirical mode decomposition via integer quadratic programming

Grouping and selecting singular spectral analysis components for denoising based on empirical mode decomposition via integer quadratic programming

Performance of analogue, digital and hybrid finite impulse response filter banks affected by realisation errors and noise

Optimal maximally decimated <i>M</i>-channel mirrored paraunitary linear phase FIR filter bank design via norm relaxed sequential quadratic programming

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