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Speech presence probability (SPP) and gain functions such as Wiener filter or MMSE estimators require an estimate of the a-priori signal-to-noise ratio (SNR). However, the estimation of the a-priori SNR is computationally involved and sensitive to noise variations. This paper proposes to approximate the SPP and the overall gain function of a speech enhancement system by using sigmoid functions to reduce the need of estimating the a-prior SNR. By applying an approximation via the sigmoid functions it is shown that only the a-posteriori estimate of SNR is needed, resulting in a low complexity system. The sigmoid function is designed with an optimization algorithm to optimize its parameters with respect to speech quality measures. The optimization algorithm is based on the idea that the solution obtained for a given problem should move towards the best solution and avoid the worst solution. The proposed algorithm requires minimal control parameters and does not require any algorithm specific parameters. Simulation results show that the proposed sigmoid functions achieve good results in terms of speech quality measures when compared with existing methods while providing significantly lower complexity for implementation. [ABSTRACT FROM AUTHOR]

This paper proposes a new adaptive algorithm for the second-order blind signal separation (BSS) problem with convolutive mixtures by utilising a combination of an accelerated gradient and a conjugate gradient method. For each iteration of the adaptive algorithm, the search point and the search direction are obtained based on the current and the previous iterations. The algorithm efficiently calculates the step size for the accelerated conjugate gradient algorithm in each iteration. Simulation results show that the proposed accelerated conjugate gradient algorithm with optimal step size converges faster than the accelerated descent algorithm and the steepest descent algorithm with optimal step size while having lower computational complexity. In particular, the number of iterations required for convergence of the accelerated conjugate gradient algorithm is significantly lower than the accelerated descent algorithm and the steepest descent algorithm. In addition, the proposed system achieves improvement in terms of the signal to interference ratio and signal to noise ratio for the dominant speech outputs. [ABSTRACT FROM AUTHOR]

Compressive speech enhancement makes use of the sparseness of speech and the non-sparseness of noise in time-frequency representation to perform speech enhancement. However, reconstructing the sparsest output may not necessarily translate to a good enhanced speech signal as speech distortion may be at risk. This paper proposes a two level optimization approach to incorporate objective quality measures in compressive speech enhancement. The proposed method combines the accelerated proximal gradient approach and a global one dimensional optimization method to solve the sparse reconstruction. By incorporating objective quality measures in the optimization process, the reconstructed output is not only sparse but also maintains the highest objective quality score possible. In other words, the sparse speech reconstruction process is now quality sparse speech reconstruction. Experimental results in a compressive speech enhancement consistently show score improvement in objectives measures in different noisy environments compared to the non-optimized method. Additionally, the proposed optimization yields a higher convergence rate with a lower computational complexity compared to the existing methods. [ABSTRACT FROM AUTHOR]

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 norm optimization problem. To find its solution, the norm optimization problem is approximated by the 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 norm optimization problem is empty or not. By repeating the above procedures, a solution of the 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 optimization problem. However, this 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. [ABSTRACT FROM AUTHOR]

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 L0 norm optimization problem. To find its solution, the L0 norm optimization problem is approximated by the L1 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 L0 norm optimization problem is empty or not. By repeating the above procedures, a solution of the 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 L0 optimization problem. However, this L0 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. [ABSTRACT FROM AUTHOR]

In this paper, we investigate robust design methods for broadband beamformers in reverberant environments. In the design formulation room reverberation as well as robustness to amplitude and phase mismatches in the microphones have been included. Particularly, the direct path and the reflections are separated in the design such that there is a penalty on the reflective part. This approach is different from the commonly studied problem of dereverberation of a single point source as the investigated design is made over a region in space. A single point derverberation is not a very practical approach due to a high sensitivity to position changes. Thus in order to obtain more practical microphone array designs, we study methods that optimize performance over areas in space. The design problem has been formulated in four different ways; (i) using direct path only representing a traditional beamformer design method, (ii) using a robust design method which considers robustness against the microphone characteristics (gain and phase) by optimizing the mean performance, (iii) by including room impulse response in the design and finally, (iv) using both robustness and room impulse response in the design. Simulation results show that robust direct path based beamformer can achieve approximately the same performance as including room response in the design in many reverberation environments. The proposed method provides robustness over larger variations in the reverberation environment. This means that the robust direct path based method which is based on mean variations in gain and phase can be used in low- to medium ( T 60 = 100–300 ms) reverberant environments with good result. [ABSTRACT FROM AUTHOR]

This paper investigates the design of non-uniform cosine modulated filter bank (CMFB) with both finite precision coefficients and infinite precision coefficients. The finite precision filter bank has been designed to reduce the computational complexity related to the multiplication operations in the filter bank. Here, non-uniform filter bank (NUFB) is obtained by merging the appropriate filters of an uniform filter bank. An efficient optimization approach is developed for the design of non-uniform CMFB with infinite precision coefficients. A new procedure based on the discrete filled function is then developed to design the filter bank prototype filter with finite precision coefficients. Design examples demonstrate that the designed filter banks with both infinite precision coefficients and finite precision coefficients have low distortion and better performance when compared with other existing methods. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Zero-forcing beamforming under per-antenna power constraints is considered for rural applications. By exploring the structures of a deterministic line-of-sight channel matrix, some properties are found for the optimal weighting matrix. Particularly, some constraints can be removed from the original formulation. With these properties, a reduced complexity zero-forcing beamformer design is proposed. Numerical examples under several different scenarios are provided. [ABSTRACT FROM AUTHOR]

This paper proposes an algorithm for the second-order blind signal separation problem with convolutive mixtures. An iterative first order gradient method based on the accelerated gradient is developed for solving the optimization problem. For each search direction, the question becomes how to effectively calculate the optimal step size in each iteration. Here, we propose an efficient algorithm for obtaining the step size by first reformulating the objective function as a fourth order polynomial in terms of the step size, where the polynomial coefficients are required to be calculated only once per iteration. An optimal step size search procedure using the Newton’s method is developed with the step size is efficiently obtained for each iteration. Simulation results in a simulated room environment and a real environment show that the proposed algorithm converges faster than the existing methods with a lower number of iterations and a lower computational complexity. In addition, the proposed algorithm can separate the speech signals and reduce the background noise simultaneously. [ABSTRACT FROM AUTHOR]

This letter proposes an optimal design of the filter bank with minimum inband aliasing, residual aliasing together with restrictions on the frequency response of the analysis filter and the distortion level for the filter bank. A new procedure that includes the combination of one parameter filled function and an iterative method is developed to solve the optimization problem. The advantage of using the iterative algorithm within the filled function is that a lower basin can be obtained with a low computational complexity. Design examples show that a significant improvement can be obtained using the proposed method over existing methods. [ABSTRACT FROM PUBLISHER]

This letter proposes a new algorithm for solving the optimal zero-forcing beamforming problem that maximizes the user achievable rate with restriction on the per-antenna element power constraints. An accelerated gradient method with step size search is proposed for solving the problem. For each iteration of the gradient approach, a quick one dimensional search is employed to obtain the step size. The advantage of the step-size search is that it is relatively fast and requires only a few calculations of the objective function. Design examples show that the proposed algorithm converges faster than the gradient approach and the accelerated gradient approach with a constant step size while achieving a low computational complexity. [ABSTRACT FROM AUTHOR]

A first-order zero-forcing beamformer design is proposed in this letter for MU-MIMO systems under per-antenna power constraints (PAPC). By forming the regularized dual problem, first-order methods can be applied. To achieve the limit convergence rate of first-order methods, an accelerated method is introduced to solve the regularized dual problem. Simulation results are provided to show the effectiveness of the proposed method. [ABSTRACT FROM PUBLISHER]

This brief investigates a tradeoff between the integral squared error and the peak deviation error for a variable fractional delay (VFD) filter with a coefficient relationship. The integral squared error is minimized subject to additional constraints on the peak deviation error. The problem is solved by utilizing second-order cone programming. In addition, the performance of the VFD filter with discrete coefficients is investigated, in which the filter coefficients are expressed as the sum of power-of-two terms to reduce the filter operations to shifts and adds. Design examples show that the peak deviation error can be significantly reduced from the least squares solution while maintaining approximately the same integral squared error. Similarly, the integral squared error can be significantly reduced from the minimax solution while maintaining approximately the same peak deviation error. Furthermore, the tradeoff filters are less sensitive with respect to quantization than the least squares and minimax solutions. [ABSTRACT FROM AUTHOR]

This brief investigates the performance of robust and nonrobust broadband beamformers with least squares and discrete coefficients to achieve low complexity and efficient hardware implementation. The broadband beamformer coefficients are expressed as the sum of power-of-two terms with a restriction on the total number of power-of-two terms for the beamformer coefficients. An iterative algorithm is employed to reduce the number of nonzero coefficients and, thereby, multipliers in both the robust and nonrobust beamformers. A quantization scheme in combination with a random search is then applied to efficiently distribute the power-of-two terms for the beamformer coefficients. Design examples show that the number of nonzero coefficients for the beamformers can be significantly reduced without a significant degradation in the integral squared error. In addition, robust beamformers are shown to be less sensitive to nonzero coefficient reduction and quantization than nonrobust beamformers. [ABSTRACT FROM PUBLISHER]

This correspondence investigates the least squares and minimax design problems for allpass variable fractional delay (VFD) filters. A two stage optimization approach is proposed to solve the resulting minimax optimization problem. This approach includes a combination of a one-dimensional global search method and an adaptive scheme to refine the discretization points. In addition, the paper investigates the design of allpass VFD filters which minimizes the weighted integral squared error subject to constraints on peak error deviation from the desired response. By using approximations, the design problem can be formulated as a quadratic optimization problem. Design examples show that a tradeoff between the weighted integral squared error and the peak error deviation can be achieved. In addition, the integral squared error can be reduced significantly from the minimax solution while maintaining approximately the same peak error deviation. Similarly, the peak error deviation can be significantly reduced from the least squares solution while maintaining approximately the same integral squared error. [ABSTRACT FROM AUTHOR]

We characterize the delay properties of uniformly modulated finite impulse response (FIR) filterbanks. Conditions on the permissable delay are developed for this class of filterbanks when the perfect reconstruction condition is relaxed. Accurate linear approximations for the phase and the group delay of the total filterbank are derived. These approximations allow linear phase or group delay constraints to be introduced in the filter optimization problem. A tractable quadratic optimization problem for the design of optimal analysis and synthesis filter prototypes is proposed. The problem involves the minimization of the aliasing distortion while constraining group delay and amplitude distortion. Thus, a new algorithm is presented to solve this optimization problem for the analysis and synthesis filterbanks simultaneously. Numerical examples are presented that confirm the theoretical results and verify that the approximations used are highly accurate. [ABSTRACT FROM AUTHOR]

Presents a study of the design of linear-phase finite impulse response digital filters for which the weighed least square error is minimized, subject to maximum error constraints. Formulation of the filter design problem; Algorithm for solving the problem; Design examples.

Presents information on a study which investigated the design of digital Laguerre networks with a complex desired frequency response and the Chebyshev error criterion. Background of the study; Complex domain specification; Linear constraints on group delay; Design example.

In this paper, an adaptive averaging a priori SNR estimation employing critical band processing is proposed. The proposed method modifies the current decision-directed a priori SNR estimation to achieve faster tracking when SNR changes. The decision-directed estimator (DD) employs a fixed weighting with the value close to one, which makes it slow in following the onsets of speech utterances. The proposed SNR estimator provides a means to solve this issue by employing an adaptive weighting factor. This allows an improved tracking of onset changes in the speech signal. As a consequence, it results in better preservation of speech components. This adaptive technique ensures that the weighting between the modified decision-directed a priori estimate and the maximum likelihood a priori estimate is a function of the speech absence probability. The estimate of the speech absence probability is modeled by a sigmoid function. Furthermore, a critical band mapping for the short-time Fourier transform analysis-synthesis system is utilized in the speech enhancement to achieve less musical noise. In addition, to evaluate the ability of the a priori SNR estimation method in preserving speech components, we proposed a modified objective measurement known as modified hamming distance. Evaluations are performed by utilizing both objective and subjective measurements. The experimental results show that the proposed method improves the speech quality under different noise conditions. Moreover, it maintains the advantage of the DD approach in eliminating the musical noise under different SNR conditions. The objective results are supported by subjective listening tests using 10 subjects (5 males and 5 females). [ABSTRACT FROM AUTHOR]

We propose a numerically efficient technique to approximate the joint detection probability of a coherent multiple input multiple output (MIMO) receiver in the presence of inter-symbol interference (ISI) and additive white Gaussian noise (AWGN). This technique approximates the probability of detection by numerically integrating the product of the characteristic function (CF) of the received filtered signal with the Fourier transform of the multi-dimension decision region. Naturally, the accuracy of the approximation is dependent on the number of points in the numerical integration. The proposed method selects the number of points to integrate over by deriving bounds on the approximation error. As such, a reduction of up to 1/100^th of the number points can be achieved when comparing with existing single input single output (SISO) techniques. Simulation results demonstrate that the proposed method is highly accurate with the calculated errors being well within the bounded approximation error. In addition, the results are closely matched with those obtained using the Monte Carlo simulations with a typical error less than 10^-4 while requiring only a fraction of the computation time. [ABSTRACT FROM PUBLISHER]